what is hypothesis in machine learning with example

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What is hypothesis in Machine Learning?

The hypothesis is a word that is frequently used in Machine Learning and data science initiatives. As we all know, machine learning is one of the most powerful technologies in the world, allowing us to anticipate outcomes based on previous experiences. Moreover, data scientists and ML specialists undertake experiments with the goal of solving an issue. These ML experts and data scientists make an initial guess on how to solve the challenge.

What is a Hypothesis?

A hypothesis is a conjecture or proposed explanation that is based on insufficient facts or assumptions. It is only a conjecture based on certain known facts that have yet to be confirmed. A good hypothesis is tested and yields either true or erroneous outcomes.

Let's look at an example to better grasp the hypothesis. According to some scientists, ultraviolet (UV) light can harm the eyes and induce blindness.

In this case, a scientist just states that UV rays are hazardous to the eyes, but people presume they can lead to blindness. Yet, it is conceivable that it will not be achievable. As a result, these kinds of assumptions are referred to as hypotheses.

Defining Hypothesis in Machine Learning

In machine learning, a hypothesis is a mathematical function or model that converts input data into output predictions. The model's first belief or explanation is based on the facts supplied. The hypothesis is typically expressed as a collection of parameters characterizing the behavior of the model.

If we're building a model to predict the price of a property based on its size and location. The hypothesis function may look something like this −

$$\mathrm{h(x)\:=\:θ0\:+\:θ1\:*\:x1\:+\:θ2\:*\:x2}$$

The hypothesis function is h(x), its input data is x, the model's parameters are 0, 1, and 2, and the features are x1 and x2.

The machine learning model's purpose is to discover the optimal values for parameters 0 through 2 that minimize the difference between projected and actual output labels.

To put it another way, we're looking for the hypothesis function that best represents the underlying link between the input and output data.

Types of Hypotheses in Machine Learning

The next step is to build a hypothesis after identifying the problem and obtaining evidence. A hypothesis is an explanation or solution to a problem based on insufficient data. It acts as a springboard for further investigation and experimentation. A hypothesis is a machine learning function that converts inputs to outputs based on some assumptions. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. Several machine learning theories are as follows −

1. Null Hypothesis

A null hypothesis is a basic hypothesis that states that no link exists between the independent and dependent variables. In other words, it assumes the independent variable has no influence on the dependent variable. It is symbolized by the symbol H0. If the p-value falls outside the significance level, the null hypothesis is typically rejected (). If the null hypothesis is correct, the coefficient of determination is the probability of rejecting it. A null hypothesis is involved in test findings such as t-tests and ANOVA.

2. Alternative Hypothesis

An alternative hypothesis is a hypothesis that contradicts the null hypothesis. It assumes that there is a relationship between the independent and dependent variables. In other words, it assumes that there is an effect of the independent variable on the dependent variable. It is denoted by Ha. An alternative hypothesis is generally accepted if the p-value is less than the significance level (α). An alternative hypothesis is also known as a research hypothesis.

3. One-tailed Hypothesis

A one-tailed test is a type of significance test in which the region of rejection is located at one end of the sample distribution. It denotes that the estimated test parameter is more or less than the crucial value, implying that the alternative hypothesis rather than the null hypothesis should be accepted. It is most commonly used in the chi-square distribution, where all of the crucial areas, related to, are put in either of the two tails. Left-tailed or right-tailed one-tailed tests are both possible.

4. Two-tailed Hypothesis

The two-tailed test is a hypothesis test in which the region of rejection or critical area is on both ends of the normal distribution. It determines whether the sample tested falls within or outside a certain range of values, and an alternative hypothesis is accepted if the calculated value falls in either of the two tails of the probability distribution. α is bifurcated into two equal parts, and the estimated parameter is either above or below the assumed parameter, so extreme values work as evidence against the null hypothesis.

Overall, the hypothesis plays a critical role in the machine learning model. It provides a starting point for the model to make predictions and helps to guide the learning process. The accuracy of the hypothesis is evaluated using various metrics like mean squared error or accuracy.

The hypothesis is a mathematical function or model that converts input data into output predictions, typically expressed as a collection of parameters characterizing the behavior of the model. It is an explanation or solution to a problem based on insufficient data. A good hypothesis contributes to the creation of an accurate and efficient machine-learning model. A two-tailed hypothesis is used when there is no prior knowledge or theoretical basis to infer a certain direction of the link.

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Best Guesses: Understanding The Hypothesis in Machine Learning

February 22, 2024
General , Supervised Learning , Unsupervised Learning

Machine learning is a vast and complex field that has inherited many terms from other places all over the mathematical domain.

It can sometimes be challenging to get your head around all the different terminologies, never mind trying to understand how everything comes together.

In this blog post, we will focus on one particular concept: the hypothesis.

While you may think this is simple, there is a little caveat regarding machine learning.

The statistics side and the learning side.

Don’t worry; we’ll do a full breakdown below.

You’ll learn the following:

What Is a Hypothesis in Machine Learning?

Is This any different than the hypothesis in statistics?
What is the difference between the alternative hypothesis and the null?
Why do we restrict hypothesis space in artificial intelligence?
Example code performing hypothesis testing in machine learning

In machine learning, the term ‘hypothesis’ can refer to two things.

First, it can refer to the hypothesis space, the set of all possible training examples that could be used to predict or answer a new instance.

Second, it can refer to the traditional null and alternative hypotheses from statistics.

Since machine learning works so closely with statistics, 90% of the time, when someone is referencing the hypothesis, they’re referencing hypothesis tests from statistics.

Is This Any Different Than The Hypothesis In Statistics?

In statistics, the hypothesis is an assumption made about a population parameter.

The statistician’s goal is to prove it true or disprove it.

This will take the form of two different hypotheses, one called the null, and one called the alternative.

Usually, you’ll establish your null hypothesis as an assumption that it equals some value.

For example, in Welch’s T-Test Of Unequal Variance, our null hypothesis is that the two means we are testing (population parameter) are equal.

This means our null hypothesis is that the two population means are the same.

We run our statistical tests, and if our p-value is significant (very low), we reject the null hypothesis.

This would mean that their population means are unequal for the two samples you are testing.

Usually, statisticians will use the significance level of .05 (a 5% risk of being wrong) when deciding what to use as the p-value cut-off.

What Is The Difference Between The Alternative Hypothesis And The Null?

The null hypothesis is our default assumption, which we are trying to prove correct.

The alternate hypothesis is usually the opposite of our null and is much broader in scope.

For most statistical tests, the null and alternative hypotheses are already defined.

You are then just trying to find “significant” evidence we can use to reject our null hypothesis.

These two hypotheses are easy to spot by their specific notation. The null hypothesis is usually denoted by H₀, while H₁ denotes the alternative hypothesis.

Example Code Performing Hypothesis Testing In Machine Learning

Since there are many different hypothesis tests in machine learning and data science, we will focus on one of my favorites.

This test is Welch’s T-Test Of Unequal Variance, where we are trying to determine if the population means of these two samples are different.

There are a couple of assumptions for this test, but we will ignore those for now and show the code.

You can read more about this here in our other post, Welch’s T-Test of Unequal Variance .

We see that our p-value is very low, and we reject the null hypothesis.

What Is The Difference Between The Biased And Unbiased Hypothesis Spaces?

The difference between the Biased and Unbiased hypothesis space is the number of possible training examples your algorithm has to predict.

The unbiased space has all of them, and the biased space only has the training examples you’ve supplied.

Since neither of these is optimal (one is too small, one is much too big), your algorithm creates generalized rules (inductive learning) to be able to handle examples it hasn’t seen before.

Here’s an example of each:

Example of The Biased Hypothesis Space In Machine Learning

The Biased Hypothesis space in machine learning is a biased subspace where your algorithm does not consider all training examples to make predictions.

This is easiest to see with an example.

Let’s say you have the following data:

Happy and Sunny and Stomach Full = True

Whenever your algorithm sees those three together in the biased hypothesis space, it’ll automatically default to true.

This means when your algorithm sees:

Sad and Sunny And Stomach Full = False

It’ll automatically default to False since it didn’t appear in our subspace.

This is a greedy approach, but it has some practical applications.

Example of the Unbiased Hypothesis Space In Machine Learning

The unbiased hypothesis space is a space where all combinations are stored.

We can use re-use our example above:

This would start to breakdown as

Happy = True

Happy and Sunny = True

Happy and Stomach Full = True

Let’s say you have four options for each of the three choices.

This would mean our subspace would need 2^12 instances (4096) just for our little three-word problem.

This is practically impossible; the space would become huge.

So while it would be highly accurate, this has no scalability.

More reading on this idea can be found in our post, Inductive Bias In Machine Learning .

Why Do We Restrict Hypothesis Space In Artificial Intelligence?

We have to restrict the hypothesis space in machine learning. Without any restrictions, our domain becomes much too large, and we lose any form of scalability.

This is why our algorithm creates rules to handle examples that are seen in production.

This gives our algorithms a generalized approach that will be able to handle all new examples that are in the same format.

Evaluating Hypotheses in Machine Learning: A Comprehensive Guide

Learn how to evaluate hypotheses in machine learning, including types of hypotheses, evaluation metrics, and common pitfalls to avoid. Improve your ML model's performance with this in-depth guide.

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Introduction

Machine learning is a crucial aspect of artificial intelligence that enables machines to learn from data and make predictions or decisions. The process of machine learning involves training a model on a dataset, and then using that model to make predictions on new, unseen data. However, before deploying a machine learning model, it is essential to evaluate its performance to ensure that it is accurate and reliable. One crucial step in this evaluation process is hypothesis testing.

In this blog post, we will delve into the world of hypothesis testing in machine learning, exploring what hypotheses are, why they are essential, and how to evaluate them. We will also discuss the different types of hypotheses, common pitfalls to avoid, and best practices for hypothesis testing.

What are Hypotheses in Machine Learning?

In machine learning, a hypothesis is a statement that proposes a possible explanation for a phenomenon or a problem. It is a conjecture that is made about a population parameter, and it is used as a basis for further investigation. In the context of machine learning, hypotheses are used to define the problem that we are trying to solve.

For example, let's say we are building a machine learning model to predict the prices of houses based on their features, such as the number of bedrooms, square footage, and location. A possible hypothesis could be: "The price of a house is directly proportional to its square footage." This hypothesis proposes a possible relationship between the price of a house and its square footage.

Why are Hypotheses Essential in Machine Learning?

Hypotheses are essential in machine learning because they provide a framework for understanding the problem that we are trying to solve. They help us to identify the key variables that are relevant to the problem, and they provide a basis for evaluating the performance of our machine learning model.

Without a clear hypothesis, it is difficult to develop an effective machine learning model. A hypothesis helps us to:

Identify the key variables that are relevant to the problem
Develop a clear understanding of the problem that we are trying to solve
Evaluate the performance of our machine learning model
Refine our model and improve its accuracy

Types of Hypotheses in Machine Learning

There are two main types of hypotheses in machine learning: null hypotheses and alternative hypotheses.

Null Hypothesis

A null hypothesis is a hypothesis that proposes that there is no significant difference or relationship between variables. It is a hypothesis of no effect or no difference. For example, let's say we are building a machine learning model to predict the prices of houses based on their features. A null hypothesis could be: "There is no significant relationship between the price of a house and its square footage."

Alternative Hypothesis

An alternative hypothesis is a hypothesis that proposes that there is a significant difference or relationship between variables. It is a hypothesis of an effect or a difference. For example, let's say we are building a machine learning model to predict the prices of houses based on their features. An alternative hypothesis could be: "There is a significant positive relationship between the price of a house and its square footage."

Evaluating Hypotheses in Machine Learning

Evaluating hypotheses in machine learning involves testing the null hypothesis against the alternative hypothesis. This is typically done using statistical methods, such as t-tests, ANOVA, and regression analysis.

Here are the general steps involved in evaluating hypotheses in machine learning:

Formulate the null and alternative hypotheses : Clearly define the null and alternative hypotheses that you want to test.
Collect and prepare the data : Collect the data that you will use to test the hypotheses. Ensure that the data is clean, relevant, and representative of the population.
Choose a statistical method : Select a suitable statistical method to test the hypotheses. This could be a t-test, ANOVA, regression analysis, or another method.
Test the hypotheses : Use the chosen statistical method to test the null hypothesis against the alternative hypothesis.
Interpret the results : Interpret the results of the hypothesis test. If the null hypothesis is rejected, it suggests that there is a significant relationship between the variables. If the null hypothesis is not rejected, it suggests that there is no significant relationship between the variables.

Common Pitfalls to Avoid in Hypothesis Testing

Here are some common pitfalls to avoid in hypothesis testing:

Overfitting : Overfitting occurs when a model is too complex and performs well on the training data but poorly on new, unseen data. To avoid overfitting, use techniques such as regularization, early stopping, and cross-validation.
Underfitting : Underfitting occurs when a model is too simple and fails to capture the underlying patterns in the data. To avoid underfitting, use techniques such as feature engineering, hyperparameter tuning, and model selection.
Data leakage : Data leakage occurs when the model is trained on data that it will also be tested on. To avoid data leakage, use techniques such as cross-validation and walk-forward optimization.
P-hacking : P-hacking occurs when a researcher selectively reports the results of multiple hypothesis tests to find a significant result. To avoid p-hacking, use techniques such as preregistration and replication.

Best Practices for Hypothesis Testing in Machine Learning

Here are some best practices for hypothesis testing in machine learning:

Clearly define the hypotheses : Clearly define the null and alternative hypotheses that you want to test.
Use a suitable statistical method : Choose a suitable statistical method to test the hypotheses.
Use cross-validation : Use cross-validation to evaluate the performance of the model on unseen data.
Avoid overfitting and underfitting : Use techniques such as regularization, early stopping, and feature engineering to avoid overfitting and underfitting.
Document the results : Document the results of the hypothesis test, including the statistical method used, the results, and any conclusions drawn.

Evaluating hypotheses is a crucial step in machine learning that helps us to understand the problem that we are trying to solve and to evaluate the performance of our machine learning model. By following the best practices outlined in this blog post, you can ensure that your hypothesis testing is rigorous, reliable, and effective.

Remember to clearly define the null and alternative hypotheses, choose a suitable statistical method, and avoid common pitfalls such as overfitting, underfitting, data leakage, and p-hacking. By doing so, you can develop machine learning models that are accurate, reliable, and effective.

[1] James, G., Witten, D., Hastie, T., & Tibshirani, R. (2013). An Introduction to Statistical Learning: With Applications in R. Springer.
[2] Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
[3] Han, J., Pei, J., & Kamber, M. (2012). Data Mining: Concepts and Techniques. Morgan Kaufmann.

I hope this helps! Let me know if you need any further assistance.

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Hypothesis in Machine Learning: Comprehensive Overview(2021)

Introduction

Supervised machine learning (ML) is regularly portrayed as the issue of approximating an objective capacity that maps inputs to outputs. This portrayal is described as looking through and assessing competitor hypothesis from hypothesis spaces.

The conversation of hypothesis in machine learning can be confused for a novice, particularly when “hypothesis” has a discrete, but correlated significance in statistics and all the more comprehensively in science.

Hypothesis Space (H)

The hypothesis space utilized by an ML system is the arrangement of all hypotheses that may be returned by it. It is ordinarily characterized by a Hypothesis Language, conceivably related to a Language Bias.

Many ML algorithms depend on some sort of search methodology: given a set of perceptions and a space of all potential hypotheses that may be thought in the hypothesis space. They see in this space for those hypotheses that adequately furnish the data or are ideal concerning some other quality standard.

ML can be portrayed as the need to utilize accessible data objects to discover a function that most reliable maps inputs to output, alluded to as function estimate, where we surmised an anonymous objective function that can most reliably map inputs to outputs on all expected perceptions from the difficult domain. An illustration of a model that approximates the performs mappings and target function of inputs to outputs is known as hypothesis testing in machine learning.

The hypothesis in machine learning of all potential hypothesis that you are looking over, paying little mind to their structure. For the wellbeing of accommodation, the hypothesis class is normally compelled to be just each sort of function or model in turn, since learning techniques regularly just work on each type at a time. This doesn’t need to be the situation, however:

Hypothesis classes don’t need to comprise just one kind of function. If you’re looking through exponential, quadratic, and overall linear functions, those are what your joined hypothesis class contains.
Hypothesis classes additionally don’t need to comprise of just straightforward functions. If you figure out how to look over all piecewise-tanh2 functions, those functions are what your hypothesis class incorporates.

The enormous trade-off is that the bigger your hypothesis class in machine learning, the better the best hypothesis models the basic genuine function, yet the harder it is to locate that best hypothesis. This is identified with the bias-variance trade-off.

Hypothesis (h)

A hypothesis function in machine learning is best describes the target. The hypothesis that an algorithm would concoct relies on the data and relies on the bias and restrictions that we have forced on the data.

The hypothesis formula in machine learning:

y is range
m changes in y divided by change in x
x is domain
b is intercept

The purpose of restricting hypothesis space in machine learning is so that these can fit well with the general data that is needed by the user. It checks the reality or deception of observations or inputs and examinations them appropriately. Subsequently, it is extremely helpful and it plays out the valuable function of mapping all the inputs till they come out as outputs. Consequently, the target functions are deliberately examined and restricted dependent on the outcomes (regardless of whether they are free of bias), in ML.

The hypothesis in machine learning space and inductive bias in machine learning is that the hypothesis space is a collection of valid Hypothesis, for example, every single desirable function, on the opposite side the inductive bias (otherwise called learning bias) of a learning algorithm is the series of expectations that the learner uses to foresee outputs of given sources of inputs that it has not experienced. Regression and Classification are a kind of realizing which relies upon continuous-valued and discrete-valued sequentially. This sort of issues (learnings) is called inductive learning issues since we distinguish a function by inducting it on data.

In the Maximum a Posteriori or MAP hypothesis in machine learning, enhancement gives a Bayesian probability structure to fitting model parameters to training data and another option and sibling may be a more normal Maximum Likelihood Estimation system. MAP learning chooses a solitary in all probability theory given the data. The hypothesis in machine learning earlier is as yet utilized and the technique is regularly more manageable than full Bayesian learning.

Bayesian techniques can be utilized to decide the most plausible hypothesis in machine learning given the data the MAP hypothesis. This is the ideal hypothesis as no other hypothesis is more probable.

Hypothesis in machine learning or ML the applicant model that approximates a target function for mapping instances of inputs to outputs.

Hypothesis in statistics probabilistic clarification about the presence of a connection between observations.

Hypothesis in science is a temporary clarification that fits the proof and can be disproved or confirmed. We can see that a hypothesis in machine learning draws upon the meaning of the hypothesis all the more extensively in science.

There are no right or wrong ways of learning AI and ML technologies – the more, the better! These valuable resources can be the starting point for your journey on how to learn Artificial Intelligence and Machine Learning. Do pursuing AI and ML interest you? If you want to step into the world of emerging tech, you can accelerate your career with this Machine Learning And AI Courses by Jigsaw Academy.

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Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

September 21, 2023

Explore the intricacies of hypothesis testing, a cornerstone of statistical analysis. Dive into methods, interpretations, and applications for making data-driven decisions.

what is hypothesis in machine learning with example

In this Blog post we will learn:

What is Hypothesis Testing?
Steps in Hypothesis Testing 2.1. Set up Hypotheses: Null and Alternative 2.2. Choose a Significance Level (α) 2.3. Calculate a test statistic and P-Value 2.4. Make a Decision
Example : Testing a new drug.
Example in python

1. What is Hypothesis Testing?

In simple terms, hypothesis testing is a method used to make decisions or inferences about population parameters based on sample data. Imagine being handed a dice and asked if it’s biased. By rolling it a few times and analyzing the outcomes, you’d be engaging in the essence of hypothesis testing.

Think of hypothesis testing as the scientific method of the statistics world. Suppose you hear claims like “This new drug works wonders!” or “Our new website design boosts sales.” How do you know if these statements hold water? Enter hypothesis testing.

2. Steps in Hypothesis Testing

Set up Hypotheses : Begin with a null hypothesis (H0) and an alternative hypothesis (Ha).
Choose a Significance Level (α) : Typically 0.05, this is the probability of rejecting the null hypothesis when it’s actually true. Think of it as the chance of accusing an innocent person.
Calculate Test statistic and P-Value : Gather evidence (data) and calculate a test statistic.
p-value : This is the probability of observing the data, given that the null hypothesis is true. A small p-value (typically ≤ 0.05) suggests the data is inconsistent with the null hypothesis.
Decision Rule : If the p-value is less than or equal to α, you reject the null hypothesis in favor of the alternative.

2.1. Set up Hypotheses: Null and Alternative

Before diving into testing, we must formulate hypotheses. The null hypothesis (H0) represents the default assumption, while the alternative hypothesis (H1) challenges it.

For instance, in drug testing, H0 : “The new drug is no better than the existing one,” H1 : “The new drug is superior .”

2.2. Choose a Significance Level (α)

When You collect and analyze data to test H0 and H1 hypotheses. Based on your analysis, you decide whether to reject the null hypothesis in favor of the alternative, or fail to reject / Accept the null hypothesis.

The significance level, often denoted by $α$, represents the probability of rejecting the null hypothesis when it is actually true.

In other words, it’s the risk you’re willing to take of making a Type I error (false positive).

Type I Error (False Positive) :

Symbolized by the Greek letter alpha (α).
Occurs when you incorrectly reject a true null hypothesis . In other words, you conclude that there is an effect or difference when, in reality, there isn’t.
The probability of making a Type I error is denoted by the significance level of a test. Commonly, tests are conducted at the 0.05 significance level , which means there’s a 5% chance of making a Type I error .
Commonly used significance levels are 0.01, 0.05, and 0.10, but the choice depends on the context of the study and the level of risk one is willing to accept.

Example : If a drug is not effective (truth), but a clinical trial incorrectly concludes that it is effective (based on the sample data), then a Type I error has occurred.

Type II Error (False Negative) :

Symbolized by the Greek letter beta (β).
Occurs when you accept a false null hypothesis . This means you conclude there is no effect or difference when, in reality, there is.
The probability of making a Type II error is denoted by β. The power of a test (1 – β) represents the probability of correctly rejecting a false null hypothesis.

Example : If a drug is effective (truth), but a clinical trial incorrectly concludes that it is not effective (based on the sample data), then a Type II error has occurred.

Balancing the Errors :

In practice, there’s a trade-off between Type I and Type II errors. Reducing the risk of one typically increases the risk of the other. For example, if you want to decrease the probability of a Type I error (by setting a lower significance level), you might increase the probability of a Type II error unless you compensate by collecting more data or making other adjustments.

It’s essential to understand the consequences of both types of errors in any given context. In some situations, a Type I error might be more severe, while in others, a Type II error might be of greater concern. This understanding guides researchers in designing their experiments and choosing appropriate significance levels.

2.3. Calculate a test statistic and P-Value

Test statistic : A test statistic is a single number that helps us understand how far our sample data is from what we’d expect under a null hypothesis (a basic assumption we’re trying to test against). Generally, the larger the test statistic, the more evidence we have against our null hypothesis. It helps us decide whether the differences we observe in our data are due to random chance or if there’s an actual effect.

P-value : The P-value tells us how likely we would get our observed results (or something more extreme) if the null hypothesis were true. It’s a value between 0 and 1. – A smaller P-value (typically below 0.05) means that the observation is rare under the null hypothesis, so we might reject the null hypothesis. – A larger P-value suggests that what we observed could easily happen by random chance, so we might not reject the null hypothesis.

2.4. Make a Decision

Relationship between $α$ and P-Value

When conducting a hypothesis test:

We first choose a significance level ($α$), which sets a threshold for making decisions.

We then calculate the p-value from our sample data and the test statistic.

Finally, we compare the p-value to our chosen $α$:

If $p−value≤α$: We reject the null hypothesis in favor of the alternative hypothesis. The result is said to be statistically significant.
If $p−value>α$: We fail to reject the null hypothesis. There isn’t enough statistical evidence to support the alternative hypothesis.

3. Example : Testing a new drug.

Imagine we are investigating whether a new drug is effective at treating headaches faster than drug B.

Setting Up the Experiment : You gather 100 people who suffer from headaches. Half of them (50 people) are given the new drug (let’s call this the ‘Drug Group’), and the other half are given a sugar pill, which doesn’t contain any medication.

Set up Hypotheses : Before starting, you make a prediction:
Null Hypothesis (H0): The new drug has no effect. Any difference in healing time between the two groups is just due to random chance.
Alternative Hypothesis (H1): The new drug does have an effect. The difference in healing time between the two groups is significant and not just by chance.
Choose a Significance Level (α) : Typically 0.05, this is the probability of rejecting the null hypothesis when it’s actually true

Calculate Test statistic and P-Value : After the experiment, you analyze the data. The “test statistic” is a number that helps you understand the difference between the two groups in terms of standard units.

For instance, let’s say:

The average healing time in the Drug Group is 2 hours.
The average healing time in the Placebo Group is 3 hours.

The test statistic helps you understand how significant this 1-hour difference is. If the groups are large and the spread of healing times in each group is small, then this difference might be significant. But if there’s a huge variation in healing times, the 1-hour difference might not be so special.

Imagine the P-value as answering this question: “If the new drug had NO real effect, what’s the probability that I’d see a difference as extreme (or more extreme) as the one I found, just by random chance?”

For instance:

P-value of 0.01 means there’s a 1% chance that the observed difference (or a more extreme difference) would occur if the drug had no effect. That’s pretty rare, so we might consider the drug effective.
P-value of 0.5 means there’s a 50% chance you’d see this difference just by chance. That’s pretty high, so we might not be convinced the drug is doing much.
If the P-value is less than ($α$) 0.05: the results are “statistically significant,” and they might reject the null hypothesis , believing the new drug has an effect.
If the P-value is greater than ($α$) 0.05: the results are not statistically significant, and they don’t reject the null hypothesis , remaining unsure if the drug has a genuine effect.

4. Example in python

For simplicity, let’s say we’re using a t-test (common for comparing means). Let’s dive into Python:

Making a Decision : “The results are statistically significant! p-value < 0.05 , The drug seems to have an effect!” If not, we’d say, “Looks like the drug isn’t as miraculous as we thought.”

5. Conclusion

Hypothesis testing is an indispensable tool in data science, allowing us to make data-driven decisions with confidence. By understanding its principles, conducting tests properly, and considering real-world applications, you can harness the power of hypothesis testing to unlock valuable insights from your data.

F statistic formula – explained, correlation – connecting the dots, the role of correlation in data analysis, sampling and sampling distributions – a comprehensive guide on sampling and sampling distributions, law of large numbers – a deep dive into the world of statistics, central limit theorem – a deep dive into central limit theorem and its significance in statistics, similar articles, complete introduction to linear regression in r, how to implement common statistical significance tests and find the p value, logistic regression – a complete tutorial with examples in r.

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What’s a Hypothesis Space?

Last updated: March 18, 2024

Math and Logic

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1. Introduction

Machine-learning algorithms come with implicit or explicit assumptions about the actual patterns in the data. Mathematically, this means that each algorithm can learn a specific family of models, and that family goes by the name of the hypothesis space.

In this tutorial, we’ll talk about hypothesis spaces and how to choose the right one for the data at hand.

2. Hypothesis Spaces

Let’s say that we have a binary classification task and that the data are two-dimensional. Our goal is to find a model that classifies objects as positive or negative. Applying Logistic Regression , we can get the models of the form:

which estimate the probability that the object at hand is positive.

2.1. Hypotheses and Assumptions

The underlying assumption of hypotheses ( 1 ) is that the boundary separating the positive from negative objects is a straight line. So, every hypothesis from this space corresponds to a straight line in a 2D plane. For instance:

2.2. Regression

3. expressivity of a hypothesis space.

We could informally say that one hypothesis space is more expressive than another if its hypotheses are more diverse and complex.

We may underfit the data if our algorithm’s hypothesis space isn’t expressive enough. For instance, linear hypotheses aren’t particularly good options if the actual data are extremely non-linear:

So, training an algorithm that has a very expressive space increases the chance of completely capturing the patterns in the data. However, it also increases the risk of overfitting. For instance, a space containing the hypotheses of the form:

would start modelling the noise, which we see from its decision boundary:

Such models would generalize poorly to unseen data.

3.1. Expressivity vs. Interpretability

Additionally, even if a complex hypothesis has a good generalization capability, it may be unusable in practice because it’s too complicated to understand or compute. What’s more, intricated hypotheses offer limited insight into the real-world process that generated the data. For example, a quadratic model:

4. How to Choose the Hypothesis Space?

We need to find the right balance between expressivity and simplicity. Unfortunately, that’s easier said than done. Most of the time, we need to rely on our intuition about the data.

So, we should start by exploring the dataset, using visualizations as much as possible. For instance, we can conclude that a straight line isn’t likely to be an adequate boundary for the above classification data. However, a high-order curve would probably be too complex even though it might split the dataset into two classes without an error.

A second-degree curve might be the compromise we seek, but we aren’t sure. So, we start with the space of quadratic hypotheses:

We get a model whose decision boundary appears to be a good fit even though it misclassifies some objects:

Since we’re satisfied with the model, we can stop here. If that hadn’t been the case, we could have tried a space of cubic models. The idea would be to iteratively try incrementally complex families until finding a model that both performs well and is easy to understand.

4. Conclusion

In this article, we talked about hypotheses spaces in machine learning. An algorithm’s hypothesis space contains all the models it can learn from any dataset.

The algorithms with too expressive spaces can generalize poorly to unseen data and be too complex to understand, whereas those with overly simple hypotheses may underfit the data. So, when applying machine-learning algorithms in practice, we need to find the right balance between expressivity and simplicity.

Evaluating Hypotheses: Estimating hypotheses Accuracy

For estimating hypothesis accuracy, statistical methods are applied. In this blog, we’ll have a look at evaluating hypotheses and estimating it’s accuracy.

Evaluating hypotheses:

Whenever you form a hypothesis for a given training data set, for example, you came up with a hypothesis for the EnjoySport example where the attributes of the instances decide if a person will be able to enjoy their favorite sport or not.

Now to test or evaluate how accurate the considered hypothesis is we use different statistical measures. Evaluating hypotheses is an important step in training the model.

To evaluate the hypotheses precisely focus on these points:

When statistical methods are applied to estimate hypotheses,

First, how well does this estimate the accuracy of a hypothesis across additional examples, given the observed accuracy of a hypothesis over a limited sample of data?
Second, how likely is it that if one theory outperforms another across a set of data, it is more accurate in general?
Third, what is the best strategy to use limited data to both learn and measure the accuracy of a hypothesis?

Motivation:

There are instances where the accuracy of the entire model plays a huge role in the model is adopted or not. For example, consider using a training model for Medical treatment. We need to have a high accuracy so as to depend on the information the model provides.

When we need to learn a hypothesis and estimate its future accuracy based on a small collection of data, we face two major challenges:

Bias in the estimation

There is a bias in the estimation. Initially, the observed accuracy of the learned hypothesis over training instances is a poor predictor of its accuracy over future cases.

Because the learned hypothesis was generated from previous instances, future examples will likely yield a skewed estimate of hypothesis correctness.

Estimation variability.

Second, depending on the nature of the particular set of test examples, even if the hypothesis accuracy is tested over an unbiased set of test instances independent of the training examples, the measurement accuracy can still differ from the true accuracy.

The anticipated variance increases as the number of test examples decreases.

When evaluating a taught hypothesis, we want to know how accurate it will be at classifying future instances.

Also, to be aware of the likely mistake in the accuracy estimate. There is an X-dimensional space of conceivable scenarios. We presume that different instances of X will be met at different times.

Assume there is some unknown probability distribution D that describes the likelihood of encountering each instance in X. This is a convenient method to model this.

A trainer draws each instance separately, according to the distribution D, and then passes the instance x together with its correct target value f (x) to the learner as training examples of the target function f.

The following two questions are of particular relevance to us in this context,

What is the best estimate of the accuracy of h over future instances taken from the same distribution, given a hypothesis h and a data sample containing n examples picked at random according to the distribution D?
What is the margin of error in this estimate of accuracy?

True Error and Sample Error:

We must distinguish between two concepts of accuracy or, to put it another way, error. One is the hypothesis’s error rate based on the available data sample.

The hypothesis’ error rate over the complete unknown distribution D of examples is the other. These will be referred to as the sampling error and real error, respectively.

The fraction of S that a hypothesis misclassifies is the sampling error of a hypothesis with respect to some sample S of examples selected from X.

Sample Error:

It is denoted by error s (h) of hypothesis h with respect to target function f and data sample S is

Where n is the number of examples in S, and the quantity is 1 if f(x) != h(x), and 0 otherwise.

True Error:

It is denoted by error D (h) of hypothesis h with respect to target function f and distribution D, which is the probability that h will misclassify an instance drawn at random according to D.

Confidence Intervals for Discrete-Valued Hypotheses:

“How accurate are error s (h) estimates of error D (h)?” – in the case of a discrete-valued hypothesis (h).

To estimate the true error for a discrete-valued hypothesis h based on its observed sample error over a sample S, where

According to the probability distribution D, the sample S contains n samples drawn independently of one another and of h.
Over these n occurrences, hypothesis h commits r mistakes error s (h) = r/n

Under these circumstances, statistical theory permits us to state the following:

If no additional information is available, the most likely value of error D (h) is error s (h).
The genuine error error D (h) lies in the interval with approximately 95% probability.

A more precise rule of thumb is that the approximation described above works well when

Programmathically

Introduction to the hypothesis space and the bias-variance tradeoff in machine learning.

In this post, we introduce the hypothesis space and discuss how machine learning models function as hypotheses. Furthermore, we discuss the challenges encountered when choosing an appropriate machine learning hypothesis and building a model, such as overfitting, underfitting, and the bias-variance tradeoff.

The hypothesis space in machine learning is a set of all possible models that can be used to explain a data distribution given the limitations of that space. A linear hypothesis space is limited to the set of all linear models. If the data distribution follows a non-linear distribution, the linear hypothesis space might not contain a model that is appropriate for our needs.

To understand the concept of a hypothesis space, we need to learn to think of machine learning models as hypotheses.

The Machine Learning Model as Hypothesis

Generally speaking, a hypothesis is a potential explanation for an outcome or a phenomenon. In scientific inquiry, we test hypotheses to figure out how well and if at all they explain an outcome. In supervised machine learning, we are concerned with finding a function that maps from inputs to outputs.

But machine learning is inherently probabilistic. It is the art and science of deriving useful hypotheses from limited or incomplete data. Our functions are not axioms that explain the data perfectly, and for most real-life problems, we will never have all the data that exists. Accordingly, we will not find the one true function that perfectly describes the data. Instead, we find a function through training a model to map from known training input to known training output. This way, the model gradually approximates the assumed true function that describes the distribution of the data. So we treat our model as a hypothesis that needs to be tested as to how well it explains the output from a given input. We do this using a test or validation data set.

The Hypothesis Space

During the training process, we select a model from a hypothesis space that is subject to our constraints. For example, a linear hypothesis space only provides linear models. We can approximate data that follows a quadratic distribution using a model from the linear hypothesis space.

Of course, a linear model will never have the same predictive performance as a quadratic model, so we can adjust our hypothesis space to also include non-linear models or at least quadratic models.

The Data Generating Process

The data generating process describes a hypothetical process subject to some assumptions that make training a machine learning model possible. We need to assume that the data points are from the same distribution but are independent of each other. When these requirements are met, we say that the data is independent and identically distributed (i.i.d.).

Independent and Identically Distributed Data

How can we assume that a model trained on a training set will perform better than random guessing on new and previously unseen data? First of all, the training data needs to come from the same or at least a similar problem domain. If you want your model to predict stock prices, you need to train the model on stock price data or data that is similarly distributed. It wouldn’t make much sense to train it on whether data. Statistically, this means the data is identically distributed . But if data comes from the same problem, training data and test data might not be completely independent. To account for this, we need to make sure that the test data is not in any way influenced by the training data or vice versa. If you use a subset of the training data as your test set, the test data evidently is not independent of the training data. Statistically, we say the data must be independently distributed .

Overfitting and Underfitting

We want to select a model from the hypothesis space that explains the data sufficiently well. During training, we can make a model so complex that it perfectly fits every data point in the training dataset. But ultimately, the model should be able to predict outputs on previously unseen input data. The ability to do well when predicting outputs on previously unseen data is also known as generalization. There is an inherent conflict between those two requirements.

If we make the model so complex that it fits every point in the training data, it will pick up lots of noise and random variation specific to the training set, which might obscure the larger underlying patterns. As a result, it will be more sensitive to random fluctuations in new data and predict values that are far off. A model with this problem is said to overfit the training data and, as a result, to suffer from high variance .

To avoid the problem of overfitting, we can choose a simpler model or use regularization techniques to prevent the model from fitting the training data too closely. The model should then be less influenced by random fluctuations and instead, focus on the larger underlying patterns in the data. The patterns are expected to be found in any dataset that comes from the same distribution. As a consequence, the model should generalize better on previously unseen data.

But if we go too far, the model might become too simple or too constrained by regularization to accurately capture the patterns in the data. Then the model will neither generalize well nor fit the training data well. A model that exhibits this problem is said to underfit the data and to suffer from high bias . If the model is too simple to accurately capture the patterns in the data (for example, when using a linear model to fit non-linear data), its capacity is insufficient for the task at hand.

When training neural networks, for example, we go through multiple iterations of training in which the model learns to fit an increasingly complex function to the data. Typically, your training error will decrease during learning the more complex your model becomes and the better it learns to fit the data. In the beginning, the training error decreases rapidly. In later training iterations, it typically flattens out as it approaches the minimum possible error. Your test or generalization error should initially decrease as well, albeit likely at a slower pace than the training error. As long as the generalization error is decreasing, your model is underfitting because it doesn’t live up to its full capacity. After a number of training iterations, the generalization error will likely reach a trough and start to increase again. Once it starts to increase, your model is overfitting, and it is time to stop training.

Ideally, you should stop training once your model reaches the lowest point of the generalization error. The gap between the minimum generalization error and no error at all is an irreducible error term known as the Bayes error that we won’t be able to completely get rid of in a probabilistic setting. But if the error term seems too large, you might be able to reduce it further by collecting more data, manipulating your model’s hyperparameters, or altogether picking a different model.

Bias Variance Tradeoff

We’ve talked about bias and variance in the previous section. Now it is time to clarify what we actually mean by these terms.

Understanding Bias and Variance

In a nutshell, bias measures if there is any systematic deviation from the correct value in a specific direction. If we could repeat the same process of constructing a model several times over, and the results predicted by our model always deviate in a certain direction, we would call the result biased.

Variance measures how much the results vary between model predictions. If you repeat the modeling process several times over and the results are scattered all across the board, the model exhibits high variance.

In their book “Noise” Daniel Kahnemann and his co-authors provide an intuitive example that helps understand the concept of bias and variance. Imagine you have four teams at the shooting range.

Team B is biased because the shots of its team members all deviate in a certain direction from the center. Team B also exhibits low variance because the shots of all the team members are relatively concentrated in one location. Team C has the opposite problem. The shots are scattered across the target with no discernible bias in a certain direction. Team D is both biased and has high variance. Team A would be the equivalent of a good model. The shots are in the center with little bias in one direction and little variance between the team members.

Generally speaking, linear models such as linear regression exhibit high bias and low variance. Nonlinear algorithms such as decision trees are more prone to overfitting the training data and thus exhibit high variance and low bias.

A linear model used with non-linear data would exhibit a bias to predict data points along a straight line instead of accomodating the curves. But they are not as susceptible to random fluctuations in the data. A nonlinear algorithm that is trained on noisy data with lots of deviations would be more capable of avoiding bias but more prone to incorporate the noise into its predictions. As a result, a small deviation in the test data might lead to very different predictions.

To get our model to learn the patterns in data, we need to reduce the training error while at the same time reducing the gap between the training and the testing error. In other words, we want to reduce both bias and variance. To a certain extent, we can reduce both by picking an appropriate model, collecting enough training data, selecting appropriate training features and hyperparameter values. At some point, we have to trade-off between minimizing bias and minimizing variance. How you balance this trade-off is up to you.

The Bias Variance Decomposition

Mathematically, the total error can be decomposed into the bias and the variance according to the following formula.

Remember that Bayes’ error is an error that cannot be eliminated.

Our machine learning model represents an estimating function \hat f(X) for the true data generating function f(X) where X represents the predictors and y the output values.

Now the mean squared error of our model is the expected value of the squared difference of the output produced by the estimating function \hat f(X) and the true output Y.

The bias is a systematic deviation from the true value. We can measure it as the squared difference between the expected value produced by the estimating function (the model) and the values produced by the true data-generating function.

Of course, we don’t know the true data generating function, but we do know the observed outputs Y, which correspond to the values generated by f(x) plus an error term.

The variance of the model is the squared difference between the expected value and the actual values of the model.

Now that we have the bias and the variance, we can add them up along with the irreducible error to get the total error.

A machine learning model represents an approximation to the hypothesized function that generated the data. The chosen model is a hypothesis since we hypothesize that this model represents the true data generating function.

We choose the hypothesis from a hypothesis space that may be subject to certain constraints. For example, we can constrain the hypothesis space to the set of linear models.

When choosing a model, we aim to reduce the bias and the variance to prevent our model from either overfitting or underfitting the data. In the real world, we cannot completely eliminate bias and variance, and we have to trade-off between them. The total error produced by a model can be decomposed into the bias, the variance, and irreducible (Bayes) error.

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parameter sharing in convolutional neural networks

$\begingroup$ A space where we can predict output by a set of some legal hypothesis (or function) and function is represented in terms of features. $\endgroup$ – Abhishek Kumar Commented Aug 9, 2019 at 17:03

3 Answers 3

Lets say you have an unknown target function $f:X \rightarrow Y$ that you are trying to capture by learning . In order to capture the target function you have to come up with some hypotheses, or you may call it candidate models denoted by H $h_1,...,h_n$ where $h \in H$ . Here, $H$ as the set of all candidate models is called hypothesis class or hypothesis space or hypothesis set .

For more information browse Abu-Mostafa's presentaton slides: https://work.caltech.edu/textbook.html

8 $\begingroup$ This answer conveys absolutely no information! What is the intended relationship between $f$, $h$, and $H$? What is meant by "hypothesis set"? $\endgroup$ – whuber ♦ Commented Nov 28, 2015 at 20:50
5 $\begingroup$ Please take a few minutes with our help center to learn about this site and its standards, JimBoy. $\endgroup$ – whuber ♦ Commented Nov 28, 2015 at 20:57
$\begingroup$ The answer says very clear, h learns to capture target function f . H is the space where h1, h2,..hn got defined. $\endgroup$ – Logan Commented Nov 29, 2018 at 21:47
$\begingroup$ @whuber I hope this is clearer $\endgroup$ – pentanol Commented Aug 6, 2021 at 8:51
$\begingroup$ @pentanol You have succeeded in providing a different name for "hypothesis space," but without a definition or description of "candidate model," it doesn't seem to add any information to the post. What would be useful is information relevant to the questions that were posed, which concern "understand[ing] operationally" and a request for an example. $\endgroup$ – whuber ♦ Commented Aug 6, 2021 at 13:55

Suppose an example with four binary features and one binary output variable. Below is a set of observations:

This set of observations can be used by a machine learning (ML) algorithm to learn a function f that is able to predict a value y for any input from the input space .

We are searching for the ground truth f(x) = y that explains the relation between x and y for all possible inputs in the correct way.

The function f has to be chosen from the hypothesis space .

To get a better idea: The input space is in the above given example $2^4$ , its the number of possible inputs. The hypothesis space is $2^{2^4}=65536$ because for each set of features of the input space two outcomes ( 0 and 1 ) are possible.

The ML algorithm helps us to find one function , sometimes also referred as hypothesis, from the relatively large hypothesis space.

A Few Useful Things to Know About ML

1 $\begingroup$ Just a small note on your answer: the size of the hypothesis space is indeed 65,536, but the a more easily explained expression for it would be $2^{(2^4)}$, since, there are $2^4$ possible unique samples, and thus $2^{(2^4)}$ possible label assignments for the entire input space. $\endgroup$ – engelen Commented Jan 10, 2018 at 9:52
1 $\begingroup$ @engelen Thanks for your advice, I've edited the answer. $\endgroup$ – So S Commented Jan 10, 2018 at 21:00
$\begingroup$ @SoS That one function is called classifier?? $\endgroup$ – user125163 Commented Aug 22, 2018 at 16:26
2 $\begingroup$ @Arjun Hedge: Not the one, but one function that you learned is the classifier. The classifier could be (and that's your aim) the one function. $\endgroup$ – So S Commented Aug 22, 2018 at 16:50

The hypothesis space is very relevant to the topic of the so-called Bias-Variance Tradeoff in maximum likelihood. That's if the number of parameters in the model(hypothesis function) is too small for the model to fit the data(indicating underfitting and that the hypothesis space is too limited), the bias is high; while if the model you choose contains too many parameters than needed to fit the data the variance is high(indicating overfitting and that the hypothesis space is too expressive).

As stated in So S ' answer, if the parameters are discrete we can easily and concretely calculate how many possibilities are in the hypothesis space(or how large it is), but normally under realy life circumstances the parameters are continuous. Therefore generally the hypothesis space is uncountable.

Here is an example I borrowed and modified from the related part in the classical machine learning textbook: Pattern Recognition And Machine Learning to fit this question:

We are selecting a hypothesis function for an unknown function hidding in the training data given by a third person named CoolGuy living in an extragalactic planet. Let's say CoolGuy knows what the function is, because the data cases are provided by him and he just generated the data using the function. Let's call it(we only have the limited data and CoolGuy has both the unlimited data and the function generating them) the ground truth function and denote it by $y(x, w)$ .

The green curve is the $y(x,w)$ , and the little blue circles are the cases we have(they are not actually the true data cases transmitted by CoolGuy because of the it would be contaminated by some transmission noise, for example by macula or other things).

We thought that that hidden function would be very simple then we make an attempt at a linear model(make a hypothesis with a very limited space): $g_1(x, w)=w_0 + w_1 x$ with only two parameters: $w_0$ and $w_1$ , and we train the model use our data and we obtain this:

We can see that no matter how many data we use to fit the hypothesis it just doesn't work because it is not expressive enough.

So we try a much more expressive hypothesis: $g_9=\sum_j^9 w_j x^j $ with ten adaptive paramaters $w_0, w_1\cdots , w_9$ , and we also train the model and then we get:

We can see that it is just too expressive and fits all data cases. We see that a much larger hypothesis space( since $g_2$ can be expressed by $g_9$ by setting $w_2, w_3, \cdots, w_9$ as all 0 ) is more powerful than a simple hypothesis. But the generalization is also bad. That is, if we recieve more data from CoolGuy and to do reference, the trained model most likely fails in those unseen cases.

Then how large the hypothesis space is large enough for the training dataset? We can find an aswer from the textbook aforementioned:

One rough heuristic that is sometimes advocated is that the number of data points should be no less than some multiple (say 5 or 10) of the number of adaptive parameters in the model.

And you'll see from the textbook that if we try to use 4 parameters, $g_3=w_0+w_1 x + w_2 x^2 + w_3 x^3$ , the trained function is expressive enough for the underlying function $y=\sin(2\pi x)$ . It's kind a black art to find the number 3(the appropriate hypothesis space) in this case.

Then we can roughly say that the hypothesis space is the measure of how expressive you model is to fit the training data. The hypothesis that is expressive enough for the training data is the good hypothesis with an expressive hypothesis space. To test whether the hypothesis is good or bad we do the cross validation to see if it performs well in the validation data-set. If it is neither underfitting(too limited) nor overfititing(too expressive) the space is enough(according to Occam Razor a simpler one is preferable, but I digress).

$\begingroup$ This approach looks relevant, but your explanation does not agree with that on p. 5 of your first reference: "A function $h:X\to\{0,1\}$ is called [an] hypothesis. A set $H$ of hypotheses among which the approximation function $y$ is searched is called [the] hypothesis space." (I would agree the slide is confusing, because its explanation implicitly requires that $C=\{0,1\}$, whereas that is generically labeled "classes" in the diagram. But let's not pass along that confusion: let's rectify it.) $\endgroup$ – whuber ♦ Commented Sep 24, 2016 at 15:33
1 $\begingroup$ @whuber I updated my answer just now more than two years later after I have learned more knowledge on the topic. Please help check if I can rectify it in a better way. Thanks. $\endgroup$ – Lerner Zhang Commented Feb 5, 2019 at 11:41

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Hypothesis | Definition, Meaning and Examples

Hypothesis is a hypothesis is fundamental concept in the world of research and statistics. It is a testable statement that explains what is happening or observed. It proposes the relation between the various participating variables.

Hypothesis is also called Theory, Thesis, Guess, Assumption, or Suggestion . Hypothesis creates a structure that guides the search for knowledge.

In this article, we will learn what hypothesis is, its characteristics, types, and examples. We will also learn how hypothesis helps in scientific research.

Table of Content

What is Hypothesis?

Characteristics of hypothesis, sources of hypothesis, types of hypothesis, functions of hypothesis, how hypothesis help in scientific research.

Hypothesis is a suggested idea or an educated guess or a proposed explanation made based on limited evidence, serving as a starting point for further study. They are meant to lead to more investigation.

It’s mainly a smart guess or suggested answer to a problem that can be checked through study and trial. In science work, we make guesses called hypotheses to try and figure out what will happen in tests or watching. These are not sure things but rather ideas that can be proved or disproved based on real-life proofs. A good theory is clear and can be tested and found wrong if the proof doesn’t support it.

Hypothesis Meaning

A hypothesis is a proposed statement that is testable and is given for something that happens or observed.

It is made using what we already know and have seen, and it’s the basis for scientific research.
A clear guess tells us what we think will happen in an experiment or study.
It’s a testable clue that can be proven true or wrong with real-life facts and checking it out carefully.
It usually looks like a “if-then” rule, showing the expected cause and effect relationship between what’s being studied.

Here are some key characteristics of a hypothesis:

Testable: An idea (hypothesis) should be made so it can be tested and proven true through doing experiments or watching. It should show a clear connection between things.
Specific: It needs to be easy and on target, talking about a certain part or connection between things in a study.
Falsifiable: A good guess should be able to show it’s wrong. This means there must be a chance for proof or seeing something that goes against the guess.
Logical and Rational: It should be based on things we know now or have seen, giving a reasonable reason that fits with what we already know.
Predictive: A guess often tells what to expect from an experiment or observation. It gives a guide for what someone might see if the guess is right.
Concise: It should be short and clear, showing the suggested link or explanation simply without extra confusion.
Grounded in Research: A guess is usually made from before studies, ideas or watching things. It comes from a deep understanding of what is already known in that area.
Flexible: A guess helps in the research but it needs to change or fix when new information comes up.
Relevant: It should be related to the question or problem being studied, helping to direct what the research is about.
Empirical: Hypotheses come from observations and can be tested using methods based on real-world experiences.

Hypotheses can come from different places based on what you’re studying and the kind of research. Here are some common sources from which hypotheses may originate:

Existing Theories: Often, guesses come from well-known science ideas. These ideas may show connections between things or occurrences that scientists can look into more.
Observation and Experience: Watching something happen or having personal experiences can lead to guesses. We notice odd things or repeat events in everyday life and experiments. This can make us think of guesses called hypotheses.
Previous Research: Using old studies or discoveries can help come up with new ideas. Scientists might try to expand or question current findings, making guesses that further study old results.
Literature Review: Looking at books and research in a subject can help make guesses. Noticing missing parts or mismatches in previous studies might make researchers think up guesses to deal with these spots.
Problem Statement or Research Question: Often, ideas come from questions or problems in the study. Making clear what needs to be looked into can help create ideas that tackle certain parts of the issue.
Analogies or Comparisons: Making comparisons between similar things or finding connections from related areas can lead to theories. Understanding from other fields could create new guesses in a different situation.
Hunches and Speculation: Sometimes, scientists might get a gut feeling or make guesses that help create ideas to test. Though these may not have proof at first, they can be a beginning for looking deeper.
Technology and Innovations: New technology or tools might make guesses by letting us look at things that were hard to study before.
Personal Interest and Curiosity: People’s curiosity and personal interests in a topic can help create guesses. Scientists could make guesses based on their own likes or love for a subject.

Here are some common types of hypotheses:

Simple Hypothesis

Complex hypothesis, directional hypothesis.

Non-directional Hypothesis

Null Hypothesis (H0)

Alternative hypothesis (h1 or ha), statistical hypothesis, research hypothesis, associative hypothesis, causal hypothesis.

Simple Hypothesis guesses a connection between two things. It says that there is a connection or difference between variables, but it doesn’t tell us which way the relationship goes. Example: Studying more can help you do better on tests. Getting more sun makes people have higher amounts of vitamin D.

Complex Hypothesis tells us what will happen when more than two things are connected. It looks at how different things interact and may be linked together. Example: How rich you are, how easy it is to get education and healthcare greatly affects the number of years people live. A new medicine’s success relies on the amount used, how old a person is who takes it and their genes.

Directional Hypothesis says how one thing is related to another. For example, it guesses that one thing will help or hurt another thing. Example: Drinking more sweet drinks is linked to a higher body weight score. Too much stress makes people less productive at work.

Non-Directional Hypothesis

Non-Directional Hypothesis are the one that don’t say how the relationship between things will be. They just say that there is a connection, without telling which way it goes. Example: Drinking caffeine can affect how well you sleep. People often like different kinds of music based on their gender.

Null hypothesis is a statement that says there’s no connection or difference between different things. It implies that any seen impacts are because of luck or random changes in the information. Example: The average test scores of Group A and Group B are not much different. There is no connection between using a certain fertilizer and how much it helps crops grow.

Alternative Hypothesis is different from the null hypothesis and shows that there’s a big connection or gap between variables. Scientists want to say no to the null hypothesis and choose the alternative one. Example: Patients on Diet A have much different cholesterol levels than those following Diet B. Exposure to a certain type of light can change how plants grow compared to normal sunlight.

Statistical Hypothesis are used in math testing and include making ideas about what groups or bits of them look like. You aim to get information or test certain things using these top-level, common words only. Example: The average smarts score of kids in a certain school area is 100. The usual time it takes to finish a job using Method A is the same as with Method B.

Research Hypothesis comes from the research question and tells what link is expected between things or factors. It leads the study and chooses where to look more closely. Example: Having more kids go to early learning classes helps them do better in school when they get older. Using specific ways of talking affects how much customers get involved in marketing activities.

Associative Hypothesis guesses that there is a link or connection between things without really saying it caused them. It means that when one thing changes, it is connected to another thing changing. Example: Regular exercise helps to lower the chances of heart disease. Going to school more can help people make more money.

Causal Hypothesis are different from other ideas because they say that one thing causes another. This means there’s a cause and effect relationship between variables involved in the situation. They say that when one thing changes, it directly makes another thing change. Example: Playing violent video games makes teens more likely to act aggressively. Less clean air directly impacts breathing health in city populations.

Hypotheses have many important jobs in the process of scientific research. Here are the key functions of hypotheses:

Guiding Research: Hypotheses give a clear and exact way for research. They act like guides, showing the predicted connections or results that scientists want to study.
Formulating Research Questions: Research questions often create guesses. They assist in changing big questions into particular, checkable things. They guide what the study should be focused on.
Setting Clear Objectives: Hypotheses set the goals of a study by saying what connections between variables should be found. They set the targets that scientists try to reach with their studies.
Testing Predictions: Theories guess what will happen in experiments or observations. By doing tests in a planned way, scientists can check if what they see matches the guesses made by their ideas.
Providing Structure: Theories give structure to the study process by arranging thoughts and ideas. They aid scientists in thinking about connections between things and plan experiments to match.
Focusing Investigations: Hypotheses help scientists focus on certain parts of their study question by clearly saying what they expect links or results to be. This focus makes the study work better.
Facilitating Communication: Theories help scientists talk to each other effectively. Clearly made guesses help scientists to tell others what they plan, how they will do it and the results expected. This explains things well with colleagues in a wide range of audiences.
Generating Testable Statements: A good guess can be checked, which means it can be looked at carefully or tested by doing experiments. This feature makes sure that guesses add to the real information used in science knowledge.
Promoting Objectivity: Guesses give a clear reason for study that helps guide the process while reducing personal bias. They motivate scientists to use facts and data as proofs or disprovals for their proposed answers.
Driving Scientific Progress: Making, trying out and adjusting ideas is a cycle. Even if a guess is proven right or wrong, the information learned helps to grow knowledge in one specific area.

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

Initiating Investigations: Hypotheses are the beginning of science research. They come from watching, knowing what’s already known or asking questions. This makes scientists make certain explanations that need to be checked with tests.
Formulating Research Questions: Ideas usually come from bigger questions in study. They help scientists make these questions more exact and testable, guiding the study’s main point.
Setting Clear Objectives: Hypotheses set the goals of a study by stating what we think will happen between different things. They set the goals that scientists want to reach by doing their studies.
Designing Experiments and Studies: Assumptions help plan experiments and watchful studies. They assist scientists in knowing what factors to measure, the techniques they will use and gather data for a proposed reason.
Testing Predictions: Ideas guess what will happen in experiments or observations. By checking these guesses carefully, scientists can see if the seen results match up with what was predicted in each hypothesis.
Analysis and Interpretation of Data: Hypotheses give us a way to study and make sense of information. Researchers look at what they found and see if it matches the guesses made in their theories. They decide if the proof backs up or disagrees with these suggested reasons why things are happening as expected.
Encouraging Objectivity: Hypotheses help make things fair by making sure scientists use facts and information to either agree or disagree with their suggested reasons. They lessen personal preferences by needing proof from experience.
Iterative Process: People either agree or disagree with guesses, but they still help the ongoing process of science. Findings from testing ideas make us ask new questions, improve those ideas and do more tests. It keeps going on in the work of science to keep learning things.

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Hypothesis is a testable statement serving as an initial explanation for phenomena, based on observations, theories, or existing knowledge . It acts as a guiding light for scientific research, proposing potential relationships between variables that can be empirically tested through experiments and observations.

The hypothesis must be specific, testable, falsifiable, and grounded in prior research or observation, laying out a predictive, if-then scenario that details a cause-and-effect relationship. It originates from various sources including existing theories, observations, previous research, and even personal curiosity, leading to different types, such as simple, complex, directional, non-directional, null, and alternative hypotheses, each serving distinct roles in research methodology .

The hypothesis not only guides the research process by shaping objectives and designing experiments but also facilitates objective analysis and interpretation of data , ultimately driving scientific progress through a cycle of testing, validation, and refinement.

Hypothesis – FAQs

What is a hypothesis.

A guess is a possible explanation or forecast that can be checked by doing research and experiments.

What are Components of a Hypothesis?

The components of a Hypothesis are Independent Variable, Dependent Variable, Relationship between Variables, Directionality etc.

What makes a Good Hypothesis?

Testability, Falsifiability, Clarity and Precision, Relevance are some parameters that makes a Good Hypothesis

Can a Hypothesis be Proven True?

You cannot prove conclusively that most hypotheses are true because it’s generally impossible to examine all possible cases for exceptions that would disprove them.

How are Hypotheses Tested?

Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data

Can Hypotheses change during Research?

Yes, you can change or improve your ideas based on new information discovered during the research process.

What is the Role of a Hypothesis in Scientific Research?

Hypotheses are used to support scientific research and bring about advancements in knowledge.

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Newbie: What is the difference between hypothesis class and models?

I am new to machine learning and I am confused with the terminology. Thus far, I used to view a hypothesis class as different instance of hypothesis function... Example: If we are talking about linear classification then different lines characterized by different weights would together form the hypothesis class.

Is my understanding correct or can a hypothesis class represent anything which could approximate the target function? For instance, can a linear or quadratic function that approximates the target function together form a single hypothesis class or both are from different hypothesis classes?

machine-learning

Your hypothesis class consists of all possible hypotheses that you are searching over, regardless of their form. For convenience's sake, the hypothesis class is usually constrained to be only one type of function or model at a time, since learning methods typically only work on one type at a time. This doesn't have to be the case, though:

Hypothesis classes don't have to consist of only one type of function. If you're searching over all linear, quadratic, and exponential functions, then those are what your combined hypothesis class contains.
Hypothesis classes also don't have to consist of only simple functions. If you manage to search over all piecewise-$\tanh^2$ functions, then those functions are what your hypothesis class includes.

The big tradeoff is that the larger your hypothesis class, the better the best hypothesis models the underlying true function, but the harder it is to find that best hypothesis. This is related to the bias–variance tradeoff .

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Hypothesis in Machine Learning
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What is a Hypothesis in Machine Learning?
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If you manage to search over all piecewise-$\tanh^2$ functions, then those functions are what your hypothesis class includes. The big tradeoff is that the larger your hypothesis class, the better the best hypothesis models the underlying true function, but the harder it is to find that best hypothesis. This is related to the bias-variance ...

What is hypothesis in Machine Learning?

What is a Hypothesis?

Defining Hypothesis in Machine Learning

Types of Hypotheses in Machine Learning

1. Null Hypothesis

2. Alternative Hypothesis

3. One-tailed Hypothesis

4. Two-tailed Hypothesis

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Hypothesis Testing – A Deep Dive into Hypothesis Testing, The Backbone of Statistical Inference

1. What is Hypothesis Testing?

2. Steps in Hypothesis Testing

2.1. Set up Hypotheses: Null and Alternative

2.2. Choose a Significance Level (α)

2.3. Calculate a test statistic and P-Value

2.4. Make a Decision

3. Example : Testing a new drug.

4. Example in python

5. Conclusion

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Machine Learning A-Z™: Hands-On Python & R In Data Science

What’s a Hypothesis Space?

1. Introduction

2. Hypothesis Spaces

2.1. Hypotheses and Assumptions

2.2. Regression

3.1. Expressivity vs. Interpretability

4. How to Choose the Hypothesis Space?

4. Conclusion

Evaluating Hypotheses: Estimating hypotheses Accuracy

Evaluating hypotheses:

To evaluate the hypotheses precisely focus on these points:

Motivation:

Bias in the estimation

Estimation variability.

True Error and Sample Error:

Sample Error:

True Error:

Confidence Intervals for Discrete-Valued Hypotheses:

Programmathically

The Machine Learning Model as Hypothesis

The Hypothesis Space

The Data Generating Process

Independent and Identically Distributed Data

Overfitting and Underfitting

Bias Variance Tradeoff

Understanding Bias and Variance

The Bias Variance Decomposition

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