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Course: biology archive > unit 1, the scientific method.
1. make an observation., 2. ask a question., 3. propose a hypothesis., 4. make predictions., 5. test the predictions..
Practical possibility, building a body of evidence, 6. iterate..
Any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples.
Let h j and h k be boolean-valued functions defined over X. h j is more general than or equal to h k (written h j ≥ g h k ) if and only if (∀ x ∈ X) [ (h k (x) = 1) → (h j (x) = 1)]
This is a partial order since it is reflexive, antisymmetric and transitive.
Outputs a description of the most specific hypothesis consistent with the training examples.
For this particular algorithm, there is a bias that the target concept can be represented by a conjunction of attribute constraints.
Outputs a description of the set of all hypotheses consistent with the training examples.
A hypothesis h is consistent with a set of training examples D if and only if h(x) = c(x) for each example < x, c(x) > in D. Consistent(h, D) ≡ (∀ < x, c(x) > ∈ D) h(x) = c(x)
The version space denoted VS H,D with respect to hypothesis space H and training examples D, is the subset of hypotheses from H consistent with the training examples in D. VS H,D ≡ { h ∈ H | Consistent(h, D) }
The general boundary G, with respect to hypothesis space H and training data D, is the set of maximally general members of H consistent with D.
The specific boundary S, with respect to hypothesis space H and training data D, is the set of maximally specific members of H consistent with D.
Let X be an arbitrary set of instances and let H be a set of boolean-valued hypotheses defined over X. Let c:X → {0,1} be an arbitrary target concept defined over X, and let D be an arbitrary set of training examples {<x, c(x)>}. For all X, H, c and D such that S and G are well defined, VS H,D = {h ∈ H | (∃s ∈ S) (∃g ∈ G) (g ≥ g h ≥ g s)}
Work exercise 2.4 on page 48.
A concept Learning Task and Inductive Learning Hypothesis
Concept Learning is a way to find all the consistent hypotheses or concepts. This article will help you understand the concept better.
We have already covered designing the learning system in the previous article and to complete that design we need a good representation of the target concept.
A lot of our learning revolves around grouping or categorizing a large data set. Each concept of learning can be viewed as describing some subset of objects or events defined over a larger set. For example, a subset of vehicles that constitute cars.
Alternatively, each dataset has certain attributes. For example, if you consider a car, its attributes will be color, size, number of seats, etc. And these attributes can be defined as Binary valued attributes.
Let’s take another elaborate example of EnjoySport, The attribute EnjoySport shows if a person is participating in his favorite water activity on this particular day.
The goal is to learn to anticipate the value of EnjoySport on any given day based on its other qualities’ values.
To simplify,
Task T: Determine the value of EnjoySport for every given day based on the values of the day’s qualities.
The total proportion of days (EnjoySport) accurately anticipated is the performance metric P .
Experience E: A collection of days with pre-determined labels (EnjoySport: Yes/No).
Each hypothesis can be considered as a set of six constraints, with the values of the six attributes Sky, AirTemp, Humidity, Wind, Water, and Forecast specified.
Sunny | Warm | Normal | Strong | Warm | Same | Yes |
Sunny | Warm | High | Strong | Warm | Same | Yes |
Rainy | Cold | High | Strong | Warm | Change | No |
Sunny | Warm | High | Strong | Cool | Change | Yes |
Here the concept = < Sky, Air Temp, Humidity, Wind, Forecast>.
The number of possible instances = 2^d.
The total number of Concepts = 2^(2^d).
Where d is the number of features or attributes. In this case, d = 5
=> The number of possible instances = 2^5 = 32.
=> The total number of Concepts = 2^(2^5) = 2^(32).
From these 2^(32) concepts we got, Your machine doesn’t have to learn about all of these topics. You’ll select a few of the concepts from 2^(32) concepts to teach the machine.
The concepts chosen need to be consistent all the time. This hypothesis is called target concept (or) hypothesis space.
To formally define Hypothesis space, The collection of all feasible legal hypotheses is known as hypothesis space. This is the set from which the machine learning algorithm will select the best (and only) function or outputs that describe the target function.
The hypothesis will either
< ?, Cold, High, ?, ? >
<?, ?, ?, ?, ?, ?>
<0, 0, 0, 0, 0, 0>
The main goal is to find the hypothesis that best fits the training data set.
Consider the examples X and hypotheses H in the EnjoySport learning task, for example.
With three potential values for the property Sky and two for AirTemp, Humidity, Wind, Water, and Forecast, the instance space X contains precisely,
=> The number of different instances possible = 3*2*2*2*2*2 = 96.
The learning aim is to find a hypothesis h that is similar to the target concept c across all instances X, with the only knowledge about c being its value throughout the training examples.
Inductive Learning Hypothesis can be referred to as, Any hypothesis that accurately approximates the target function across a large enough collection of training examples will likewise accurately approximate the target function over unseen cases.
Over the training data, inductive learning algorithms can only ensure that the output hypothesis fits the goal notion.
The optimum hypothesis for unseen occurrences, we believe, is the hypothesis that best matches the observed training data. This is the basic premise of inductive learning.
The job of searching through a wide set of hypotheses implicitly described by the hypothesis representation may be considered as concept learning.
The purpose of this search is to identify the hypothesis that most closely matches the training instances.
Our editors will review what you’ve submitted and determine whether to revise the article.
scientific hypothesis , an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an “If…then” statement summarizing the idea and in the ability to be supported or refuted through observation and experimentation. The notion of the scientific hypothesis as both falsifiable and testable was advanced in the mid-20th century by Austrian-born British philosopher Karl Popper .
The formulation and testing of a hypothesis is part of the scientific method , the approach scientists use when attempting to understand and test ideas about natural phenomena. The generation of a hypothesis frequently is described as a creative process and is based on existing scientific knowledge, intuition , or experience. Therefore, although scientific hypotheses commonly are described as educated guesses, they actually are more informed than a guess. In addition, scientists generally strive to develop simple hypotheses, since these are easier to test relative to hypotheses that involve many different variables and potential outcomes. Such complex hypotheses may be developed as scientific models ( see scientific modeling ).
Depending on the results of scientific evaluation, a hypothesis typically is either rejected as false or accepted as true. However, because a hypothesis inherently is falsifiable, even hypotheses supported by scientific evidence and accepted as true are susceptible to rejection later, when new evidence has become available. In some instances, rather than rejecting a hypothesis because it has been falsified by new evidence, scientists simply adapt the existing idea to accommodate the new information. In this sense a hypothesis is never incorrect but only incomplete.
The investigation of scientific hypotheses is an important component in the development of scientific theory . Hence, hypotheses differ fundamentally from theories; whereas the former is a specific tentative explanation and serves as the main tool by which scientists gather data, the latter is a broad general explanation that incorporates data from many different scientific investigations undertaken to explore hypotheses.
Countless hypotheses have been developed and tested throughout the history of science . Several examples include the idea that living organisms develop from nonliving matter, which formed the basis of spontaneous generation , a hypothesis that ultimately was disproved (first in 1668, with the experiments of Italian physician Francesco Redi , and later in 1859, with the experiments of French chemist and microbiologist Louis Pasteur ); the concept proposed in the late 19th century that microorganisms cause certain diseases (now known as germ theory ); and the notion that oceanic crust forms along submarine mountain zones and spreads laterally away from them ( seafloor spreading hypothesis ).
Possible attribute constraints:
< Sky= Sunny, Temp= ? , Humidity= High, Wind= ? , Water= ? , Forecast= ? >
< Sunny, ? , High, ?, ?, ? >
This is equivalent to a (restricted) logical expression:
Sky ( Sunny ) ^ Humidity ( High )
Most general hypothesis: < ?, ?, ?, ?, ?, ? >
Most specific hypothesis: < Ø, Ø, Ø, Ø, Ø, Ø >
Positive and negative training examples for the concept EnjoySport :
Task is to search hypothesis space for a hypothesis consistent with examples.
Inductive learning hypothesis: Any hypothesis found to approximate the target function well over a sufficiently large set of training examples will also approximate the target function well over other unobserved examples.
In this case, space is very small:
1 + ( 4 · 3 · 3 · 3 · 3 · 3 ) = 973
Ø + ( { Sunny, Cold, Rainy, ?} · { Warm, Cold, ? } · . . . )
Need a way of searching very large or infinite hypothesis spaces efficiently.
h1 = < Sunny, ?, ? , Strong, ?, ? >
h2 = < Sunny, ?, ?, ?, ?, ? >
h2 > h1 ("more general than or equal to")
> relation defines a partial-order on H .
We can use this structure to search for a hypothesis consistent with the examples.
most specific hypothesis in { in { is not satisfied by { by next more general constraint that is satisfied by } |
This method works, provided that:
Not possible to find a consistent hypothesis using FIND-S.
FIND-S: < ?, Warm, Normal, Strong, Cool, Change > won't work
CBH: ( Sky ( Sunny ) v Sky ( Cloudy )) ^ Temp ( Warm ) ^ . . . ^ Forecast ( Change )
Idea: output the set of all hypotheses consistent with training data, rather than just one (of possibly many).
No need to explicitly enumerate all consistent hypotheses.
VS and training examples , is the subset of hypotheses from consistent with the training examples . |
How to represent a version space?
One approach: Just list all the members.
a list of all hypotheses in > { any hypothesis such that != |
Only works if H is finite and small (usually an unrealistic assumption).
Better representation for version spaces: Use 2 boundary sets:
|
How can Experiment-Generator module use current VS to suggest new problems to try?
Partially-learned concepts ( VS with > 1 hypothesis) can still be useful
Example:
VS from earlier example says:
Computer graphics opengl mini projects, download final year projects, consistent hypothesis, version space and list then eliminate algorithm, consistent hypothesis.
The idea: output a description of the set of all hypotheses consistent with the training examples (correctly classify training examples).
Version Space is a representation of the set of hypotheses that are consistent with D
Hypothesis h is consistent with a set of training examples D iff h ( x ) = c ( x ) for each example in D
Example to demonstrate the consistent hypothesis
1 | Some | Small | No | Affordable | One | No |
2 | Many | Big | No | Expensive | Many | Yes |
h1 = (?, ?, No, ?, Many) – Yes —- is a consistent hypothesis
h2 = (?, ?, No, ?, ?) – yes —- is inconsistent hypothesis
The version space VS H,D is the subset of the hypothesis from H consistent with the training example in D
Version space as a list of hypotheses
VersionSpace <– a list containing every hypothesis in H
For each training example, <x, c(x)> Remove from VersionSpace any hypothesis h for which h(x) != c(x)
Output the list of hypotheses in VersionSpace
Example: List-Then-Eliminate algorithm
F1 – > A, B
F2 – > X, Y
Instance Space: (A, X), (A, Y), (B, X), (B, Y) – 4 Examples
Hypothesis Space: (A, X), (A, Y), (A, ø ), (A, ?), (B, X), (B, Y), (B, ø ), (B, ?), ( ø , X), ( ø , Y), ( ø , ø ), ( ø , ?), ( ? , X), ( ? , Y), ( ? , ø ), ( ? , ?) – 16 Hypothesis
Semantically Distinct Hypothesis : (A, X), (A, Y), (A, ?), (B, X), (B, Y), (B, ?), ( ? , X), ( ? , Y ( ? , ?), ( ø , ø ) – 10
Version Space: (A, X), (A, Y), (A, ?), (B, X), (B, Y), (B, ?), (?, X), (?, Y) (?, ?), ( ø , ø ),
Training Instances
F1 F2 Target
A X Yes
A Y Yes
Consistent Hypothesis are: (A, ?), (?, ?)
Problems: List-Then-Eliminate algorithm
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The hypothesis is a common term in Machine Learning and data science projects. As we know, machine learning is one of the most powerful technologies across the world, which helps us to predict results based on past experiences. Moreover, data scientists and ML professionals conduct experiments that aim to solve a problem. These ML professionals and data scientists make an initial assumption for the solution of the problem. This assumption in Machine learning is known as Hypothesis. In Machine Learning, at various times, Hypothesis and Model are used interchangeably. However, a Hypothesis is an assumption made by scientists, whereas a model is a mathematical representation that is used to test the hypothesis. In this topic, "Hypothesis in Machine Learning," we will discuss a few important concepts related to a hypothesis in machine learning and their importance. So, let's start with a quick introduction to Hypothesis. It is just a guess based on some known facts but has not yet been proven. A good hypothesis is testable, which results in either true or false. : Let's understand the hypothesis with a common example. Some scientist claims that ultraviolet (UV) light can damage the eyes then it may also cause blindness. In this example, a scientist just claims that UV rays are harmful to the eyes, but we assume they may cause blindness. However, it may or may not be possible. Hence, these types of assumptions are called a hypothesis. The hypothesis is one of the commonly used concepts of statistics in Machine Learning. It is specifically used in Supervised Machine learning, where an ML model learns a function that best maps the input to corresponding outputs with the help of an available dataset. There are some common methods given to find out the possible hypothesis from the Hypothesis space, where hypothesis space is represented by and hypothesis by Th ese are defined as follows: It is used by supervised machine learning algorithms to determine the best possible hypothesis to describe the target function or best maps input to output. It is often constrained by choice of the framing of the problem, the choice of model, and the choice of model configuration. . It is primarily based on data as well as bias and restrictions applied to data. Hence hypothesis (h) can be concluded as a single hypothesis that maps input to proper output and can be evaluated as well as used to make predictions. The hypothesis (h) can be formulated in machine learning as follows: Where, Y: Range m: Slope of the line which divided test data or changes in y divided by change in x. x: domain c: intercept (constant) : Let's understand the hypothesis (h) and hypothesis space (H) with a two-dimensional coordinate plane showing the distribution of data as follows: Hypothesis space (H) is the composition of all legal best possible ways to divide the coordinate plane so that it best maps input to proper output. Further, each individual best possible way is called a hypothesis (h). Hence, the hypothesis and hypothesis space would be like this: Similar to the hypothesis in machine learning, it is also considered an assumption of the output. However, it is falsifiable, which means it can be failed in the presence of sufficient evidence. Unlike machine learning, we cannot accept any hypothesis in statistics because it is just an imaginary result and based on probability. Before start working on an experiment, we must be aware of two important types of hypotheses as follows: A null hypothesis is a type of statistical hypothesis which tells that there is no statistically significant effect exists in the given set of observations. It is also known as conjecture and is used in quantitative analysis to test theories about markets, investment, and finance to decide whether an idea is true or false. An alternative hypothesis is a direct contradiction of the null hypothesis, which means if one of the two hypotheses is true, then the other must be false. In other words, an alternative hypothesis is a type of statistical hypothesis which tells that there is some significant effect that exists in the given set of observations.The significance level is the primary thing that must be set before starting an experiment. It is useful to define the tolerance of error and the level at which effect can be considered significantly. During the testing process in an experiment, a 95% significance level is accepted, and the remaining 5% can be neglected. The significance level also tells the critical or threshold value. For e.g., in an experiment, if the significance level is set to 98%, then the critical value is 0.02%. The p-value in statistics is defined as the evidence against a null hypothesis. In other words, P-value is the probability that a random chance generated the data or something else that is equal or rarer under the null hypothesis condition. If the p-value is smaller, the evidence will be stronger, and vice-versa which means the null hypothesis can be rejected in testing. It is always represented in a decimal form, such as 0.035. Whenever a statistical test is carried out on the population and sample to find out P-value, then it always depends upon the critical value. If the p-value is less than the critical value, then it shows the effect is significant, and the null hypothesis can be rejected. Further, if it is higher than the critical value, it shows that there is no significant effect and hence fails to reject the Null Hypothesis. In the series of mapping instances of inputs to outputs in supervised machine learning, the hypothesis is a very useful concept that helps to approximate a target function in machine learning. It is available in all analytics domains and is also considered one of the important factors to check whether a change should be introduced or not. It covers the entire training data sets to efficiency as well as the performance of the models. Hence, in this topic, we have covered various important concepts related to the hypothesis in machine learning and statistics and some important parameters such as p-value, significance level, etc., to understand hypothesis concepts in a better way. |
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We study natural links between various types of consistency: usual consistency, strong consistency, uniform consistency, and pointwise consistency. On the base of these results, we provide both sufficient conditions and necessary conditions for the existence of various types of consistent tests for a wide spectrum of problems of hypothesis testing which arise in statistics: on a probability measure of an independent sample, on a mean measure of a Poisson process, on a solution of an ill-posed linear problem in a Gaussian noise, on a solution of the deconvolution problem, for signal detection in a Gaussian white noise. In the last three cases, the necessary and sufficient conditions coincide.
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Institute of Problems of Mechanical Engineering of RAS, St. Petersburg State University, St. Petersburg, Russia
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Correspondence to M. Ermakov .
Translated from Zapiski Nauchnykh Seminarov POMI , Vol. 442, 2015, pp. 48–74.
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Ermakov, M. On Consistent Hypothesis Testing. J Math Sci 225 , 751–769 (2017). https://doi.org/10.1007/s10958-017-3491-4
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Issue Date : September 2017
DOI : https://doi.org/10.1007/s10958-017-3491-4
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An hypothesis is a partial assignment of values to the features. That is, by "applying the hypothesis" we obtain a subset of instances for which the features satisfy the hypothesis. An hypothesis is consistent with the data if the target variable (called "concept" apparently, here EnjoySport in the example) has the same value for any instance ...
Consistent Hypothesis, Version Space and List Then Eliminate Algorithm by Mahesh Huddarhttps://www.vtupulse.com/machine-learning/version-space-and-list-then-...
Definition — Consistent —. A hypothesis h is consistent with a set of training examples D if and only if h (x) = c (x) for each example (x, c (x)) in D. Note the difference between definitions ...
Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question.
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...
A hypothesis is a function that best describes the target in supervised machine learning. The hypothesis that an algorithm would come up depends upon the data and also depends upon the restrictions and bias that we have imposed on the data. The Hypothesis can be calculated as: y = mx + b y =mx+b. Where, y = range. m = slope of the lines.
It seeks to explore and understand a particular aspect of the research subject. In contrast, a research hypothesis is a specific statement or prediction that suggests an expected relationship between variables. It is formulated based on existing knowledge or theories and guides the research design and data analysis. 7.
Consistent Hypothesis: Definition A hypothesis h is consistent with a set of training examples D if and only if h(x)=c(x) for each example <x, c(x)>in D. A hypothesis is consistent with the training samples if it correctly classifies the samples
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories. ... consistent with our hypothesis that there is a difference in height between men and women. These are superficial differences ...
A hypothesis is an educated guess, based on observation. It's a prediction of cause and effect. Usually, a hypothesis can be supported or refuted through experimentation or more observation. A hypothesis can be disproven but not proven to be true. Example: If you see no difference in the cleaning ability of various laundry detergents, you might ...
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question. A hypothesis is not just a guess — it should be based on ...
Hypothesis is a prediction of the outcome of a study. Hypotheses are drawn from theories and research questions or from direct observations. In fact, a research problem can be formulated as a hypothesis. To test the hypothesis we need to formulate it in terms that can actually be analysed with statistical tools.
The scientific method. At the core of biology and other sciences lies a problem-solving approach called the scientific method. The scientific method has five basic steps, plus one feedback step: Make an observation. Ask a question. Form a hypothesis, or testable explanation. Make a prediction based on the hypothesis.
Outputs a description of the most specific hypothesis consistent with the training examples. Initialize h to the most specific hypothesis in H. For each positive training instance x. For each attribute constraint a i in h. If the constraint a i is NOT satisfied by x, then replace a i in h by the next more general constraint that is satisfied by x.
The concepts chosen need to be consistent all the time. This hypothesis is called target concept (or) hypothesis space. Hypothesis Space: To formally define Hypothesis space, The collection of all feasible legal hypotheses is known as hypothesis space. This is the set from which the machine learning algorithm will select the best (and only ...
hypothesis. science. scientific hypothesis, an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world. The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an "If…then" statement summarizing the idea and in the ...
Version Spaces. Idea: output the set of all hypotheses consistent with training data, rather than just one (of possibly many). No need to explicitly enumerate all consistent hypotheses. Take advantage of partial ordering of H. The version space VS H,D with respect to hypothesis space H and training examples D , is the subset of hypotheses from ...
The version space VS H,D is the subset of the hypothesis from H consistent with the training example in D. List-Then-Eliminate algorithm. Version space as a list of hypotheses. VersionSpace <- a list containing every hypothesis in H. For each training example, <x, c(x)> Remove from VersionSpace any hypothesis h for which h(x) != c(x)
The hypothesis is one of the commonly used concepts of statistics in Machine Learning. It is specifically used in Supervised Machine learning, where an ML model learns a function that best maps the input to corresponding outputs with the help of an available dataset. In supervised learning techniques, the main aim is to determine the possible ...
Consistency (statistics) In statistics, consistency of procedures, such as computing confidence intervals or conducting hypothesis tests, is a desired property of their behaviour as the number of items in the data set to which they are applied increases indefinitely. In particular, consistency requires that as the dataset size increases, the ...
Learning Bound for Finite H - Consistent Case. Theorem: let H be a finite set of functions from X to 1} and L an algorithm that for any target concept c H and sample S returns a consistent hypothesis hS : . Then, for any 0 , with probability at least. (hS ) = 0 >.
In settings where there is a generality-ordering on hypotheses, it is possible to represent the version space by two sets of hypotheses: (1) the most specific consistent hypotheses, and (2) the most general consistent hypotheses, where "consistent" indicates agreement with observed data.. The most specific hypotheses (i.e., the specific boundary SB) cover the observed positive training ...
On Consistent Hypothesis Testing. We study natural links between various types of consistency: usual consistency, strong consistency, uniform consistency, and pointwise consistency. On the base of these results, we provide both sufficient conditions and necessary conditions for the existence of various types of consistent tests for a wide ...