define inductive learning hypothesis

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. 

Why Concept learning? 

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.

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. 

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 

• Indicate with a “?” that any value is acceptable for this attribute.
• Define a specific necessary value (e.g., Warm).
• Indicate with a “0” that no value is acceptable for this attribute.
• The expression that represents the hypothesis that the person loves their favorite sport exclusively on chilly days with high humidity (regardless of the values of the other criteria) is –

  < ?, Cold, High, ?, ? >

• The most general hypothesis that each day is a positive example is represented by 

                   <?, ?, ?, ?, ?, ?> 

• The most specific possible hypothesis that none of the day is a positive example is represented by

                         <0, 0, 0, 0, 0, 0>

Concept Learning as Search: 

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. 

Inductive Learning Hypothesis

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.

Inductive Learning Algorithms Assumptions:

• The population is represented in the training sample.
• Discrimination is possible thanks to the input characteristics.

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.

Inductive Learning: Examples, Definition, Pros, Cons

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

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Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

Inductive learning is a teaching strategy where students discover operational principles by observing examples.

It is used in inquiry-based and project-based learning where the goal is to learn through observation rather than being ‘told’ the answers by the teacher.

It is consistent with a constructivist approach to learning as it holds that knowledge should be constructed in the mind rather than transferred from the teacher to student.

Inductive Learning Definition

Inductive learning involves the students ‘constructing’ theories and ideas through observation. We contrast it to deductive learning , where the teacher presents the theories then students examine examples.

It is argued that learning with the inductive approach results in deep cognitive processing of information, creative independent thinking, and a rich understanding of the concepts involved.

It can also lead to long memory retention and strong transferability of knowledge to other situations.

Prince and Felder (2006) highlight that this concept explains a range of approaches to teaching and learning:

“Inductive teaching and learning is an umbrella term that encompasses a range of instructional methods, including inquiry learning, problem-based learning, project-based learning, case-based teaching, discovery learning, and just-in-time teaching” (Prince & Felder, 2006, p. 124).

Inductive Learning vs Deductive Learning

While both inductive and deductive learning are used in education, they are distinct in terms of their underlying principles and teaching methods.

Generally, inductive learning is a bottom-up approach meaning the observations precede the conclusions. It involves making observations, recognizing patterns, and forming generalizations .

On the other hand, deductive learning is a top-down approach meaning that it involves a teacher presenting general principles which are then examined using scientific research.

Both are legitimate methods, and in fact, despite its limitations, many students get a lot of pleasure out of doing deductive research in a physics or chemistry class.

Below is a table comparing the differences:

Inductive Learning Strengths and Limitations

Inductive learning is praised as an effective approach because it involves students constructing knowledge through observation, active learning and trial and error.

As a result, it helps develop critical thinking skills and fosters creativity because students must create the theories rather than being presented with them at the beginning of the lesson.

However, inductive learning isn’t always beneficial. To start with, students often don’t understand what the end goal of the activity is, which leads to confusion and disillusionment.

Secondly, it can be more challenging for novice learners who don’t have strong frameworks for systematic analysis and naturalistic observation .

Below is a table summary of the strengths and weaknesses:

Inductive Learning Examples

• Mrs. Williams shows her art students a wide range of masterpieces from different genres. Students then develop their own categorical definitions and classify the artwork accordingly.   
• Children in third grade are shown photos of different musical instruments and then asked to categorize them based on their own definitions.
• A company has customers try out a new product while the design team observes behind a two-way mirror. The team tries to identify common concerns, operational issues, and desirable features.
• A team of researchers observes the verbal interactions between parents and children in households. They then try to identify patterns and characteristics that affect language acquisition.
• A biologist observes the foraging and hunting behavior of the Artic fox to determine types of terrain and environmental features conducive to survival.
• Researchers interested in group dynamics and decision-making analyze the functional statements of personnel during meetings and try to find patterns that facilitate problem-solving . 
• Chef Phillips presents 5 desserts to his students and asks them to identify the qualities that make each one distinct….and tasty.
• Dr. Guttierrez gives each team of students in his advertising class a set of effective and ineffective commercials. Each team then develops a set of criteria for what makes a good commercial. 
• The Career Center shows a range of video-recorded job interviews and asks students to identify the characteristics that make some of them impressive and others not.
• Kumar demonstrates different yoga poses in a Far East Religions class and then the students try to identify the areas of the body and problem each pose is meant to address.

Case Studies and Research Basis

1. inductive learning in an inquiry-based classroom.

On the surface, this would appear to be a very straightforward question with a very straightforward answer. Many formal definitions share several common characteristics: existence of a m etabolism, replication, evolution, responsiveness, growth, movement, and cellular structure.

However, Prud’homme-Généreux (2013) points out that in one popular biology textbook there are 48 different experts offering different definitions.

In this inductive learning class activity by Prud’homme-Généreux (2013), the instructor prepares two sets of cards (A and B). Each card in set A contains an image of a living organism; each card in set B contains an image of an object that is not living.

Before distributing the cards, teams of 3 are formed and asked:

Why do we need a definition of life?

Each team then generates a new definition of life. Afterwards, the teams receive 3 cards from both sets.

For class discussion, one characteristic of a team’s definition is written on the board. Teams examine their cards and determine if that characteristic applies.

Prud’homme-Généreux states:

“…that the approach elicits curiosity, triggers questions, and leads to a more nuanced understanding of the concept…leads to confidence in their ability to think.”

2. Inductive Learning in Peer Assessment

Inductive learning methods can be applied in a wide range of circumstances. One strategy is aimed at helping students understand grading criteria and how to develop a critical eye for their work and the work of others.

The procedure involves having students form teams of 3-5. The instructor then supplies each team with 5 essays that vary in terms of quality and assigned grade.

Each team examines the essays, discuss them amongst themselves, and then try to identify the grading criteria.

Class discussion can ensue with the instructor projecting new essays on the board and asking the class to apply their team’s criteria.

This activity is an excellent way for students to develop a deeper understanding of the grading process.

3. Problem-Based Inductive Learning in Medical School

The conventional approach to teaching involves the teacher presenting the principles of a subject and then having students apply that knowledge to different situations. As effective as that approach is, medical schools have found that student learning is more advanced with a problem-based inductive approach.

So, instead of students being told what the symptoms are for a specific disease, students are presented with a clinical case and then work together to identify the ailment.

Although each team is assigned an experienced tutor, they try to provide as little assistance as possible.

Medical schools have found that this form of inductive learning leads to a much deeper understanding of medical conditions and helps students develop the kind of advanced critical-thinking skills they will need throughout their careers.

4. Inductive Learning in Traffic Management

Traffic management involves controlling the movement of people and vehicles. The goal is to ensure safety and improve flow efficiency. In the early days of traffic management, personnel would monitor traffic conditions at various times of the day, and try to identify patterns in traffic dynamics and the causal factors involved.

Those insights were then extrapolated to the broader city context and various rules and regulations were devised.

Today, much of that inductive analysis is conducted through sophisticated software algorithms. Through carefully placed cameras, the software tracks traffic flow, identifies operating paramenters, and then devises solutions to improve flow rate and safety.

For example, the software will monitor average traffic speed, congestion detection, journey times between key locations, as well as vehicle counts and flow rate estimates.

Traffic management is an example of software that is capable of inductive learning.

5. Inductive Learning in Theory Development

Inductive learning is a key way in which scholars and researchers come up with ground-breaking theories. One example is in Mary Ainsworth’s observational research, where she used observations to induce a theory, as explained below.

Although most people mention the Strange Situations test developed by Dr. Mary Ainsworth, she conducted naturalistic observations many years prior to its initial creation.

For two years, starting in 1954, she visited the homes of families in Uganda. She took detailed notes on infant/caregiver interactions, in addition to interviewing mothers about their parenting practices.

Through inductive reasoning and learning, she was able to identify patterns of behavior that could be categorized into several distinct attachment profiles.

Along with her work with John Bowlby, these notes formed the basis of her theory of attachment.

As reported by Bretherton (2013),

“…secure-attached infants cried little and engaged in exploration when their mother was present, while insecure-attached infants were frequently fussy even with mother in the same room” (p. 461).

Inductive learning is when students are presented with examples and case studies from which they are to derive fundamental principles and characteristics.

It many ways, it is the opposite of conventional instructional strategies where teachers define the principles and then students apply them to examples.

Inductive learning is a powerful approach. It leads to students developing a very rich understanding of the subject under study, increases student engagement, prolongs retention, and helps build student confidence in their ability to learn.

We can see examples of inductive learning in the world’s best medical schools, research that has had a profound impact on our understanding of infant/caregiver relations, and even its use by sophisticated algorithms that control traffic in our largest cities.

Ainsworth, M. D. S. (1967). Infancy in Uganda . Baltimore: Johns Hopkins University Press.

Bretherton, I. (2013). Revisiting Mary Ainsworth’s conceptualization and assessments of maternal sensitivity-insensitivity. Attachment & Human Development, 15 (5–6), 460–484. http://dx.doi.org/10.1080/14616734.2013.835128

Prince, M. & Felder, R. (2006). Inductive teaching and learning methods: Definitions, comparisons, and research bases. Journal of Engineering Education, 95 , 123-137. https://doi.org/10.1002/j.2168-9830.2006.tb00884.x

Prud’homme-Généreux, A. (2013). What Is Life? An Activity to Convey the Complexities of This Simple Question. The American Biology Teacher, 75 (1), 53-57.

Shemwell, J. T., Chase, C. C., & Schwartz, D. L. (2015). Seeking the general explanation: A test of inductive activities for learning and transfer. Journal of Research in Science Teaching, 52 (1), 58-83.

Lahav, N. (1999). Biogenesis: Theories of life’s origin . Oxford, U.K.: Oxford University Press.

• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 23 Achieved Status Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Defense Mechanisms Examples
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• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 18 Adaptive Behavior Examples

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 23 Achieved Status Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Ableism Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Defense Mechanisms Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Theory of Planned Behavior Examples

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Inductive Inference

Inductive inference is the process of reaching a general conclusion from specific examples.

The general conclusion should apply to unseen 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.

Identified relevant attributes: x, y, z

if x = 2 and z = 5, then y = 3. if x = 4 and z = 10, then y = 6. if x = 5 and z = 7, then y = 2. otherwise y = 1.

Model 2 is likely overfitting.

Inductive bias: explicit or implicit assumption(s) about what kind of model is wanted.

Typical inductive bias:

• Select the shortest one.
• The decision tree ID3 algorithm searches the complete hypothesis space, and there is no restriction on the number of hypthotheses that could eventually be enumerated. However, this algorithm searches incompletely through the set of possibly hypotheses and preferentially selects those hypotheses that lead to a smaller decision tree. This type of bias is called a preference (or search ) bias.
• In contrast, the version space candidate-elimination algorithm searches through only a subset of the possible hypotheses (an incomplete hypothesis space), yet searches this space completely. This type of bias is called a restriction (or language ) bias, because the number of possible hyptheses considered is restricted.
• Restricting the hypothesis space being searched (a restriction bias) is less desirable because the target function may not be within the set of hypotheses considered.

Some languages of interest:

• e.g., A(~B)(~C) + A(~B)C + AB(~C)
• Algebraic expressions.

Positive and Negative Examples

Positive Examples

• Are all true.

Negative Examples

• Constrain the set of models consistent with the examples.

Search for Description

Description keeps getting larger or longer.

Finite language - algorithm terminates.

Infinite language - algorithm runs

• Until out of memory.
• Until a final answer is reached.

X = example space/instance space (all possible examples)

D = description space (set of descriptions defined as a language L )

Success Criterion

• description can be relaxed to match all instances.
• inductive bias can be expressed in the success criterion.

L = {x op y = z}, op = {+, -, *, /}

Given a precise specification of language and data, write a program to test descriptions one by one against the examples.

• finite language: size = |L|
• finite number of examples: size = |X|

Why is Machine Learning Hard (Slow)?

It is very difficult to specify a small finite language that contains a description of the examples.

e.g., algebraic expressions on 3 variables is an infinite language

← ^ →

Inductive Learning Hypothesis

• With n attributes, each with 3 values, we have that | H | = 3 n
• We assume that one of those hypothesis will match the target function c ( x ) .
• Furthermore, all we know about c ( x ) is given by the examples we have seen. We must assume that the future examples will resemble past ones.
• The inductive learning hypothesis states that 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.
• Why should this be true? Its not true for the stock market, or is it?

What Is Inductive Bias in Machine Learning?

Last updated: March 18, 2024

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1. Overview

In this tutorial, we’ll discuss a definition of inductive bias and go over its different forms in machine learning and deep learning.

2. Definition

Every machine learning model requires some type of architecture design and possibly some initial assumptions about the data we want to analyze. Generally, every building block and every belief that we make about the data is a form of inductive bias.

Inductive biases play an important role in the ability of machine learning models to generalize to the unseen data. A strong inductive bias can lead our model to converge to the global optimum. On the other hand, a weak inductive bias can cause the model to find only the local optima and be greatly affected by random changes in the initial states.

We can categorize inductive biases into two different groups called relational and non-relational. The former represents the relationship between entities in the network, while the latter is a set of techniques that further constrain the learning algorithm.

3. Inductive Biases in Machine Learning

In traditional machine learning, every algorithm has its own inductive biases. In this section, we mention some of these algorithms.

3.1. Bayesian Models

Inductive bias in Bayesian models shows itself in the form of the prior distributions that we choose for the variables. Consequently, the prior can shape the posterior distribution in a way that the latter can turn out to be a similar distribution to the former. In addition, we assume that the variables are conditionally independent, meaning that given the parents of a node in the network, it’ll be independent from its ancestors. As a result, we can make use of conditional probability to make the inference. Also, the structure of the Bayesian net can facilitate the analysis of causal relationships between entities.

3.2. k-Nearest Neighbors (k-NN) Algorithm

3.3. linear regression, 3.4. logistic regression.

In logistic regression , we assume that there’s a hyperplane that separates the two classes from each other. This simplifies the problem, but one can imagine that if the assumption is not valid, we won’t have a good model.

4. Relational Inductive Biases in Deep Learning

Relational inductive biases define the structure of the relationships between different entities or parts in our model. These relations can be arbitrary, sequential, local, and so on.

4.1. Weak Relation

Sometimes the relationship between the neural units is weak, meaning that they’re somewhat independent of each other. The choice of including a fully connected layer in the net can represent this kind of relationship:

4.2. Locality

In order to process an image, we start by capturing the local information. One way to do that is the use of a convolutional layer. It can capture the local relationship between the pixels of an image. Then, as we go deeper in the model, the local feature extractors help to extract the global features:

4.3. Sequential Relation

Sometimes our data has a sequential characteristic. For instance, time series and sentences consist of sequential elements that appear one after another. To model this pattern, we can introduce a recurrent layer to our network:

4.4. Arbitrary Relation

To solve problems related to a group of things or people, it might be more informative to see them as a graph. The graph structure imposes arbitrary relationships between the entities, which is ideal when there’s no clear sequential or local relation in the model:

5. Non-Relational Inductive Biases in Deep Learning

Other than relational inductive biases, there are also some concepts that impose additional constraints on our model . In this section, we list some of these concepts.

5.1. Non-linear Activation Functions

Non-linear activation functions  allow the model to capture the non-linearity hidden in the data. Without them, a deep neural network wouldn’t be able to work better than a single-layer network. The reason is that the combination of several linear layers would still be a linear layer.

5.2. Dropout

Dropout is a regularization technique that helps the network avoid memorizing the data by forcing random subsets of the network to each learn the data pattern. As a result, the obtained model, in the end, is able to generalize better and avoid overfitting .

5.3. Weight Decay

5.4. normalization.

Normalization techniques can help our model in several ways, such as making the training faster and regularizing. But most importantly, it reduces the change in the distribution of the net’s activations which is called internal co-variate shift . There are different normalization techniques such as batch normalization , instance normalization , and layer normalization .

5.5. Data Augmentation

We can think of data augmentation as another regularization method. What it imposes on the model depends on its algorithm. For instance, adding noise or word substitution in sentences are two types of data augmentation. They assume that the addition of the noise or word substitution should not change the category of a sequence of words in a classification task.

5.6. Optimization Algorithm

The optimization algorithm has a key role in the model’s outcome we want to learn. For example, different versions of the gradient descent algorithm can lead to different optima. Subsequently, the resulting models will have other generalization properties. Moreover, each optimization algorithm has its own parameters that can greatly influence the convergence and optimality of the model.

6. Conclusion

In this tutorial, we learned about the two types of inductive biases in traditional machine learning and deep learning. In addition, we went through a list of examples for each type and explained the effects of the given examples.

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Inductive Learning Algorithm

In this article, we will learn about Inductive Learning Algorithm which generally comes under the domain of Machine Learning.

What is Inductive Learning Algorithm?

Inductive Learning Algorithm (ILA) is an iterative and inductive machine learning algorithm that is used for generating a set of classification rules, which produces rules of the form “IF-THEN”, for a set of examples, producing rules at each iteration and appending to the set of rules.

There are basically two methods for knowledge extraction firstly from domain experts and then with machine learning. For a very large amount of data, the domain experts are not very useful and reliable. So we move towards the machine learning approach for this work. To use machine learning One method is to replicate the expert’s logic in the form of algorithms but this work is very tedious, time taking, and expensive. So we move towards the inductive algorithms which generate the strategy for performing a task and need not instruct separately at each step.

Why you should use Inductive Learning?

The ILA is a new algorithm that was needed even when other reinforcement learnings like ID3 and AQ were available.

• The need was due to the pitfalls which were present in the previous algorithms, one of the major pitfalls was the lack of generalization of rules.
• The ID3 and AQ used the decision tree production method which was too specific which were difficult to analyze and very slow to perform for basic short classification problems.
• The decision tree-based algorithm was unable to work for a new problem if some attributes are missing.
• The ILA uses the method of production of a general set of rules instead of decision trees , which overcomes the above problems

Basic Requirements to Apply Inductive Learning Algorithm

• List the examples in the form of a table ‘T’ where each row corresponds to an example and each column contains an attribute value.
• Create a set of m training examples, each example composed of k attributes and a class attribute with n possible decisions.
• Create a rule set, R, having the initial value false.
• Initially, all rows in the table are unmarked.

Necessary Steps for Implementation

• Step 1: divide the table ‘T’ containing m examples into n sub-tables (t1, t2,…..tn). One table for each possible value of the class attribute. (repeat steps 2-8 for each sub-table)
• Step 2: Initialize the attribute combination count ‘ j ‘ = 1.
• Step 3: For the sub-table on which work is going on, divide the attribute list into distinct combinations, each combination with ‘j ‘ distinct attributes.
• Step 4: For each combination of attributes, count the number of occurrences of attribute values that appear under the same combination of attributes in unmarked rows of the sub-table under consideration, and at the same time, not appears under the same combination of attributes of other sub-tables. Call the first combination with the maximum number of occurrences the max-combination ‘ MAX’.
• Step 5: If ‘MAX’ == null, increase ‘ j ‘ by 1 and go to Step 3.
• Step 6: Mark all rows of the sub-table where working, in which the values of ‘MAX’ appear, as classified.
• Step 7: Add a rule (IF attribute = “XYZ” –> THEN decision is YES/ NO) to R whose left-hand side will have attribute names of the ‘MAX’ with their values separated by AND, and its right-hand side contains the decision attribute value associated with the sub-table.
• Step 8: If all rows are marked as classified, then move on to process another sub-table and go to Step 2. Else, go to Step 4. If no sub-tables are available, exit with the set of rules obtained till then. 

An example showing the use of ILA suppose an example set having attributes Place type, weather, location, decision, and seven examples, our task is to generate a set of rules that under what condition is the decision.

Subset – 1

Subset – 2

• At iteration 1 rows 3 & 4 column weather is selected and rows 3 & 4 are marked. the rule is added to R IF the weather is warm then a decision is yes. 
• At iteration 2 row 1 column place type is selected and row 1 is marked. the rule is added to R IF the place type is hilly then the decision is yes. 
• At iteration 3 row 2 column location is selected and row 2 is marked. the rule is added to R IF the location is Shimla then the decision is yes. 
• At iteration 4 row 5&6 column location is selected and row 5&6 are marked. the rule is added to R IF the location is Mumbai then a decision is no. 
• At iteration 5 row 7 column place type & the weather is selected and row 7 is marked. the rule is added to R IF the place type is beach AND the weather is windy then the decision is no. 

Finally, we get the rule set:- Rule Set

• Rule 1: IF the weather is warm THEN the decision is yes.
• Rule 2: IF the place type is hilly THEN the decision is yes.
• Rule 3: IF the location is Shimla THEN the decision is yes.
• Rule 4: IF the location is Mumbai THEN the decision is no.
• Rule 5: IF the place type is beach AND the weather is windy THEN the decision is no.

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Chapter 2: Concept Learning and the General-to-Specific Ordering

• Concept Learning: Inferring a boolean valued function from training examples of its input and output.
• X: set of instances
• x: one instance
• c: target concept, c:X → {0, 1}
• < x, c(x) >, training instance, can be a positive example or a negative example
• D: set of training instances
• H: set of possible hypotheses
• h: one hypothesis, h: X → { 0, 1 }, the goal is to find h such that h(x) = c(x) for all x in X

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.

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.

Find-S Algorithm

Outputs a description of the most specific hypothesis consistent with the training examples.

• Initialize h to the most specific hypothesis 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.
• Output hypothesis h

For this particular algorithm, there is a bias that the target concept can be represented by a conjunction of attribute constraints.

Candidate Elimination Algorithm

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.

Version Space Representation

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)}

• Initialize G to the set of maximally general hypotheses in H
• Initialize S to the set of maximally specific hypotheses in H
• Remove from G any hypothesis inconsistent with d
• Remove s from S
• Add to S all minimal generalizations h of s such that h is consistent with d, and some member of G is more general than h
• Remove from S any hypothesis that is more general than another hypothesis in S
• Remove from S any hypothesis inconsistent with d
• Remove g from G
• Add to G all minimal specializations h of g such that h is consistent with d, and some member of S is more specific than h
• Remove from G any hypothesis that is less general than another hypothesis in G

Candidate Elimination Algorithm Issues

• Will it converge to the correct hypothesis? Yes, if (1) the training examples are error free and (2) the correct hypothesis can be represented by a conjunction of attributes.
• If the learner can request a specific training example, which one should it select?
• How can a partially learned concept be used?

Inductive Bias

• Definition: Consider a concept learning algorithm L for the set of instances X. Let c be an arbitrary concept defined over X and let D c = {<x, c(x)>} be an arbitrary set of training examples of c. Let L(x i , D c ) denote the classification assigned to the instance x i by L after training on the data D c . The inductive bias of L is any minimal set of assertions B such that for any target concept c and corresponding training examples D c (∀ x i ∈ X) [ L(x i , D c ) follows deductively from (B ∧ D c ∧ x i ) ]
• Thus, one advantage of an inductive bias is that it gives the learner a rational basis for classifying unseen instances.
• What is another advantage of bias?
• What is one disadvantage of bias?
• What is the inductive bias of the candidate elimination algorithm? Answer: the target concept c is a conjunction of attributes.
• What is meant by a weak bias versus a strong bias?

Sample Exercise

Work exercise 2.4 on page 48.

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• Inductive vs. Deductive Research Approach | Steps & Examples

Inductive vs. Deductive Research Approach | Steps & Examples

Published on April 18, 2019 by Raimo Streefkerk . Revised on June 22, 2023.

The main difference between inductive and deductive reasoning is that inductive reasoning aims at developing a theory while deductive reasoning aims at testing an existing theory .

In other words, inductive reasoning moves from specific observations to broad generalizations . Deductive reasoning works the other way around.

Both approaches are used in various types of research , and it’s not uncommon to combine them in your work.

Table of contents

Inductive research approach, deductive research approach, combining inductive and deductive research, other interesting articles, frequently asked questions about inductive vs deductive reasoning.

When there is little to no existing literature on a topic, it is common to perform inductive research , because there is no theory to test. The inductive approach consists of three stages:

• A low-cost airline flight is delayed
• Dogs A and B have fleas
• Elephants depend on water to exist
• Another 20 flights from low-cost airlines are delayed
• All observed dogs have fleas
• All observed animals depend on water to exist
• Low cost airlines always have delays
• All dogs have fleas
• All biological life depends on water to exist

Limitations of an inductive approach

A conclusion drawn on the basis of an inductive method can never be fully proven. However, it can be invalidated.

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When conducting deductive research , you always start with a theory. This is usually the result of inductive research. Reasoning deductively means testing these theories. Remember that if there is no theory yet, you cannot conduct deductive research.

The deductive research approach consists of four stages:

• If passengers fly with a low cost airline, then they will always experience delays
• All pet dogs in my apartment building have fleas
• All land mammals depend on water to exist
• Collect flight data of low-cost airlines
• Test all dogs in the building for fleas
• Study all land mammal species to see if they depend on water
• 5 out of 100 flights of low-cost airlines are not delayed
• 10 out of 20 dogs didn’t have fleas
• All land mammal species depend on water
• 5 out of 100 flights of low-cost airlines are not delayed = reject hypothesis
• 10 out of 20 dogs didn’t have fleas = reject hypothesis
• All land mammal species depend on water = support hypothesis

Limitations of a deductive approach

The conclusions of deductive reasoning can only be true if all the premises set in the inductive study are true and the terms are clear.

• All dogs have fleas (premise)
• Benno is a dog (premise)
• Benno has fleas (conclusion)

Many scientists conducting a larger research project begin with an inductive study. This helps them develop a relevant research topic and construct a strong working theory. The inductive study is followed up with deductive research to confirm or invalidate the conclusion. This can help you formulate a more structured project, and better mitigate the risk of research bias creeping into your work.

Remember that both inductive and deductive approaches are at risk for research biases, particularly confirmation bias and cognitive bias , so it’s important to be aware while you conduct your research.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Chi square goodness of fit test
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Inclusion and exclusion criteria

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

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Inductive reasoning is a bottom-up approach, while deductive reasoning is top-down.

Inductive reasoning takes you from the specific to the general, while in deductive reasoning, you make inferences by going from general premises to specific conclusions.

Inductive reasoning is a method of drawing conclusions by going from the specific to the general. It’s usually contrasted with deductive reasoning, where you proceed from general information to specific conclusions.

Inductive reasoning is also called inductive logic or bottom-up reasoning.

Deductive reasoning is a logical approach where you progress from general ideas to specific conclusions. It’s often contrasted with inductive reasoning , where you start with specific observations and form general conclusions.

Deductive reasoning is also called deductive logic.

Exploratory research aims to explore the main aspects of an under-researched problem, while explanatory research aims to explain the causes and consequences of a well-defined problem.

Explanatory research is used to investigate how or why a phenomenon occurs. Therefore, this type of research is often one of the first stages in the research process , serving as a jumping-off point for future research.

Exploratory research is often used when the issue you’re studying is new or when the data collection process is challenging for some reason.

You can use exploratory research if you have a general idea or a specific question that you want to study but there is no preexisting knowledge or paradigm with which to study it.

A research project is an academic, scientific, or professional undertaking to answer a research question . Research projects can take many forms, such as qualitative or quantitative , descriptive , longitudinal , experimental , or correlational . What kind of research approach you choose will depend on your topic.

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Statistical Learning Theory and Induction

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Nondeductive reasoning ; Pattern classification ; Pattern recognition ; Supervised learning

Induction is here taken to be a kind of reasoning from premises that may not guarantee the truth of the conclusion drawn from those premises. It is to be distinguished from “mathematical induction” which is a kind of deductive reasoning. The philosophical problem of induction is whether and how inductive reasoning can be justified.

Statistical learning theory (SLT) is a mathematical theory of a certain type of inductive reasoning involving learning from examples. SLT makes relatively minimal assumptions about an assumed background probability distribution responsible for connections between features of examples and their correct classification, the probability that particular examples will occur, etc. The theory seeks to describe various learning methods and say how well they can be expected to do at producing rules with minimum expected error on new cases.

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Devroye, L., Györfi, L., & Lugosi, G. A. (1996). Probabilistic theory of pattern recognition . New York: Springer.

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Harman, G., & Kulkarni, S. (2007). Reliable reasoning: Induction and statistical learning theory . Cambridge, MA: MIT Press.

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Inductive bias is the set of assumptions and constraints that affect the generalization ability of machine learning models. Learn about the different types of inductive biases in traditional and deep learning, such as Bayesian models, k-NN, linear regression, convolutional layers, and more. Inductive Learning Algorithm Learn about Inductive Learning Algorithm (ILA), a machine learning method that generates classification rules from examples. ILA is different from decision tree-based algorithms in that it produces general rules instead of specific ones. PDF Motivation Inductive Learning (1/2) Inductive Learning Scheme Hypothesis space H {[CONCEPT(x) ⇔S(A,B, …)]} Training set D Inductive hypothesis h 17 Size of Hypothesis Space n observable predicates 2n entries in truth table defining CONCEPT and each entry can be filled with True or False In the absence of any restriction Inductive reasoning Inductive reasoning is a method of deriving generalizations or principles from observations. Learn about the types, examples, and fallacies of inductive reasoning, such as generalization, prediction, analogy, and causal inference. Definition h: one hypothesis, h: X → { 0, 1 }, the goal is to find h such that h(x) = c(x) for all x in X; 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. Definition PDF Concept Learning Learning Chapter 2 Concept Learning 22 Inductive Bias Consider - concept learning algorithm L - instances X, target concept c - training examples Dc={<x,c(x)>} -let L(xi,Dc) denote the classification assigned to the instance xi by L after training on data Dc. Definition: The inductive bias of L is any minimal set of assertions B PDF The Many Faces of Inductive Teaching and Learning By Michael Prince and ing the terms problem-based learning, project-based learning, and discovery learning to refer to instruction that has the defining characteristics of those methods, and use inquiry-based learning as an umbrella category for any other inductive approach. Discovery learning In discovery learning, students are confronted with a challenge and left Inductive vs. Deductive Research Approach Inductive reasoning is a method of developing a theory from specific observations. Learn how it works, its limitations and how it differs from deductive reasoning. Statistical Learning Theory and Induction The philosophical problem of induction is whether and how inductive reasoning can be justified. Statistical learning theory (SLT) is a mathematical theory of a certain type of inductive reasoning involving learning from examples. SLT makes relatively minimal assumptions about an assumed background probability distribution responsible for ... Inductive reasoning 2.0 Graphical Abstract. Inductive reasoning is projecting from what we know to make inferences about what we do not know. This review describes key inductive phenomena and theories. It highlights the latest trends in induction research including the role of sampling processes, and the relations between induction and deduction, memory, and decision ... Inductive Learning Hypothesis Inductive Learning Hypothesis. 6.034 Artificial Intelligence - Recitations, fall 2004 online slides on learning : ... 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. ... assignment essay homework paper phd report resume review speech thesis