hypothesis space and inductive bias

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Hypothesis in Machine Learning

The concept of a hypothesis is fundamental in Machine Learning and data science endeavours. In the realm of machine learning, a hypothesis serves as an initial assumption made by data scientists and ML professionals when attempting to address a problem. Machine learning involves conducting experiments based on past experiences, and these hypotheses are crucial in formulating potential solutions.

It’s important to note that in machine learning discussions, the terms “hypothesis” and “model” are sometimes used interchangeably. However, a hypothesis represents an assumption, while a model is a mathematical representation employed to test that hypothesis. This section on “Hypothesis in Machine Learning” explores key aspects related to hypotheses in machine learning and their significance.

Table of Content

How does a Hypothesis work?

Hypothesis space and representation in machine learning, hypothesis in statistics, faqs on hypothesis in machine learning.

A hypothesis in machine learning is the model’s presumption regarding the connection between the input features and the result. It is an illustration of the mapping function that the algorithm is attempting to discover using the training set. To minimize the discrepancy between the expected and actual outputs, the learning process involves modifying the weights that parameterize the hypothesis. The objective is to optimize the model’s parameters to achieve the best predictive performance on new, unseen data, and a cost function is used to assess the hypothesis’ accuracy.

In most supervised machine learning algorithms, our main goal is to find a possible hypothesis from the hypothesis space that could map out the inputs to the proper outputs. The following figure shows the common method to find out the possible hypothesis from the Hypothesis space:

Hypothesis Space (H)

Hypothesis space is the set of all the possible legal hypothesis. This is the set from which the machine learning algorithm would determine the best possible (only one) which would best describe the target function or the outputs.

Hypothesis (h)

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:

• m = slope of the lines
• b = intercept

To better understand the Hypothesis Space and Hypothesis consider the following coordinate that shows the distribution of some data:

Say suppose we have test data for which we have to determine the outputs or results. The test data is as shown below:

We can predict the outcomes by dividing the coordinate as shown below:

So the test data would yield the following result:

But note here that we could have divided the coordinate plane as:

The way in which the coordinate would be divided depends on the data, algorithm and constraints.

• All these legal possible ways in which we can divide the coordinate plane to predict the outcome of the test data composes of the Hypothesis Space.
• Each individual possible way is known as the hypothesis.

Hence, in this example the hypothesis space would be like:

The hypothesis space comprises all possible legal hypotheses that a machine learning algorithm can consider. Hypotheses are formulated based on various algorithms and techniques, including linear regression, decision trees, and neural networks. These hypotheses capture the mapping function transforming input data into predictions.

Hypothesis Formulation and Representation in Machine Learning

Hypotheses in machine learning are formulated based on various algorithms and techniques, each with its representation. For example:

In the case of complex models like neural networks, the hypothesis may involve multiple layers of interconnected nodes, each performing a specific computation.

Hypothesis Evaluation:

The process of machine learning involves not only formulating hypotheses but also evaluating their performance. This evaluation is typically done using a loss function or an evaluation metric that quantifies the disparity between predicted outputs and ground truth labels. Common evaluation metrics include mean squared error (MSE), accuracy, precision, recall, F1-score, and others. By comparing the predictions of the hypothesis with the actual outcomes on a validation or test dataset, one can assess the effectiveness of the model.

Hypothesis Testing and Generalization:

Once a hypothesis is formulated and evaluated, the next step is to test its generalization capabilities. Generalization refers to the ability of a model to make accurate predictions on unseen data. A hypothesis that performs well on the training dataset but fails to generalize to new instances is said to suffer from overfitting. Conversely, a hypothesis that generalizes well to unseen data is deemed robust and reliable.

The process of hypothesis formulation, evaluation, testing, and generalization is often iterative in nature. It involves refining the hypothesis based on insights gained from model performance, feature importance, and domain knowledge. Techniques such as hyperparameter tuning, feature engineering, and model selection play a crucial role in this iterative refinement process.

In statistics , a hypothesis refers to a statement or assumption about a population parameter. It is a proposition or educated guess that helps guide statistical analyses. There are two types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha).

• Null Hypothesis(H 0 ): This hypothesis suggests that there is no significant difference or effect, and any observed results are due to chance. It often represents the status quo or a baseline assumption.
• Aternative Hypothesis(H 1 or H a ): This hypothesis contradicts the null hypothesis, proposing that there is a significant difference or effect in the population. It is what researchers aim to support with evidence.

Q. How does the training process use the hypothesis?

The learning algorithm uses the hypothesis as a guide to minimise the discrepancy between expected and actual outputs by adjusting its parameters during training.

Q. How is the hypothesis’s accuracy assessed?

Usually, a cost function that calculates the difference between expected and actual values is used to assess accuracy. Optimising the model to reduce this expense is the aim.

Q. What is Hypothesis testing?

Hypothesis testing is a statistical method for determining whether or not a hypothesis is correct. The hypothesis can be about two variables in a dataset, about an association between two groups, or about a situation.

Q. What distinguishes the null hypothesis from the alternative hypothesis in machine learning experiments?

The null hypothesis (H0) assumes no significant effect, while the alternative hypothesis (H1 or Ha) contradicts H0, suggesting a meaningful impact. Statistical testing is employed to decide between these hypotheses.

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Introduction to machine learning.

Introduction to Machine Learning. Instructor: Prof. Sudeshna Sarkar, Department of Computer Science and Engineering, IIT Kharagpur. This course provides a concise introduction to the fundamental concepts in machine learning and popular machine learning algorithms. We will cover the standard and most popular supervised learning algorithms including linear regression, logistic regression, decision trees, k-nearest neighbour, an introduction to Bayesian learning and the naive Bayes algorithm, support vector machines and kernels and neural networks with an introduction to Deep Learning. We will also cover the basic clustering algorithms. Feature reduction methods will also be discussed. We will introduce the basics of computational learning theory. In the course we will discuss various issues related to the application of machine learning algorithms. We will discuss hypothesis space, overfitting, bias and variance, tradeoffs between representational power and learnability, evaluation strategies and cross-validation. The course will be accompanied by hands-on problem solving with programming in Python and some tutorial sessions. (from nptel.ac.in )

This lecture describes Hypothesis Space and Inductive Bias. Inductive learning has been explained. Notions of Restriction and Preference have also been introduced in the context of Inductive Bias. Finally the lecture introduces the concept of generalization of a learned model and its connection with overfitting and underfitting.

Go to the Course Home or watch other lectures:

Inductive Bias in Machine Learning

The phrase “inductive bias” refers to a collection of (explicit or implicit) assumptions made by a learning algorithm in order to conduct induction, or generalize a limited set of observations (training data) into a general model of the domain. 

In this article, we’ll have a look at what is Inductive Bias, and how does it help the machine make better decisions.

Why Inductive Bias? 

As seen in the previous article on Candidate-Elimination Algorithm, we get two hypotheses, one specific and one general at the end as a final solution. 

Now, we also need to check if the hypothesis we got from the algorithm is actually correct or not, also make decisions like what training examples should the machine learn next. 

Some of the fundamental questions for inductive reference are, 

• What happens if the target concept isn’t in the hypothesis space?
• Is it possible to avoid this problem by adopting a hypothesis space that contains all potential hypotheses?
• What effect does the size of the hypothesis space have on the algorithm’s capacity to generalize to unseen instances?
• What effect does the size of the hypothesis space have on the number of training instances required?

Let’s have a look at what is Inductive and Deductive learning to understand more about Inductive Bias. 

Inductive Learning: 

This basically means learning from examples, learning on the go. 

We are given input samples (x) and output samples (f(x)) in the context of inductive learning, and the objective is to estimate the function (f). The goal is to generalize from the samples and map such that the output may be estimated for fresh samples in the future.

In practice, estimating the function is nearly always too difficult, thus we seek extremely excellent estimates of the function.

The following are some instances of induction in practice:

Assessment of credit risk: 

The x represents the customer’s properties.

Whether or whether the f(x) has been accepted for credit.

The diagnosis of disease:

The x represents the patient’s characteristics.

The f(x) is the illness they are afflicted with.

Face recognition: is a technique for recognizing someone’s face.

Bitmaps of people’s faces make up the x.

The f(x) is used to give the face a name.

Deductive Learning: 

Learners are initially exposed to concepts and generalizations, followed by particular examples and exercises to aid learning.

Already existing rules are applied to the training examples. 

Biased Hypothesis Space: 

It does not include all types of training instances. The issue is that we have skewed the learner’s thinking to only evaluate conjunctive possibilities. In this instance, a more expressive hypothesis space is required.

Unbiased Hypothesis Space: 

The obvious answer to the challenge of ensuring that the target idea is represented in hypothesis space H is to create a hypothesis space that can represent any teachable notion.

What is Inductive Bias?

As discussed in the introduction, Inductive bias refers to a set of assumptions made by a learning algorithm in order to conduct induction or generalize a limited set of observations (training data) into a general model of the domain. 

Induction would be impossible without such a bias, because observations may generally be extended in a variety of ways. 

Predictions for new scenarios could not be formed if all of these options were treated equally, that is, without any bias in the sense of a preference for certain forms of generalization (representing previous information about the target function to be learned).

The idea of inductive bias is to let the learner generalize beyond the observed training examples to deduce new examples. 

‘ > ’ -> Inductively inferred from.

For example, 

x > y means y is inductively deduced from x. 

Types of Inductive Bias: 

• Maximum conditional independence: It aims to maximize conditional independence if the hypothesis can be put in a Bayesian framework. The Naive Bayes classifier employs this bias.
• Minimum cross-validation error: Select the hypothesis with the lowest cross-validation error when deciding between hypotheses. Despite the fact that cross-validation appears to be bias-free, the “no free lunch” theorems prove that cross-validation is biased.
• Maximum margin: While creating a border between two classes, try to make the boundary as wide as possible. In support vector machines, this is the bias. The idea is that distinct classes are usually separated by large gaps.
• Minimum hypothesis description length: When constructing a hypothesis, try to keep the description as short as possible. Simpler theories are seen to be more likely to be correct. Occam’s razor does not suggest this. Simpler models are easier to test, not necessarily “more likely to be true.” See the principle of Occam’s Razor.
• Minimum features: features should be removed unless there is strong evidence that they are helpful. Feature selection methods are based on this premise.
• Nearest neighbors: Assume that the majority of the examples in a local neighborhood in feature space are from the same class.

If the class of a case is unknown, assume that it belongs to the same class as the majority of the people in its near vicinity. The k-nearest neighbor’s algorithm employs this bias. Cases that are close to each other are assumed to belong to the same class.

What is Inductive Bias in Machine Learning?

• February 22, 2024
• General , Supervised Learning

As I’m sure you know, Machine learning is the process by which a computer system can learn from past events to recognize patterns to predict the future.

With this comes some dense math and some exciting concepts.

In machine learning, there is this idea called inductive bias, which is the ability of your algorithm to generalize beyond the observed training examples to handle unseen data.

This guide will take you on a journey to explain the “why.” – why machines approach generalizability in this way and how you can use it in your algorithms to improve your predictions.

After reading this quick 3-minute guide, you’ll learn the following:

• What Inductive Bias is all about
• Why We Need Inductive Bias In Machine Learning
• A Quick Recap on Inductive Learning and Deductive Learning
• Overview of the Biased Hypothesis Space and the Unbiased Hypothesis Space
• And some terminology cleanup on Machine Learning Bias vs. Inductive Bias

Let’s do this!

What is Inductive Bias?

Inductive bias is simply the ability of your machine learning algorithms to generalize beyond the observed training examples to handle unseen data.

Why Do We Need Inductive Bias In Machine Learning?

In machine learning, to create our models, we build systems that can make assumptions about the world based on the data we give.

It wouldn’t be very helpful if we had a machine learning algorithm that could only make predictions on data it had already seen.

Think about it this way; if you wanted to predict fraud in real-time, and you could only predict fraud in situations you’ve seen before, you’d miss most new fraud cases.

What if the company has released a new store or a bank has released a new credit card that your algorithm hasn’t seen before?

Without an inductive bias, it would be impossible to learn from data because there would be no way to generalize.

Where did the Idea of Inductive Bias Come From?

At its core, machine learning is all about math.

After all, computers aren’t smarter than you or me; they just can process (do math) at highly efficient rates.

Inductive bias is part of the recipe that makes up the core of machine learning, which leverages some core ideas to achieve both practicality, accuracy, and computational efficiency.

While that sentence is a little weird, let me introduce you to 4 topics that will help me guide you through the path of fully understanding the role of inductive bias in machine learning.

What is Inductive Learning?

In everyday life, you often learn by example.

For instance, we might see someone else order food at a restaurant and then imitate their behavior when it’s our turn.

This type of learning is called inductive learning, a powerful way to quickly acquire new skills.

When we observe others, we can pick up on the important cues and “rules” that govern their behavior.

By imitating these examples, we learn the correct way to do things without explicitly being taught.

Inductive learning is instrumental when we encounter situations similar to those we’ve been in before, as we subconsciously apply our previous knowledge to the current scenario.

What is Deductive Learning

Deductive learning is a method of reasoning where you start with a general principle and then apply it to a specific situation.

This differs from inductive learning, where you’re deriving the rules yourself.

In deductive learning, the rules are already laid out, and now we apply them to our unique scenario.

For example, let’s say you want to learn how to bake a cake.

You open an old cookbook and find some recipes about baking all different types of cake.

You read all of these, go into your cabinet, and piece together some different recipes to make a wonderful cake.

In other words, deductive learning is a way of moving from general to specific.

It’s an efficient way to learn new information because it lets you focus on the task without getting bogged down in details.

What is 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.

What is the Unbiased Hypothesis Space?

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.

Bringing it all together, inductive bias in machine learning

Now that we know the difference between inductive and deductive learning and the positives and negatives of our hypothesis space, we can fully grasp what inductive bias is and how these all play a role in the core of machine learning.

As we said earlier, inductive bias is the ability of our algorithm to generalize beyond the observed training examples to infer new examples.

Since we do not have the “rules” already laid out (like in deductive learning), our algorithm has to create them (inductive learning).

Our algorithm can’t just depend on the training examples to make predictions (biased hypothesis space) since our accuracy would plummet on anything outside our space.

Our algorithm also can’t take every possible instance since we lack the scale and data access to make this feasible.

Our algorithm then has to generalize past the training examples, creating rules to apply to your predictions (inductive bias).

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