Inductive bias is the set of assumptions that a learning algorithm makes to generalize from a finite set of training examples to unseen instances. It is essential for any learning algorithm to have some form of inductive bias, otherwise it would not be able to make any predictions beyond the observed data.

One of the most popular and influential learning algorithms is ID3, which stands for Iterative Dichotomiser 3. ID3 is a greedy algorithm that constructs a decision tree from a set of labeled examples, by recursively choosing the best attribute to split the data according to some criterion. A decision tree is a graphical representation of a function that maps a set of input attributes to a discrete output value, such as a class label. Each node in the tree corresponds to a test on an attribute, and each branch corresponds to a possible value of that attribute. The leaf nodes represent the output values.

But how does ID3 choose the best attribute to split the data at each node? And what kind of inductive bias does it have? To answer these questions, we need to understand the concept of information gain, which is the measure that ID3 uses to evaluate the quality of an attribute. Information gain is based on the idea of entropy, which is a measure of the uncertainty or disorder in a set of examples. Entropy is calculated as the negative sum of the probabilities of each class multiplied by the logarithm of those probabilities. The lower the entropy, the more homogeneous the set of examples is. Information gain is defined as the difference between the entropy of the parent node and the weighted average of the entropies of the child nodes after splitting by an attribute. The higher the information gain, the more information the attribute provides about the output value, and the more the entropy is reduced.

ID3’s inductive bias is based on the ordering of hypotheses by its search strategy, which is to prefer the attribute that maximizes the information gain at each node. This means that ID3 prefers shorter trees over longer trees, and trees that place high information gain attributes close to the root over those that do not. This form of bias is typically called a preference bias or a search bias, because it does not restrict the hypothesis space, but rather guides the search towards certain regions of the space. ID3’s hypothesis space is the set of all possible decision trees, which is a very expressive and flexible space that can represent any finite discrete-valued function. However, this also means that ID3’s hypothesis space introduces no additional bias, and that ID3 can overfit the data if the tree grows too large or complex.

One of the limitations of ID3 is that it is biased to select attributes with more possible values, which are not necessarily the best attributes. This is because the information gain criterion tends to favor attributes that have a large number of distinct values, as they can create more partitions of the data and reduce the entropy more. However, this may lead to problems such as overfitting, where the tree becomes too specific to the training data and fails to generalize well to new data. For example, if an attribute has a unique value for each example, such as an ID number, then splitting by that attribute will result in a perfect information gain, but it will also create a leaf node for each example, which is useless for prediction.

To summarize, ID3 is a learning algorithm that constructs a decision tree from a set of labeled examples, by choosing the best attribute to split the data according to the information gain criterion. ID3’s inductive bias is to prefer shorter trees and high information gain attributes, which is a preference bias that follows from its search strategy. ID3’s hypothesis space is the set of all possible decision trees, which is a very expressive and flexible space that introduces no additional bias. ID3 is a simple and powerful algorithm, but it also has some limitations and challenges, such as handling continuous attributes, missing values, noisy data, and pruning the tree to avoid overfitting. These topics will be discussed in future blog posts.

Stay tuned!