Introduction to learning, hypothesis space and evaluation notes — Unit 1

Machine Learning (ML) is a subset of Artificial Intelligence that provides systems the ability to automatically learn and improve from experience without being explicitly programmed.

⇒1.1 Tom Mitchell's Formal Definition

A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at tasks in T, as measured by P, improves with experience E.

Example: Spam Filter

• Task (T): Classifying emails as spam or not spam.
• Experience (E): Observing a dataset of emails already labeled by users.
• Performance (P): The percentage of new emails correctly classified.

⇒2.1 Supervised Learning

The model is trained on a labeled dataset (data where the 'answer' is provided). The algorithm learns the mapping from inputs (X) to outputs (Y). Example: Predicting house prices based on historical sales.

⇒2.2 Unsupervised Learning

The model is provided with data that has no labels. The algorithm must find hidden patterns or groupings in the data itself. Example: Segmenting customers into groups based on purchasing behavior.

⇒2.3 Reinforcement Learning

An agent learns to make decisions by performing actions in an environment and receiving rewards or penalties. Example: Training a computer to play chess or autonomous driving.

When a machine learning algorithm is training, it is essentially searching for a mathematical function that best fits the data.

⇒3.1 What is a Hypothesis?

A hypothesis (h) is a single, specific mathematical function that maps inputs to outputs. For example, `y = 2x + 1` is one hypothesis.

⇒3.2 The Hypothesis Space (H)

The hypothesis space `H` is the set of all possible hypotheses that the algorithm is allowed to consider. The goal of the ML algorithm is to search through `H` to find the hypothesis that minimizes the error on the training data.

If an algorithm is perfectly unbiased, it cannot generalize to data it has never seen before. It will only memorize the training data.

⇒4.1 What is Inductive Bias?

The set of assumptions that the learning algorithm uses to predict outputs given inputs that it has not encountered. Without inductive bias, learning is impossible.

Example: Linear regression has a very strong inductive bias: it assumes that the relationship between the inputs and outputs is a straight line. If the true relationship is a curve, linear regression will fail (Underfitting).

⇒5.1 Underfitting (High Bias)

Occurs when the model is too simple to capture the underlying patterns in the data. (e.g., trying to fit a straight line to a U-shaped scatter plot). It performs poorly on both training and test data.

⇒5.2 Overfitting (High Variance)

Occurs when the model is too complex (too many parameters). It essentially memorizes the noise and random fluctuations in the training data, rather than the true pattern. It performs perfectly on training data, but terribly on new test data.

⇒5.3 The Sweet Spot

The goal is a model complex enough to capture the pattern, but simple enough to generalize. We control this using Regularization (penalizing complex models).

How do we know if our model is any good before deploying it to the real world? We cannot test it on the data it trained on, because of the risk of overfitting.

⇒6.1 Train / Test Split

We randomly divide the dataset into a Training Set (e.g., 80%) and a Testing Set (e.g., 20%). The model learns on the 80%, and is evaluated on the remaining 20% that it has never seen.

⇒6.2 K-Fold Cross Validation

A more robust method. The dataset is divided into `K` equal subsets (folds). The model is trained on `K-1` folds and tested on the remaining fold. This process is repeated `K` times, with each fold serving as the test set exactly once. The final score is the average of all `K` tests.

When predicting categories (e.g., Spam/Not Spam, Cancer/No Cancer), simple 'Accuracy' is often misleading. If 99% of emails are Not Spam, a model that blindly guesses 'Not Spam' is 99% accurate, but completely useless.

⇒7.1 The Confusion Matrix

• True Positives (TP): Predicted Spam, actually Spam.
• True Negatives (TN): Predicted Not Spam, actually Not Spam.
• False Positives (FP): Predicted Spam, actually Not Spam. (Type I Error).
• False Negatives (FN): Predicted Not Spam, actually Spam. (Type II Error).

• Precision: `TP / (TP + FP)`. Out of all the emails the model claimed were spam, what percentage actually were? (Crucial when false positives are costly, e.g., sending important emails to the spam folder).
• Recall (Sensitivity): `TP / (TP + FN)`. Out of all the actual spam emails in the dataset, what percentage did the model successfully find? (Crucial when false negatives are deadly, e.g., missing a cancer diagnosis).

⇒8.1 The Trade-off

There is always a trade-off between Precision and Recall. To balance them, we use the F1-Score, which is the harmonic mean of the two: `2 (Precision Recall) / (Precision + Recall)`.