Statistical Learning & Supervised Machine Learning

Agenda

• The topics are course introduction and supervised machine learning.

Book

• "An Introduction to Statistical Learning with Applications in Python" is the recommended book.
• The book is available at https://www.statlearning.com/.

Course Tour

• Includes syllabus, course site, course outline, and Data Camp.

Learning from Data

• A learning algorithm detects patterns, builds rules, and creates a model.
• Learning involves small, iterative adjustments.
• A learned model represents a decision boundary.

Trial and Error

• Machine learning can be achieved through trial and error.

Machine Learning

• Arthur Samuel (1959) defined machine learning as the field of study that gives computers the ability to learn without being explicitly programmed.
• Herb Simon (1978) defined machine learning as being concerned with computer programs that automatically improve their performance through experience.
• Tom Mitchell (1997) stated that a computer program learns from experience E with respect to a task T and performance measure P if performance on T, measured by P, improves with experience E.

Artificial Intelligence

• Alan Turing (1950) explored the question, "Can machines think?"
• The Turing Test involves a conversation through typed notes with a physical barrier.
• If you can't tell if you are talking with a human or a machine, the machine passes the Turing test, meaning it is intelligent.
• The 1956 Dartmouth Conference is considered the founding of AI.

AI Advances

• AI outperforms doctor diagnoses (2024).
• Chat GPT 4.0 passes law and business school exams (2023).
• IBM Watson defeated Ken Jennings in Jeopardy (2011).
• AlphaGo beat Lee Sedol in Go (2016).
• Arthur Samuel created a checkers program in 1959. Garry Kasporov vs Deep Blue Chess was in 1997.

Why Now

• More data, increased computational power, progress on algorithms/theory/tools, and accessible computing are all reasons why now is a good time for AI.

Categories of Machine Learning

• Supervised learning involves labeled data, direct feedback, and predicting outcomes/future.
• Unsupervised learning has no labels/targets or feedback, aiming to find hidden structure in data.
• Reinforcement learning uses a decision process, reward system, and learns a series of actions.

Supervised Machine Learning

• In regression tasks, the output is a continuous variable.
• In classification tasks, the output is a discrete variable.
• Supervised machine learning estimates a function (f) from training examples to capture the relationship between inputs and outputs.
• A learning algorithm infers a function (f) to predict the output (ŷ) accurately given new inputs.
• Algorithms learn to predict output given input by observing training examples in <input, output> pairs.
• Algorithm performance is measured by how well the model predicts outcomes on test examples.
• The goal is for the model to perform well on new, unseen examples, known as generalization.
• Training examples learn relationships between input (X) and output (Y) variables.

Binary Classification

• Many predictive problems are framed as binary classification problems.
• Examples include predicting customer churn if the price of oil drops, unit failure in the next 30 days, construction site running out of fuel, fraudulent transactions, and pneumonia detection from X-rays.

Evaluating Regression Model

• For continuous output, quality is measured by mean squared error (MSE).
• MSE = (1/n) * Σ(yi - ŷi)², where ŷi is the predicted value for observation i.
• Quality of a continuous model is determined by prediction error.
• The evaluation should be based on test samples not used for training.

Regression Model Overfitting

• One can hypothesize that Y is a fourth-degree polynomial function of X.
• Estimate the coefficients for the polynomial curve that best fits the training observations.
• The estimated curve is used to predict values for Y in the test examples.
• A straight line does a better job with test examples even if a polynomial fits training examples well.
• Occam's razor suggests using the simplest model that does a good enough job.

Bias Variance Tradeoff

• Simpler models struggle to detect relationships between input features and prediction labels and have high bias, low variance, and underfitting.
• Complex models are sensitive to noise and may not generalize well to new unseen examples, with low bias, high variance, and overfitting.

Evaluating a Classification Model

• For classification problems, model quality is measured by correctly classified observations (accuracy) and the expected cost of misclassification (confusion matrix).
• Accuracy = Correct Predictions / Total Observations
• It is more useful to evaluate model accuracy on the test set rather than the training set.
• Test accuracy indicates the ability of the model to generalize to new unseen examples.
• Accuracy can be a misleading measure for imbalanced datasets.
• Sensitivity = True Positive rate (same as Recall)
• Specificity = TN / (FP+TN) (True Negative Rate)
• ROC curves plot True Positive Rate (TPR) against False Positive Rate (FPR).
• Classifiers predict the probability (p) an observation is in the positive class; observations are rated as positive if p > t for some threshold t.
• Area under the ROC curve serves as a measure of accuracy when data is imbalanced.
• ROC curves select a threshold t that minimizes the expected cost of error, given relative costs of False Positive and False Negative.

Training and Prediction

• Split data into X_train, y_train, X_test, and y_test using splitData(X, y).
• Create the model with model = modelName(parameters).
• Train the model with model.fit(X_train, y_train).
  • x_train are the training examples and y_train are the outputs for the training examples
• Predict using the trained model on test examples using y_predicted = model.predict(X_test).
  • x_test are the inputs for prediction
• Check the accuracy of the trained model on the test examples with accuracy_score(y_test, y_predicted).
  • y_test are for correct outputs for prediction examples