Statistical inference is the backbone of machine learning and data science. It provides methods to draw conclusions from data and quantify uncertainty in predictions, playing a crucial role in various ML applications.
Feature selection techniques help identify the most relevant variables for modeling. From filter methods using correlation tests to wrapper methods like recursive feature elimination, these approaches optimize model performance and interpretability.
Statistical Foundations in Machine Learning and Data Science
Role of statistical inference
- Statistical inference forms backbone of ML and data science providing methods to draw conclusions from data and quantify uncertainty in predictions
- Key ML applications include hypothesis testing for model selection, confidence intervals for parameter estimation, and probabilistic modeling for predictive tasks
- Bayesian inference updates prior beliefs with observed data using probabilistic programming languages (PyMC, Stan)
- Frequentist inference employs maximum likelihood estimation and bootstrapping for uncertainty quantification
Techniques for feature selection
- Filter methods utilize correlation-based and chi-squared tests to select relevant features
- Wrapper methods like recursive feature elimination iteratively remove features to find optimal subset
- Embedded methods such as LASSO and Ridge regression incorporate feature selection into model training process
- Cross-validation techniques (K-fold, leave-one-out, stratified) assess model performance on unseen data
- Statistical tests (paired t-test, ANOVA) compare model performances across different feature sets
- Information criteria (AIC, BIC) balance model fit and complexity for optimal feature selection
Overfitting vs underfitting
- Overfitting occurs when model learns noise in training data resulting in high variance, low bias, and poor generalization
- Underfitting happens when model fails to capture underlying patterns leading to low variance, high bias, and poor performance on both training and test data
- Bias-variance tradeoff balances model complexity with generalization ability
- Regularization techniques (L1, L2, Elastic Net) prevent overfitting by adding penalty terms to loss function
- Learning curves diagnose overfitting and underfitting by comparing training error vs validation error
- Confusion matrix components include true positives, true negatives, false positives, and false negatives
- Accuracy measures overall correctness of predictions: $(TP + TN) / (TP + TN + FP + FN)$
- Precision calculates proportion of correct positive predictions: $TP / (TP + FP)$
- Recall (Sensitivity) determines proportion of actual positives correctly identified: $TP / (TP + FN)$
- F1-score computes harmonic mean of precision and recall: $2 * (Precision * Recall) / (Precision + Recall)$
- ROC curve and AUC visualize tradeoff between true positive rate and false positive rate
- Specificity measures proportion of actual negatives correctly identified: $TN / (TN + FP)$