Statistics and Probability for Machine Learning

Essential statistical concepts and probability theory for machine learning applications

Core Concepts

1. Probability Theory

  • Probability distributions (Gaussian, Bernoulli, Poisson)
  • Conditional probability and Bayes' theorem
  • Random variables and expectations
  • Joint and marginal distributions
  • Applications in Bayesian inference and probabilistic models

2. Statistical Inference

  • Hypothesis testing
  • Confidence intervals
  • Maximum Likelihood Estimation (MLE)
  • Bayesian inference
  • Applications in model evaluation and validation

3. Descriptive Statistics

  • Measures of central tendency (mean, median, mode)
  • Measures of dispersion (variance, standard deviation)
  • Correlation and covariance
  • Skewness and kurtosis
  • Applications in data preprocessing and feature engineering

4. Statistical Learning

  • Bias-variance tradeoff
  • Cross-validation
  • Resampling methods
  • Statistical significance in ML
  • Applications in model selection and evaluation

Practical Applications

  • Model uncertainty quantification
  • Anomaly detection
  • Statistical hypothesis testing in ML
  • Probabilistic programming
  • Bayesian neural networks
  • Statistical significance in feature selection