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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