Statistical Techniques in ML

Statistical concepts and approaches are critical for success in machine learning projects from data collection to model evaluation. This guide systematically prepares ML interview candidates for statistical coding challenges through practical implementations, focusing on common interview requirements and implementation pitfalls. We emphasize computational efficiency, numerical stability, and interpretation skills needed for real-world ML systems.

Core Knowledge

Probability Foundations
- • Basic Probability
- • Essential Probability Distributions
- • Multivariate Analysis
Statistical Computations
- • Distribution Properties
- • Efficient Algorithms
Hypothesis Testing
- • Test Selection Criteria
- • Critical Implementations
ML-Specific Statistics
- • Model Diagnostics
- • Evaluation Metrics

Key Questions

Status	Question	Category
	Implement Numerically Stable Descriptive Statistics	Statistical Techniques in ML
	Compute Confidence Intervals for ML Evaluation Results Using Bootstrap	Statistical Techniques in ML
	Hypothesis Test Framework with Error Rate Tracking	Statistical Techniques in ML
	Optimized Correlation Matrix Computation	Statistical Techniques in ML
	Implement χ² Test for Categorical Feature Analysis	Statistical Techniques in ML
	Multicollinearity Detector Using Variance Inflation Factor (VIF)	Statistical Techniques in ML
	Permutation Test for Model Comparison	Statistical Techniques in ML
	Streaming Data Statistics: Exponential Moving Average and Rolling Variance	Statistical Techniques in ML

Common Pitfalls

Extended Questions

Status	Question	Category
	Confidence Intervals with Multi-Threaded Bootstrap Resampling	Scalable Implementations
	Sparse Matrix Correlation Computation	Scalable Implementations
	Bayesian A/B Testing Implementation	Advanced Methods
	Regularized Correlation Matrices	Advanced Methods

Applications of Stats in ML

Model Validation
- Confidence intervals for classification metrics
- Statistical significance of model improvements
Feature Engineering
- Correlation analysis for feature selection
- Multicollinearity detection in linear models
Experimentation
- A/B test power analysis implementation
- Causal impact estimation in observation

Statistical Techniques in ML

Core Knowledge

Probability Foundations

Statistical Computations

Hypothesis Testing

ML-Specific Statistics

Key Questions

Common Pitfalls

Population vs sample variance confusion

Floating-point errors in iterative calculations

Incorrect degrees of freedom in test statistics

Normality assumption violations in parametric tests

Mishandling of tied ranks in Spearman correlation

Categorical encoding errors in χ² tests

p-value misinterpretation in multiple testing

Edge case failures (zero variance, small samples)

Extended Questions

Applications of Stats in ML

Core Knowledge

Probability Foundations

◦ Discrete/continuous random variables

◦ PMF/PDF and CDF relationships

◦ Convergence concepts (LLN, CLT)

◦ Gaussian, Binomial, Poisson properties

◦ Exponential vs Uniform use cases

◦ Hypothesis testing distributions (t, χ²)

◦ Joint/conditional probability handling

◦ Covariance matrix properties

◦ Correlation pitfalls in ML features

Statistical Computations

◦ Robust variance calculation (Bessel's correction)

◦ Moment-based skewness/kurtosis

◦ Quantile estimation methods

◦ Welford's online variance algorithm

◦ Streaming median approximation

◦ Log-space probability calculations

Hypothesis Testing

◦ Parametric vs non-parametric conditions

◦ Sample size considerations

◦ Multiple comparison corrections

◦ t-test variants (one-sample, paired, Welch's)

◦ ANOVA F-value computation

◦ Chi-square test for feature selection

ML-Specific Statistics

◦ Variance Inflation Factor (VIF) implementation

◦ Heteroscedasticity detection

◦ QQ-plot interpretation

◦ Confidence intervals for performance metrics

◦ Bootstrapped error estimates

◦ Correlation matrix optimization

Key Questions

Common Pitfalls

Population vs sample variance confusion

Floating-point errors in iterative calculations

Incorrect degrees of freedom in test statistics

Normality assumption violations in parametric tests

Mishandling of tied ranks in Spearman correlation

Categorical encoding errors in χ² tests

p-value misinterpretation in multiple testing

Edge case failures (zero variance, small samples)

Extended Questions

Applications of Stats in ML