Uncertainty Quantification Bayesian Deep Learning is methods estimating prediction uncertainty, distinguishing between epistemic (model) uncertainty and aleatoric (data) uncertainty, enabling confident predictions and risk quantification — essential for safety-critical applications. Uncertainty crucial for decision-making. Epistemic Uncertainty model uncertainty: given observed data, uncertainty about true parameters. Reduces with more data. Comes from limited training data. Aleatoric Uncertainty data uncertainty: irreducible noise in observations. Examples: measurement noise, inherent randomness. Cannot reduce with more data. Bayesian Neural Networks place probability distributions over weights rather than point estimates. Predictions are distributions, not scalars. Variational Inference approximate posterior over weights with variational distribution q(w). Optimize KL divergence between q and true posterior p(w|data). Computationally efficient. Monte Carlo Dropout Bayesian interpretation of dropout: different dropout masks correspond to samples from approximate posterior. Multiple forward passes with dropout provide uncertainty. Uncertainty in Layers different layers contribute differently to uncertainty. Analyze layer-wise contributions. Predictive Posterior p(y|x, data) = ∫ p(y|x,w) p(w|data) dw. Integral over parameter distribution. Approximated via sampling. Calibration model calibration: predicted uncertainty matches empirical error. Well-calibrated model's 90% confidence predictions correct 90% of time. Overconfidence neural networks often overconfident (predictions poorly calibrated). Temperature scaling: divide logits by learnable temperature. Adversarial Examples and Uncertainty adversarial examples often high-confidence incorrect predictions. Uncertainty estimation detects some (but not all) adversarial examples. Out-of-Distribution Detection uncertain predictions on out-of-distribution inputs. Separate epistemic uncertainty (OOD) from aleatoric (test distribution). Laplace Approximation approximate posterior with Gaussian around MAP estimate. Second-order Taylor expansion of log posterior. Deep Ensembles train multiple models, predictions averaged. Disagreement among ensemble measures uncertainty. Approximates Bayesian averaging. Heteroscedastic Regression aleatoric uncertainty: output distribution variance alongside mean. Network predicts both μ and σ. Selective Prediction models abstain on uncertain predictions. Improves reliability by ignoring uncertain cases. Uncertainty for Active Learning select most uncertain examples for labeling. Reduces annotation cost. Reinforcement Learning Uncertainty uncertainty in Q-learning, policy gradients. Exploration-exploitation tradeoff. Uncertainty-driven exploration. Risk-Sensitive Decisions use uncertainty for risk-aware decisions. Medical diagnosis: high uncertainty → require more tests. Information Theory and Entropy entropy of prediction: high entropy = high uncertainty. Mutual information: epistemic information. Bayesian Optimization select next point to evaluate minimizing posterior uncertainty of optimum. Acquisition functions (expected improvement, uncertainty-based). Neural Network Approximations sampling-based (Monte Carlo Dropout, deep ensembles) vs. parametric (variational inference). Trade-offs: accuracy vs. computational cost. Applications autonomous driving (uncertain predictions trigger caution), medical diagnosis (uncertain predictions need review), exploration in RL. Benchmarks and Evaluation metrics: calibration error, Brier score, negative log-likelihood. Scalability Challenges uncertainty estimation adds computational cost. Sampling multiple models/forward passes. Uncertainty Quantification is increasingly important for deploying AI systems in high-stakes settings.