Prediction Intervals and Ensemble Learning 30 Cases - English Technical Courses - 029-AI for CAE Simulation VVUQ & Geometric Deep Learning

Quantile Regression for Prediction Intervals

Implement quantile regression with a linear model to produce lower and upper prediction bounds at a specified coverage level, and verify empirical coverage on a held-out dataset.

QuantileRegression

02

Bootstrap Prediction Intervals for Regression

Generate prediction intervals via residual bootstrap and case bootstrap for a regression model, comparing interval width and coverage stability across resampling schemes.

BootstrapPrediction

03

Conformal Prediction with a Point Forecaster

Wrap a standard regression model with split conformal prediction to obtain distribution-free prediction intervals, and evaluate coverage and interval efficiency on calibration and test splits.

ConformalPrediction

04

Jackknife+ Prediction Intervals

Implement jackknife+ and jackknife+ after bootstrap for a regression model, and compare their finite-sample coverage guarantees against split conformal intervals.

Jackknife+Prediction

05

Cross-Conformal and CV+ Intervals

Build cross-conformal and CV+ prediction intervals using K-fold splits, and analyze the trade-off between computational cost, coverage, and interval width relative to split conformal.

Cross-ConformalCV+

06

Prediction Intervals for Time Series with Block Bootstrap

Construct prediction intervals for a time series forecast using block bootstrap to preserve autocorrelation, and validate coverage on rolling-origin evaluation.

PredictionIntervals

07

Quantile Regression Forest Prediction Intervals

Train a quantile regression forest to output conditional quantiles and derive prediction intervals, then assess coverage and sharpness against a linear quantile baseline.

QuantileRegression

08

Gradient Boosting with Quantile Loss for Interval Estimation

Fit gradient boosted trees with quantile loss at lower and upper quantile levels to form prediction intervals, and tune hyperparameters for coverage calibration.

GradientBoosting

09

Bootstrap Aggregating for Interval Width Reduction

Apply bagging to a high-variance base learner and measure how averaging reduces prediction interval width while maintaining nominal coverage.

BootstrapAggregating

10

Random Forest Prediction Intervals via Quantile Aggregation

Derive prediction intervals from random forest leaf distributions using quantile aggregation, and compare with split conformal intervals on the same forest.

PredictionIntervals

11

Ensemble of Quantile Regressors with Weighted Combination

Combine multiple quantile regression models via weighted ensembling to improve interval calibration, and optimize weights on a validation set for coverage and width.

EnsembleQuantile

12

Stacked Ensemble for Prediction Intervals

Build a stacked ensemble of heterogeneous regressors and generate prediction intervals from the stack, evaluating whether stacking improves interval efficiency over individual models.

EnsemblePrediction

13

Bayesian Model Averaging for Predictive Intervals

Implement Bayesian model averaging over a set of candidate regressors to produce predictive intervals, and compare posterior predictive coverage with frequentist conformal intervals.

BayesianAveraging

14

Ensemble Kalman Filter for State Prediction Intervals

Use an ensemble Kalman filter to forecast a dynamical system and derive prediction intervals from the ensemble spread, validating coverage against noisy observations.

EnsemblePrediction

15

Prediction Intervals for Neural Network Ensembles

Train a deep ensemble of neural networks and construct prediction intervals from ensemble variance, then calibrate intervals using a held-out set to achieve target coverage.

PredictionIntervals

16

Monte Carlo Dropout for Predictive Uncertainty Intervals

Generate prediction intervals via Monte Carlo dropout at inference time, and compare interval quality with deep ensembles under the same coverage target.

PredictiveUncertainty

17

Quantile Regression Neural Network for Interval Forecasting

Train a neural network with pinball loss to output conditional quantiles, and form prediction intervals that are evaluated for coverage and sharpness on a regression benchmark.

QuantileRegression

18

Conformalized Quantile Regression

Apply conformalized quantile regression to calibrate quantile regression intervals, and demonstrate improved coverage on heteroscedastic data compared to raw quantile intervals.

ConformalizedQuantile

19

Adaptive Conformal Inference for Distribution Shift

Implement adaptive conformal inference to maintain prediction interval coverage under distribution shift in a streaming setting, and track coverage over time.

AdaptiveConformal

20

Ensemble-Based Conformal Prediction with Out-of-Bag Calibration

Use out-of-bag predictions from a bagged ensemble as conformal calibration scores, and compare interval efficiency with split conformal using a separate calibration set.

Ensemble-BasedConformal

21

Prediction Interval Evaluation and Diagnostic Plots

Design and implement a suite of metrics and diagnostic plots (coverage, width, Winkler score, calibration curves) to compare prediction interval methods across multiple datasets.

PredictionInterval

22

Tuning Ensemble Size for Interval Stability

Systematically vary the number of ensemble members and measure the effect on prediction interval width variance and coverage stability, identifying a practical ensemble size.

EnsembleInterval

23

Hyperparameter Optimization for Interval Coverage

Perform hyperparameter search for an ensemble model with the objective of achieving nominal prediction interval coverage with minimal width on a validation set.

HyperparameterOptimization

24

Handling Heteroscedasticity with Ensemble Variance Scaling

Estimate input-dependent variance from an ensemble and scale prediction intervals accordingly, then validate improved conditional coverage on heteroscedastic data.

HandlingHeteroscedasticity

25

Prediction Intervals for Imbalanced Regression via Ensembles

Train an ensemble on imbalanced regression data and construct prediction intervals that maintain coverage across the target distribution, including rare extreme values.

PredictionIntervals

26

Ensemble Interval Estimation for Multi-Output Regression

Extend ensemble-based prediction intervals to multi-output regression, producing joint or marginal intervals and evaluating coverage per output dimension.

EnsembleInterval

27

Fault Detection in Ensemble Interval Coverage

Diagnose and debug an ensemble prediction interval system that exhibits undercoverage, by tracing calibration scores, ensemble diversity, and data leakage issues.

DetectionEnsemble

28

Comparing Interval Methods under Computational Budgets

Benchmark split conformal, CV+, jackknife+, and ensemble quantile methods under fixed time and memory budgets, and recommend a method based on coverage-width trade-offs.

ComparingInterval

29

Deploying a Prediction Interval Service with Ensemble Backend

Package an ensemble-based prediction interval model into a reproducible inference service, including calibration artifact storage and runtime interval generation with coverage monitoring.

DeployingPrediction

30

Case Study: End-to-End Ensemble Prediction Intervals for Energy Load Forecasting

Integrate ensemble learning, quantile calibration, and conformal methods into a complete pipeline for day-ahead load forecasting, and report interval performance against operational coverage requirements.

End-to-EndEnsemble