🏞️ ML Analysis of Sediment Load: Advanced Uncertainty Quantification

A comprehensive machine learning framework designed to predict Suspended Sediment Load ($S_t$) in hydrological systems. This project moves beyond standard point predictions by implementing rigorous Uncertainty Quantification (UQ) workflows—specifically tailored for time-series data using Adaptive Conformal Prediction—ensuring that environmental engineering decisions are backed by statistical confidence.

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📑 Table of Contents (Navigation)

1. 📌 Project Overview
2. 📂 Repository Structure
3. 📊 Dataset Details
4. 🛠️ Workflow & Methodology
   • Phase 1: Hyperparameter Tuning
   • Phase 2: Quantile Regression
   • Phase 3: Probabilistic Distribution
   • Phase 4: Standard Conformal Predictions
   • Phase 5: Adaptive & Non-Exchangeable CP

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📌 Project Overview

Accurate sediment load prediction is vital for reservoir management and hydraulic design. This repository provides a robust pipeline for analyzing hydrometric data using advanced Machine Learning regressors. Key features include:

• Advanced Optimization: Automated hyperparameter tuning using Optuna with various pruners and samplers.
• Interval Estimation: Quantile Regression to estimate the range of probable sediment loads.
• Full Distribution Modeling: Using NGBoost and PGBM to predict the entire probability distribution of the target.
• Time-Series Uncertainty: Specialized NEXCP (Non-Exchangeable Conformal Prediction) and Adaptive CP methods to handle data drift and temporal dependencies, ensuring valid coverage even during extreme events.

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📂 Repository Structure

The project is organized into modular directories representing the analysis pipeline.

1. 🗂️ Data

Contains the hydrological time-series dataset.

• train.csv: Historical data with lagged features used for model training.
• test.csv: Held-out data for final model evaluation.

2. 🎛️ Hyperparameter Tuning

Before training UQ models, base regressors are optimized to minimize error.

• Optuna_autosampler_SEDIMENT.ipynb: Implements Bayesian Optimization via Optuna to find optimal parameters.
• Models/: Stores serialized (.pkl) model files (e.g., CatBoost_HyperbandPruner_BEST.pkl).
• test_results.xlsx: Detailed comparative scores of different pruners and samplers.

3. 📉 Quantile Regression

Focuses on predicting conditional quantiles (e.g., $Q_{0.05}$ and $Q_{0.95}$) rather than just the mean.

• Quantile_Regression_SEDIMENT.ipynb: Trains models to minimize Pinball Loss.
• Results/: Contains prediction files for XGBoost, LightGBM, CatBoost, HGBM, GPBoost, and PGBM.

4. 📊 Probabilistic Distribution

Treats the target variable as a distribution to capture aleatoric uncertainty.

• Probabilistic__Distribution_SEDIMENT.ipynb: Implements NGBoost and PGBM to output $\mu$ (mean) and $\sigma$ (standard deviation).
• Results/: Includes CRPS (Continuous Ranked Probability Score) metrics and Calibration plots.

5. 🛡️ Conformal Prediction (Standard & Adaptive)

Applies rigorous statistical calibration. This module is split into standard methods and advanced time-series methods.

• Conformal Predictions(MAPIE,PUNCC)_SEDIMENT.ipynb: Standard Split Conformal Prediction and CV+.
• Conformal_Predictions(NEXCP, Adaptive CP, mfcs)_SEDIMENT.ipynb: Implements NEXCP and Adaptive Conformal Prediction to handle distribution shifts in sediment data.

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📊 Dataset Details

The analysis is based on hydrometric time-series data containing current flow and historical lags:

Feature	Description	Role
Qt	Discharge (Flow) at current time $t$	Predictor
Qt-1	Discharge at previous time step $t-1$	Predictor (Lag)
St-1	Sediment Load at previous time step $t-1$	Predictor (Lag)
St	Target Variable: Sediment Load at time $t$	Target

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🛠️ Workflow & Methodology

Phase 1: Hyperparameter Tuning

We utilize Optuna to optimize regressors (XGBoost, CatBoost, etc.).

1. Search Space: Defined for Learning Rate, Depth, Regularization, and Estimators.
2. Pruning: Tested various pruners (Hyperband, Median, SuccessiveHalving) to efficiently discard unpromising trials.
3. Outcome: The best models are saved in the Models/ directory for subsequent UQ phases.

Phase 2: Quantile Regression

Standard regression predicts the conditional mean $E[Y|X]$. Quantile regression predicts $Q_\tau(Y|X)$.

• Application: We predict the 5th and 95th percentiles to create a 90% prediction interval.
• Metric: Pinball Loss (Quantile Loss).

Phase 3: Probabilistic Distribution

This approach assumes $Y|X \sim \mathcal{D}(\theta)$.

• Models: NGBoost (Natural Gradient Boosting) and PGBM.
• Analysis: Evaluates the probabilistic fit using NLL (Negative Log-Likelihood) and PIT (Probability Integral Transform) histograms to ensure the model is well-calibrated.

Phase 4: Standard Conformal Predictions

Uses libraries like MAPIE and PUNCC for exchangeable data.

• Methods: Jackknife+, CV+, and Split Conformal.
• Guarantee: Provides marginal coverage guarantees (e.g., 90%) over the entire dataset.

Phase 5: Adaptive & Non-Exchangeable CP

Crucial for Sediment Data: Sediment load data often violates the "exchangeability" assumption due to temporal dependencies.

• NEXCP: Weights recent observations higher to account for distribution drift.

• Adaptive CP: Dynamically adjusts the prediction interval width ($C_t$) based on recent errors.

• Benefit: Maintains valid coverage even during "bursty" periods like floods or seasonal shifts.

  ^**This repository is a collaborative project developed by Prakriti Bisht and Danesh Selwal.

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