Technology Category
Reasoning under Uncertainty: Relational Probabilistic ModelsMachine Learning: Calibration & Uncertainty QuantificationSearch and Optimization: Mixed Discrete/Continuous Search
Robust Spatio-Temporal Distributional Regression
🤖 AI Summary
This paper addresses the recovery of conditional distribution functions for continuous variables under threshold-classified observations—particularly when the distribution frequently attains boundary values (0 or 1) and exhibits spatiotemporal dependence and covariate effects, rendering standard binomial models inadequate. We propose a boundary-inflated binomial mixture model that jointly incorporates a Dirac measure (to capture point mass at boundaries) and a binomial kernel (to model interior continuity), embedded within a dynamic Gaussian process to account for spatiotemporal dependence. A Bayesian inference framework is developed using Pólya–Gamma data augmentation, enabling efficient and robust distributional regression. Simulation studies demonstrate that our method significantly improves distributional fit and predictive stability near boundaries compared to conventional binomial regression. The approach holds substantial practical value for ecological and environmental applications involving threshold-based measurements.
Technology Category
Application Category
📝 Abstract
Motivated by investigating spatio-temporal patterns of the distribution of continuous variables, we consider describing the conditional distribution function of the response variable incorporating spatio-temporal components given predictors. In many applications, continuous variables are observed only as threshold-categorized data due to measurement constraints. For instance, ecological measurements often categorize sizes into intervals rather than recording exact values due to practical limitations. To recover the conditional distribution function of the underlying continuous variables, we consider a distribution regression employing models for binomial data obtained at each threshold value. However, depending on spatio-temporal conditions and predictors, the distribution function may frequently exhibit boundary values (zero or one), which can occur either structurally or randomly. This makes standard binomial models inadequate, requiring more flexible modeling approaches. To address this issue, we propose a boundary-inflated binomial model incorporating spatio-temporal components. The model is a three-component mixture of the binomial model and two Dirac measures at zero and one. We develop a computationally efficient Bayesian inference algorithm using Pólya-Gamma data augmentation and dynamic Gaussian predictive processes. Extensive simulation experiments demonstrate that our procedure significantly outperforms distribution regression methods based on standard binomial models across various scenarios.
Problem
Research questions and friction points this paper is trying to address.
Recovering conditional distribution of threshold-categorized continuous variables
Addressing boundary values in spatio-temporal distribution functions
Developing flexible binomial models for spatio-temporal data analysis
Innovation
Methods, ideas, or system contributions that make the work stand out.
Boundary-inflated binomial model with spatio-temporal components
Pólya-Gamma data augmentation for efficient Bayesian inference
Dynamic Gaussian predictive processes for computational efficiency
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