Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption
Abstract
Online learning in non-stationary streams is often formulated as tracking a point estimate, although many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and bounded causal adversarial corruption. Candidate laws are represented by variable-size latent cluster configurations that induce predictive distributions. A Gibbs quasi-posterior over configurations yields an online predictor by posterior averaging and can be sampled using reversible-jump MCMC. The method uses no stream likelihood but specifies a kernel-mixture predictive family. We evaluate cumulative Wasserstein-1 regret against the time-varying true law and study periodic restart, sliding-window, and exponential-discounting memory against full history. The bounds separate PAC-Bayesian complexity, corruption-sensitive posterior perturbation, and drift through ATOT=∑t=2T W22(pt−1*,pt*). Under bounded support, latent quadratic growth, predictive-map regularity, and localized-comparator assumptions, restart has sublinear high-probability cumulative regret when 0≤ a<1, q,ζ,b<1, 0≤γ<β<1, and 0<h<(1−a)/2. Here a,q,ζ,b control the polynomial growth of drift, predictive-family approximation error, off-order posterior mass, and oracle-order switch cost; λsasymp s−β and Hasymp Th. Corruptions satisfy the segment-local condition Λr,s=O(sγ), so a sublinear global budget alone is insufficient. The regime requires oracle-informed tuning, εT=o(1), and fixed confidence or log(1/δ0)=To(1). Sliding-window and discounted guarantees additionally require the stated localized-memory condition.
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BibTeX
@misc{mahla2026online,
title = {{Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption}},
author = {Navyansh Mahla and Prateek Chanda and Ganesh Ramakrishnan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.18778},
eprint = {2606.18778},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.18778},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption
AU - Navyansh Mahla
AU - Prateek Chanda
AU - Ganesh Ramakrishnan
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2606.18778
UR - https://arxiv.org/abs/2606.18778
AB - Online learning in non-stationary streams is often formulated as tracking a point estimate, although many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and bounded causal adversarial corruption. Candidate laws are represented by variable-size latent cluster configurations that induce predictive distributions. A Gibbs quasi-posterior over configurations yields an online predictor by posterior averaging and can be sampled using reversible-jump MCMC. The method uses no stream likelihood but specifies a kernel-mixture predictive family. We evaluate cumulative Wasserstein-1 regret against the time-varying true law and study periodic restart, sliding-window, and exponential-discounting memory against full history. The bounds separate PAC-Bayesian complexity, corruption-sensitive posterior perturbation, and drift through A_T^OT=∑_t=2^T W_2^2(p_t−1^*,p_t^*). Under bounded support, latent quadratic growth, predictive-map regularity, and localized-comparator assumptions, restart has sublinear high-probability cumulative regret when 0≤ a<1, q,ζ,b<1, 0≤γ<β<1, and 0<h<(1−a)/2. Here a,q,ζ,b control the polynomial growth of drift, predictive-family approximation error, off-order posterior mass, and oracle-order switch cost; λ_sasymp s^−β and Hasymp T^h. Corruptions satisfy the segment-local condition Λ_r,s=O(s^γ), so a sublinear global budget alone is insufficient. The regime requires oracle-informed tuning, ε_T=o(1), and fixed confidence or log(1/δ_0)=T^o(1). Sliding-window and discounted guarantees additionally require the stated localized-memory condition.
ER -