# Online Distributional Prediction via Latent Cluster Geometry Under Drift and Corruption

arXiv: https://arxiv.org/abs/2606.18778 · HTML: https://mlsanity.com/paper/2606.18778/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 25 references that are in the map.
- First posted on arXiv 17 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Non-stationary Stochastic Optimization](https://mlsanity.com/paper/1307.5449/) (2013)
- [Time-Series Anomaly Detection Service at Microsoft](https://mlsanity.com/paper/1906.03821/) (2019)
- [Kitsune: An Ensemble of Autoencoders for Online Network Intrusion Detection](https://mlsanity.com/paper/1802.09089/) (2018)
- [Stochastic Optimization with Heavy-Tailed Noise via Accelerated Gradient Clipping](https://mlsanity.com/paper/2005.10785/) (2020)
- [Optimal Dynamic Regret in Exp-Concave Online Learning](https://mlsanity.com/paper/2104.11824/) (2021)
- [Algorithms of Robust Stochastic Optimization Based on Mirror Descent Method](https://mlsanity.com/paper/1907.02707/) (2019)
- [Mirror Descent Strikes Again: Optimal Stochastic Convex Optimization under Infinite Noise Variance](https://mlsanity.com/paper/2202.11632/) (2022)
- [Stochastic Nonsmooth Convex Optimization with Heavy-Tailed Noises: High-Probability Bound, In-Expectation Rate and Initial Distance Adaptation](https://mlsanity.com/paper/2303.12277/) (2023)
- [Heavy-tailed Streaming Statistical Estimation](https://mlsanity.com/paper/2108.11483/) (2021)
- [Robust Online Convex Optimization in the Presence of Outliers](https://mlsanity.com/paper/2107.01881/) (2021)

## Abstract (arXiv)

Online learning in non-stationary streams is often formulated as tracking a point estimate, but many applications require predicting the full data-generating distribution. We study online distributional prediction under drift and adversarial corruption. Our approach represents each candidate law through a latent cluster geometry: a variable-size configuration of centers that organizes probability mass and induces a predictive distribution. A Gibbs quasi-posterior over these configurations yields an online predictor by posterior averaging, and the resulting variable-dimensional posterior can be sampled with reversible-jump MCMC. The method therefore avoids specifying a parametric streaming law while retaining a structured latent space for uncertainty, regularization, and comparison. We evaluate performance by cumulative Wasserstein-1 regret against the time-varying true law. The analysis separates two effects: corruption perturbs the loss-based posterior update, whereas drift makes long-horizon posterior memory stale. We address the latter with a restarted variant that temporally localizes the same quasi-Bayesian update. The resulting high-probability bounds decompose into a PAC-Bayesian complexity term, a corruption-sensitive posterior perturbation term, and a dynamic optimal-transport term driven by (ATOT=sumt=2T W22(pt-1^*,pt^*)). Under bounded support, stable latent geometry, predictive-map regularity, oracle realizability, localized restart windows, sublinear transport action, and sublinear corruption budget, the restarted predictor achieves sublinear cumulative Wasserstein regret. These guarantees require no parametric model for the stream, drift mechanism, or corruption process.