March 2026

arXiv:2506.01324v3 Announce Type: replace Abstract: We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the clustering error rate, governed by the stationary-weighted KL divergence between transition kernels. We then propose a two-stage algorithm: Stage I applies spectral clustering via a new injective Euclidean embedding for ergodic Markov chains, a contribution […]

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arXiv:2505.07272v2 Announce Type: replace Abstract: Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample. Heteroscedastic methods aim to deal with such mixed data quality. This paper develops a subspace learning method, named ALPCAH, that can estimate the sample-wise noise variances and use this information to improve the estimate of the subspace basis associated […]

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arXiv:2504.13336v2 Announce Type: replace Abstract: Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different perspective by connecting Flow Matching to kernel density estimation. We first verify that the kernel density estimator matches the optimal rate of convergence in Wasserstein distance up to logarithmic factors, improving existing bounds for the Gaussian kernel. Based on […]

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arXiv:2504.09347v4 Announce Type: replace Abstract: While deep neural networks (DNNs) are used for prediction, inference on DNN-estimated subject-specific means for categorical or exponential family outcomes remains underexplored. We address this by proposing a DNN estimator under generalized nonparametric regression models (GNRMs) and developing a rigorous inference framework. Unlike existing approaches that assume independence between estimation errors and inputs to establish the error bound, a condition often violated in GNRMs, we allow for dependence and our theoretical analysis demonstrates […]

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arXiv:2407.19892v2 Announce Type: replace Abstract: Motivation: Networks underlie the generation and interpretation of many biological datasets: gene networks shed light on the regulatory structure of the genome, and cell networks can capture structure of the tumor micro-environment. However, most methods that learn such networks make the faulty ‘independence assumption’; to learn the gene network, they assume that no cell network exists. ‘Multi-axis’ methods, which do not make this assumption, fail to scale beyond a few thousand cells or […]

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arXiv:2603.16798v1 Announce Type: cross Abstract: We study mean estimation for a Gaussian distribution with identity covariance in $mathbb{R}^d$ under a missing data scheme termed realizable $epsilon$-contamination model. In this model an adversary can choose a function $r(x)$ between 0 and $epsilon$ and each sample $x$ goes missing with probability $r(x)$. Recent work Ma et al., 2024 proposed this model as an intermediate-strength setting between Missing Completely At Random (MCAR) — where missingness is independent of the data — […]

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arXiv:2603.16741v1 Announce Type: cross Abstract: Objective. We establish a principled method for inferring mental health related psychometric variables from neural and behavioral data using the Implicit Association Test (IAT) as the data generation engine, aiming to overcome the limited predictive performance (typically under 0.7 AUC) of the gold-standard D-score method, which relies solely on reaction times. Approach. We propose a sparse hierarchical Bayesian model that leverages multi-modal data to predict experiences related to mental illness symptoms in new […]

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arXiv:2603.16729v1 Announce Type: cross Abstract: Benchmarking the performance of complex systems such as rail networks, renewable generation assets and national economies is central to transport planning, regulation and macroeconomic analysis. Classical frontier methods, notably Data Envelopment Analysis (DEA) and Stochastic Frontier Analysis (SFA), estimate an efficient frontier in the observed input-output space and define efficiency as distance to this frontier, but rely on restrictive assumptions on the production set and only indirectly address heterogeneity and scale effects. We […]

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arXiv:2603.16712v1 Announce Type: cross Abstract: We consider computationally-efficient estimation of population parameters when observations are subject to missing data. In particular, we consider estimation under the realizable contamination model of missing data in which an $epsilon$ fraction of the observations are subject to an arbitrary (and unknown) missing not at random (MNAR) mechanism. When the true data is Gaussian, we provide evidence towards statistical-computational gaps in several problems. For mean estimation in $ell_2$ norm, we show that in […]

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arXiv:2603.16535v1 Announce Type: cross Abstract: Transformers owe much of their empirical success in natural language processing to the self-attention blocks. Recent perspectives interpret attention blocks as interacting particle systems, whose mean-field limits correspond to gradient flows of interaction energy functionals on probability density spaces equipped with Wasserstein-$2$-type metrics. We extend this viewpoint by introducing accelerated attention blocks derived from inertial Nesterov-type dynamics on density spaces. In our proposed architecture, tokens carry both spatial (feature) and velocity variables. The […]

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