March 2026

arXiv:2503.07327v2 Announce Type: replace-cross Abstract: Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data. It performs dimension reduction similar to PCA for multivariate data. However, standard MPCA is sensitive to outliers. It is highly influenced by observations deviating from the bulk of the data, called casewise outliers, as well as by individual outlying cells in the tensors, so-called cellwise outliers. This latter type of outlier is highly likely to occur in tensor data, as […]

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arXiv:2405.19553v2 Announce Type: replace-cross Abstract: We prove bounds on the variance of a function $f$ under the empirical measure of the samples obtained by the Sequential Monte Carlo (SMC) algorithm, with time complexity depending on local rather than global Markov chain mixing dynamics. SMC is a Markov Chain Monte Carlo (MCMC) method, which starts by drawing $N$ particles from a known distribution, and then, through a sequence of distributions, re-weights and re-samples the particles, at each instance applying […]

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arXiv:2310.12032v3 Announce Type: replace-cross Abstract: The Linear Model of Co-regionalization (LMC) is a very general multitask gaussian process model for regression or classification. While its expressiveness and conceptual simplicity are appealing, naive implementations have cubic complexity in the product (number of datapoints $times$ number of tasks), making approximations mandatory for most applications. However, recent work has shown that in some settings the latent processes of the model can be decoupled, leading to a complexity that is only linear […]

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arXiv:2603.15057v2 Announce Type: replace Abstract: Global feature effects such as partial dependence (PD) and accumulated local effects (ALE) plots are widely used to interpret black-box models. However, they are only estimates of true underlying effects, and their reliability depends on multiple sources of error. Despite the popularity of global feature effects, these error sources are largely unexplored. In particular, the practically relevant question of whether to use training or holdout data to estimate feature effects remains unanswered. We […]

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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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