机器学习

Binary classification from positive-only samples is a variant of PAC learning in which the learner receives i.i.d. samples from the positive region of an unknown target concept, but is evaluated under the original distribution (which places…

Score-based generative models and Langevin samplers rely on estimating the score function $\nabla_x\log p_t(x)$ of a forward diffusion. Classically this is tractable when the drift is linear: the marginal density is Gaussian and the score…

Pervasive data contamination -- stemming from measurement errors, outliers, or adversarial corruption -- has motivated the development of robust statistical methods. In this context, we propose a two-stage Adversarial…

The global minimum-variance portfolio (GMVP) is the canonical decision built from an estimated covariance matrix, yet covariance estimators are universally evaluated by matrix-norm loss, which is not the object the decision depends on. We…

We address the problem of inferring a directed network from nodal measurements generated by linear diffusion dynamics on the sought graph. Observations are modeled as the outputs of a graph convolutional filter, i.e., a polynomial (with…

Many decoding methods for large language models can be understood as shifting probability mass toward outputs that are more likely under the model, either locally at the token level or globally at the sequence level. Therefore, their…

Reliably quantifying predictive uncertainty is difficult for complex, high-dimensional, or misspecified models. Both fully Bayesian and bootstrap resampling methods provide principled uncertainty estimates but are often too expensive for…

Global objectives, such as KL divergence and ELBO, are widely used in Bayesian inference for measuring distributional discrepancy. This paper studies their local-mass behaviour that is not directly captured by such objectives. We introduce…

Empirical Bayes (EB) estimators can match the first-order asymptotic risk of maximum likelihood (ML) while behaving very differently at second order: recent excess mean squared error (XMSE) analysis shows that kernel-based EB estimation may…

This paper presents a probabilistic framework for online test-time adaptation problems. In them, a model is trained on labeled data but must adapt to unlabeled data at test time under the assumption that training and test distributions…

Several theoretical works have tried to explain the adversarial vulnerability of deep neural networks through properties of high-dimensional geometry. However, the assumptions underlying these works are rarely examined empirically, and…

A central goal of modern causal inference is estimating heterogeneous treatment effects to answer questions like "how does an intervention affect each unit," rather than only on average. We study this problem with panel-data where we…

Conformal prediction methods enjoy strong theoretical and empirical predictive inference performance, provided the data is exchangeable, and predictors are trained in a memoryless fashion. However, these assumptions and constraints are…

We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results…

Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and…

Score-based diffusion models have demonstrated remarkable empirical success in learning high-dimensional distributions, particularly those exhibiting low-dimensional and multi-modal structures. However, theoretical understanding of their…

Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian…

We study the Lipschitz bandit problem, where a learner sequentially maximizes an unknown Lipschitz function $f$ over a domain $\mathcal{X} \subset [0,1]^d$ using noisy pointwise evaluations. Existing regret bounds are either worst-case,…

Recent work in random matrix theory (RMT) has developed the notion of deterministic equivalents: typically linear surrogate models that approximate the spectral behavior of large nonlinear random matrices, such as nonlinear feature maps in…

In federated language modeling, $K$ nodes each hold $n$ samples but cannot pool data or exchange full-precision gradients or weights. We study the minimax rate at which a conditional distribution over $V$ tokens can be estimated when each…