Related papers: Finite-Sample Identification of Linear Regression …
Distribution Regression (DR) on stochastic processes describes the learning task of regression on collections of time series. Path signatures, a technique prevalent in stochastic analysis, have been used to solve the DR problem. Recent…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
The phase retrieval problem in the presence of noise aims to recover the signal vector of interest from a set of quadratic measurements with infrequent but arbitrary corruptions, and it plays an important role in many scientific…
We assume a nonparametric regression model where the signal is given by the sum of a piecewise constant function and a smooth function. To detect the change-points and estimate the regression functions, we propose PCpluS, a combination of…
We propose Amortized Posterior Sampling (APS), a novel variational inference approach for efficient posterior sampling in inverse problems. Our method trains a conditional flow model to minimize the divergence between the variational…
Consider a randomized algorithm that draws samples exactly from a distribution using recursion. Such an algorithm is called a perfect simulation, and here a variety of methods for building this type of algorithm are shown to derive from the…
We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localised regions in data sequences which each must contain a change-point (understood as an abrupt change in the parameters of…
In this paper, we consider a weighted local linear estimator based on the inverse selection probability for nonparametric regression with missing covariates at random. The asymptotic distribution of the maximal deviation between the…
Solving inverse problems with the reverse process of a diffusion model represents an appealing avenue to produce highly realistic, yet diverse solutions from incomplete and possibly noisy measurements, ultimately enabling uncertainty…
Inspired by recent work on neural subspaces and mode connectivity, we revisit parameter subspace sampling for shifted and/or interpolatable input distributions (instead of a single, unshifted distribution). We enforce a compressed geometric…
Recent advancements in large language models (LLMs) integrating explicit reasoning, such as OpenAI's o3-mini, DeepSeek-R1, and QWQ-32B, enable smaller models to solve complex tasks by generating intermediate reasoning steps prior to…
We study nonparametric regression with covariates $X$ and outcome $Y$ under random unbiased perturbations (RUPs) of the conditional distribution $Y|X$, where the marginal distribution of covariates, $P^X$, remains fixed but the conditional…
We propose a series-based nonparametric specification test for a regression function when data are spatially dependent, the `space' being of a general economic or social nature. Dependence can be parametric, parametric with increasing…
We consider a machine learning setup where one training dataset is used to train multiple models across slightly different data distributions. This occurs when customized models are needed for various deployment environments. To reduce…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
While Gaussian processes (GPs) are the method of choice for regression tasks, they also come with practical difficulties, as inference cost scales cubic in time and quadratic in memory. In this paper, we introduce a natural and expressive…
In this study, we propose a method Distributionally Robust Safe Screening (DRSS), for identifying unnecessary samples and features within a DR covariate shift setting. This method effectively combines DR learning, a paradigm aimed at…
In this article, we introduce a new variable selection technique through trimming for finite mixture of regression models. Compared to the traditional variable selection techniques, the new method is robust and not sensitive to outliers.…
This work presents a novel simulation-based approach for constructing confidence regions in parametric models, which is particularly suited for generative models and situations where limited data and conventional asymptotic approximations…