Related papers: Finite-Sample Identification of Linear Regression …
Random permutation set (RPS) is a new formalism for reasoning with uncertainty involving order information. Measuring the conflict between two pieces of evidence represented by permutation mass functions remains an open issue in…
Large Language Models (LLMs) have shown improved generation performance through retrieval-augmented generation (RAG) following the retriever-reader paradigm, which supplements model inputs with externally retrieved knowledge. However, prior…
We address the problem of learning an unknown smooth function and its derivatives from noisy pointwise evaluations under the supremum norm. While classical nonparametric regression provides a strong theoretical foundation, traditional…
Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP),…
We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…
With the rapid development of diffusion models and flow-based generative models, there has been a surge of interests in solving noisy linear inverse problems, e.g., super-resolution, deblurring, denoising, colorization, etc, with generative…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
Linearly parametrized models are widely used in control and signal processing, with the least-squares (LS) estimate being the archetypical solution. When the input is insufficiently exciting, the LS problem may be unsolvable or numerically…
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian noise without…
Unified image restoration is a significantly challenging task in low-level vision. Existing methods either make tailored designs for specific tasks, limiting their generalizability across various types of degradation, or rely on training…
The recent developments in the machine learning domain have enabled the development of complex multivariate probabilistic forecasting models. Therefore, it is pivotal to have a precise evaluation method to gauge the performance and…
The sum-product or belief propagation (BP) algorithm is a widely used message-passing technique for computing approximate marginals in graphical models. We introduce a new technique, called stochastic orthogonal series message-passing…
We introduce an efficient message passing scheme for solving Constraint Satisfaction Problems (CSPs), which uses stochastic perturbation of Belief Propagation (BP) and Survey Propagation (SP) messages to bypass decimation and directly…
Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions,…
This report studies diffusion posterior sampling (DPS) for single-image super-resolution (SISR) under a known degradation model. We implement a likelihood-guided sampling procedure that combines an unconditional diffusion prior with…
We introduce Volume-Sorted Prediction Set (VSPS), a novel method for uncertainty quantification in multi-target regression that uses conditional normalizing flows with conformal calibration. This approach constructs flexible, non-convex…
Conformal prediction provides model-agnostic and distribution-free uncertainty quantification through prediction sets that are guaranteed to include the ground truth with any user-specified probability. Yet, conformal prediction is not…
Probabilistic inference problems arise naturally in distributed systems such as sensor networks and teams of mobile robots. Inference algorithms that use message passing are a natural fit for distributed systems, but they must be robust to…
This article presents a novel, general, and effective simulation-inspired approach, called {\it repro samples method}, to conduct statistical inference. The approach studies the performance of artificial samples, referred to as {\it repro…
We study the problem of estimating an unknown deterministic signal that is observed through an unknown deterministic data matrix under additive noise. In particular, we present a minimax optimization framework to the least squares problems,…