相关论文: VEXPA: Validated EXPonential Analysis through regu…

This paper introduces a novel eXtended virtual element method, an extension of the conforming virtual element method. The XVEM is formulated by incorporating appropriate enrichment functions in the local spaces. The method is designed to…

In the standard setting of one-way ANOVA with normal errors, a new algorithm, called the Step Down Maximum Mean Selection Algorithm (SDMMSA), is proposed to estimate the treatment means under an assumption that the treatment mean is…

Exponential family extensions of principal component analysis (EPCA) have received a considerable amount of attention in recent years, demonstrating the growing need for basic modeling tools that do not assume the squared loss or Gaussian…

In high-dimensional linear regression, the goal pursued here is to estimate an unknown regression function using linear combinations of a suitable set of covariates. One of the key assumptions for the success of any statistical procedure in…

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Principal component analysis (PCA) is a foundational tool in modern data analysis, and a crucial step in PCA is selecting the number of components to keep. However, classical selection methods (e.g., scree plots, parallel analysis, etc.)…

Resampling techniques are widely used in statistical inference and ensemble learning, in which estimators' statistical properties are essential. However, existing methods are computationally demanding, because repetitions of…

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy…

A variety of methods have been proposed to try to explain how deep neural networks make their decisions. Key to those approaches is the need to sample the pixel space efficiently in order to derive importance maps. However, it has been…

Recent advances in data collection technologies have led to the emergence of massive spatial datasets, with measurements obtained at millions of spatial locations. Geostatistical models typically employ Gaussian processes (GPs) to capture…

The field of text-conditioned image generation has made unparalleled progress with the recent advent of latent diffusion models. While remarkable, as the complexity of given text input increases, the state-of-the-art diffusion models may…

Numerous signals in relevant signal processing applications can be modeled as a sum of complex exponentials. Each exponential term entails a particular property of the modeled physical system, and it is possible to define families of…

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

Deep learning has achieved remarkable success in processing and managing unstructured data. However, its "black box" nature imposes significant limitations, particularly in sensitive application domains. While existing interpretable machine…

We introduce a new discriminant analysis method (Empirical Discriminant Analysis or EDA) for binary classification in machine learning. Given a dataset of feature vectors, this method defines an empirical feature map transforming the…

Iterative refinement is particularly popular for numerical solution of linear systems of equations. We extend it to Low Rank Approximation of a matrix (LRA) and observe close link of the resulting algorithm to oversampling techniques,…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

We present new results on the classical algorithm of variable elimination, which underlies many algorithms including for probabilistic inference. The results relate to exploiting functional dependencies, allowing one to perform inference…

Conformal prediction provides rigorous distribution-free finite-sample guarantees for marginal coverage under the assumption of exchangeability, but may exhibit systematic undercoverage or overcoverage for specific subpopulations. Assessing…

Branching bisimilarity on normed BPA processes was recently shown to be decidable by Yuxi Fu (ICALP 2013) but his proof has not provided any upper complexity bound. We present a simpler approach based on relative prime decompositions that…