Related papers: Robust Ellipsoid-specific Fitting via Expectation …
The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…
PDE learning is an emerging field that combines physics and machine learning to recover unknown physical systems from experimental data. While deep learning models traditionally require copious amounts of training data, recent PDE learning…
Linear inverse problems are ubiquitous. Often the measurements do not follow a Gaussian distribution. Additionally, a model matrix with a large condition number can complicate the problem further by making it ill-posed. In this case, the…
Detecting the reflection symmetry plane of an object represented by a 3D point cloud is a fundamental problem in 3D computer vision and geometry processing due to its various applications, such as compression, object detection, robotic…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
This paper deals with Elliptical Wishart distributions - which generalize the Wishart distribution - in the context of signal processing and machine learning. Two algorithms to compute the maximum likelihood estimator (MLE) are proposed: a…
Training the parameters of statistical models to describe a given data set is a central task in the field of data mining and machine learning. A very popular and powerful way of parameter estimation is the method of maximum likelihood…
Linear and Quadratic Discriminant Analysis are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not robust. To…
In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods…
The Minimum Volume Covering Ellipsoid (MVCE) problem, characterised by $n$ observations in $d$ dimensions where $n \gg d$, can be computationally very expensive in the big data regime. We apply methods from randomised numerical linear…
We give a novel algorithm for enumerating lattice points in any convex body, and give applications to several classic lattice problems, including the Shortest and Closest Vector Problems (SVP and CVP, respectively) and Integer Programming…
The minimum error entropy (MEE) criterion has been verified as a powerful approach for non-Gaussian signal processing and robust machine learning. However, the implementation of MEE on robust classification is rather a vacancy in the…
This paper addresses the issue of matching rigid and articulated shapes through probabilistic point registration. The problem is recast into a missing data framework where unknown correspondences are handled via mixture models. Adopting a…
Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We provide the currently fastest randomized (1+epsilon)-approximation algorithm for the closest vector problem in the infinity norm. The running time of our method depends on the dimension n and the approximation guarantee epsilon by 2^O(n)…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…
We study the local geometry of testing a mean vector within a high-dimensional ellipse against a compound alternative. Given samples of a Gaussian random vector, the goal is to distinguish whether the mean is equal to a known vector within…
The integration of Large Language Models (LLMs) into autonomous driving systems offers promising enhancements in environmental understanding and decision-making. However, the substantial computational demands of deploying LLMs locally on…