相关论文: Approximating faces of marginal polytopes in discr…

We consider the problem of approximating a semialgebraic set with a sublevel-set of a polynomial function. In this setting, it is standard to seek a minimum volume outer approximation and/or maximum volume inner approximation. As there is…

Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of…

In this paper, we propose iterative inner/outer approximations based on a recent notion of block factor-width-two matrices for solving semidefinite programs (SDPs). Our inner/outer approximating algorithms generate a sequence of upper/lower…

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are generally considered to be intractable for large models. The intractability of these algorithms is to a large extent a…

Let $P$ be a convex $d$-polytope and $0 \leq k \leq d-1$. In 2023, this author proved the following inequalities, resolving a question of B\'ar\'any: \[ \frac{f_k(P)}{f_0(P)} \geq \frac{1}{2}\biggl[{\lceil \frac{d}{2} \rceil \choose k} +…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold-adaptive Farahmand-Szepesv\'ari-Audibert (FSA) dimension…

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables where the functional forms are left unspecified.…

The Fr\'{e}chet distance is a well studied and commonly used measure to capture the similarity of polygonal curves. Unfortunately, it exhibits a high sensitivity to the presence of outliers. Since the presence of outliers is a frequently…

Motivated principally by the low-rank matrix completion problem, we present an extension of the Frank-Wolfe method that is designed to induce near-optimal solutions on low-dimensional faces of the feasible region. This is accomplished by a…

We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…

We consider the problem of computing the nearest matrix polynomial with a non-trivial Smith Normal Form. We show that computing the Smith form of a matrix polynomial is amenable to numeric computation as an optimization problem.…

We consider the problem of estimating the $L_1$ distance between two discrete probability measures $P$ and $Q$ from empirical data in a nonasymptotic and large alphabet setting. When $Q$ is known and one obtains $n$ samples from $P$, we…

Estimating the density of a distribution from its samples is a fundamental problem in statistics. Hypothesis selection addresses the setting where, in addition to a sample set, we are given $n$ candidate distributions -- referred to as…

High-dimensional data commonly lies on low-dimensional submanifolds, and estimating the local intrinsic dimension (LID) of a datum -- i.e. the dimension of the submanifold it belongs to -- is a longstanding problem. LID can be understood as…

Facial feature detection from facial images has attracted great attention in the field of computer vision. It is a nontrivial task since the appearance and shape of the face tend to change under different conditions. In this paper, we…

In this paper, we propose a novel image set representation and classification method by maximizing the margin of image sets. The margin of an image set is defined as the difference of the distance to its nearest image set from different…

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms.…

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best…

The most widely used internal measure for clustering evaluation is the silhouette coefficient, whose naive computation requires a quadratic number of distance calculations, which is clearly unfeasible for massive datasets. Surprisingly,…