Related papers: A determinantal point process for column subset se…
Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. The present paper proposes the use of…
A determinantal point process (DPP) is an ensemble of random nonnegative-integer-valued Radon measures, whose correlation functions are all given by determinants specified by an integral kernel called the correlation kernel. First we show…
Determinantal Point Processes (DPPs) are popular models for point processes with repulsion. They appear in numerous contexts, from physics to graph theory, and display appealing theoretical properties. On the more practical side of things,…
Beam search is a go-to strategy for decoding neural sequence models. The algorithm can naturally be viewed as a subset optimization problem, albeit one where the corresponding set function does not reflect interactions between candidates.…
Let $M$ be a real $r\times c$ matrix and let $k$ be a positive integer. In the column subset selection problem (CSSP), we need to minimize the quantity $\|M-SA\|$, where $A$ can be an arbitrary $k\times c$ matrix, and $S$ runs over all…
The problem of column subset selection has recently attracted a large body of research, with feature selection serving as one obvious and important application. Among the techniques that have been applied to solve this problem, the greedy…
Symmetric positive semidefinite (SPSD) matrix approximation is an important problem with applications in kernel methods. However, existing SPSD matrix approximation methods such as the Nystr\"om method only have weak error bounds. In this…
Determinantal Point Process (DPPs) are statistical models for repulsive point patterns. Both sampling and inference are tractable for DPPs, a rare feature among models with negative dependence that explains their popularity in machine…
Discrete Determinantal Point Processes (DPPs) have a wide array of potential applications for subsampling datasets. They are however held back in some cases by the high cost of sampling. In the worst-case scenario, the sampling cost scales…
Multistage stochastic programming deals with operational and planning problems that involve a sequence of decisions over time while responding to realizations that are uncertain. Algorithms designed to address multistage stochastic linear…
Given a fixed matrix, the problem of column subset selection requests a column submatrix that has favorable spectral properties. Most research from the algorithms and numerical linear algebra communities focuses on a variant called…
We study the problem of detecting change points (CPs) that are characterized by a subset of dimensions in a multi-dimensional sequence. A method for detecting those CPs can be formulated as a two-stage method: one for selecting relevant…
We study the low rank approximation problem of any given matrix $A$ over $\mathbb{R}^{n\times m}$ and $\mathbb{C}^{n\times m}$ in entry-wise $\ell_p$ loss, that is, finding a rank-$k$ matrix $X$ such that $\|A-X\|_p$ is minimized. Unlike…
Autonomous navigation in intelligent mobile systems represents a core research focus within artificial intelligence-driven robotics. Contemporary path planning approaches face constraints in dynamic environmental responsiveness and…
We review how to simulate continuous determinantal point processes (DPPs) and improve the current simulation algorithms in several important special cases as well as detail how certain types of conditional simulation can be carried out.…
We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random…
We consider the problem of selecting the best subset of exactly $k$ columns from an $m \times n$ matrix $A$. We present and analyze a novel two-stage algorithm that runs in $O(\min\{mn^2,m^2n\})$ time and returns as output an $m \times k$…
Determinantal point processes (DPPs for short) are a class of repulsive point processes. They have found some statistical applications to model spatial point pattern datasets with repulsion between close points. In the case of DPPs on…
We develop an implementable stochastic proximal point (SPP) method for a class of weakly convex, composite optimization problems. The proposed stochastic proximal point algorithm incorporates a variance reduction mechanism and the resulting…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…