相关论文: A continuation method for computing the multilinea…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
The question of knowing whether the policy Iteration algorithm (PI) for solving Markov Decision Processes (MDPs) has exponential or (strongly) polynomial complexity has attracted much attention in the last 50 years. Recently, Fearnley…
We study the complexity of solving the \emph{generalized MinRank problem}, i.e. computing the set of points where the evaluation of a polynomial matrix has rank at most $r$. A natural algebraic representation of this problem gives rise to a…
Real-world recommender systems often need to balance multiple objectives when deciding which recommendations to present to users. These include behavioural signals (e.g. clicks, shares, dwell time), as well as broader objectives (e.g.…
We introduce AlphaRank, an artificial intelligence approach to address the fixed-budget ranking and selection (R&S) problems. We formulate the sequential sampling decision as a Markov decision process and propose a Monte Carlo…
This work demonstrates that applying a fixed-effect multiple linear regression (MLR) model to an overparameterized dataset is mathematically equivalent to fitting a hyper-curve parameterized by a single scalar. This reformulation shifts the…
We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches,…
We present a preference learning framework for multiple criteria sorting. We consider sorting procedures applying an additive value model with diverse types of marginal value functions (including linear, piecewise-linear, splined, and…
In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The…
Online learning to rank is a core problem in machine learning. In Lattimore et al. (2018), a novel online learning algorithm was proposed based on topological sorting. In the paper they provided a set of self-normalized inequalities (a) in…
Nonlinear two-point boundary value problems arise in numerous areas of application. The existence and number of solutions for various cases has been studied from a theoretical standpoint. These results generally rely upon growth conditions…
Holomorphic functions are amazing because their values in an ever so small disk in the complex plane completely determine the function values at arbitrary points in their maximum possible domain. The process of extending such a function…
PageRank is an algorithm introduced in 1998 and used by the Google Internet search engine. It assigns a numerical value to each element of a set of hyperlinked documents (that is, web pages) within the World Wide Web with the purpose of…
We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets…
As the final stage of recommender systems, re-ranking presents ordered item lists to users that best match their interests. It plays such a critical role and has become a trending research topic with much attention from both academia and…
We study the \emph{Proximal Alternating Predictor-Corrector} (PAPC) algorithm introduced recently by Drori, Sabach and Teboulle to solve nonsmooth structured convex-concave saddle point problems consisting of the sum of a smooth convex…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
We consider the problem of estimating the number of distinct elements in a large data set (or, equivalently, the support size of the distribution induced by the data set) from a random sample of its elements. The problem occurs in many…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…