相关论文: The Geometry of Linear Program Compression: An Exa…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
We propose a framework for sensitivity analysis of linear programs (LPs) in minimization form, allowing for simultaneous perturbations in the objective coefficients and right-hand sides, where the perturbations are modeled in a compact,…
The problem of high-dimensional and large-scale representation of visual data is addressed from an unsupervised learning perspective. The emphasis is put on discrete representations, where the description length can be measured in bits and…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Joint object matching, also known as multi-image matching, namely, the problem of finding consistent partial maps among all pairs of objects within a collection, is a crucial task in many areas of computer vision. This problem subsumes…
We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…
Nonlinear Parametric Optimization Network (NLPOpt-Net) is an unsupervised learning architecture to solve constrained nonlinear programs (NLP). Given the structure of an NLP, it learns the parametric solution maps with guaranteed constraint…
We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements…
The impressive growth of data throughput in optical microscopy has triggered a widespread use of supervised learning (SL) models running on compressed image datasets for efficient automated analysis. However, since lossy image compression…
In many data science applications, the objective is to extract appropriately-ordered smooth low-dimensional data patterns from high-dimensional data sets. This is challenging since common sorting algorithms are primarily aiming at finding…
We study the expressibility and learnability of convex optimization solution functions and their multi-layer architectural extension. The main results are: \emph{(1)} the class of solution functions of linear programming (LP) and quadratic…
We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…
A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) in which the constraint matrix is revealed column by column along with the corresponding…
Offline reinforcement learning (RL) aims to find an optimal policy for Markov decision processes (MDPs) using a pre-collected dataset. In this work, we revisit the linear programming (LP) reformulation of Markov decision processes for…
This note demonstrates that, for all compact convex sets, high-precision linear minimization can be performed via a single evaluation of the projection and a scalar-vector multiplication. In consequence, if $\varepsilon$-approximate linear…
In grammar-based compression a string is represented by a context-free grammar, also called a straight-line program (SLP), that generates only that string. We refine a recent balancing result stating that one can transform an SLP of size…
In this note, we develop fast and deterministic dimensionality reduction techniques for a family of subspace approximation problems. Let $P\subset \mathbbm{R}^N$ be a given set of $M$ points. The techniques developed herein find an $O(n…
Linear models are used in online decision making, such as in machine learning, policy algorithms, and experimentation platforms. Many engineering systems that use linear models achieve computational efficiency through distributed systems…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of approaches to inference in these models, nearly all of them amount to solving a linear program (LP)…