相关论文: The Geometry of Linear Program Compression: An Exa…
We present an algorithm for computing the Lyndon factorization of a string that is given in grammar compressed form, namely, a Straight Line Program (SLP). The algorithm runs in $O(n^4 + mn^3h)$ time and $O(n^2)$ space, where $m$ is the…
Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…
We study the problem of compression for the purpose of similarity identification, where similarity is measured by the mean square Euclidean distance between vectors. While the asymptotical fundamental limits of the problem - the minimal…
The article proposes an n-dimensional mathematical model of the visual representation of a linear programming problem. This model makes it possible to use artificial neural networks to solve multidimensional linear optimization problems,…
Here we study the complexity of string problems as a function of the size of a program that generates input. We consider straight-line programs (SLP), since all algorithms on SLP-generated strings could be applied to processing…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
Typical behavior of the linear programming problem (LP) is studied as a relaxation of the minimum vertex cover problem, which is a type of the integer programming problem (IP). To deal with the LP and IP by statistical mechanics, a…
When model predictions inform downstream decision making, a natural question is under what conditions can the decision-makers simply respond to the predictions as if they were the true outcomes. Calibration suffices to guarantee that simple…
It is generally well understood that predictive classification and compression are intrinsically related concepts in information theory. Indeed, many deep learning methods are explained as learning a kind of compression, and that better…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
Reinforcement learning (RL) algorithms can be used to provide personalized services, which rely on users' private and sensitive data. To protect the users' privacy, privacy-preserving RL algorithms are in demand. In this paper, we study RL…
In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov…
Mixed-integer linear programming (MILP) is at the core of many advanced algorithms for solving fundamental problems in combinatorial optimization. The complexity of solving MILPs directly correlates with their support size, which is the…
We explore unique considerations involved in fitting ML models to data with very high precision, as is often required for science applications. We empirically compare various function approximation methods and study how they scale with…
Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…
Linear Programming (LP) is an important decoding technique for binary linear codes. However, the advantages of LP decoding, such as low error floor and strong theoretical guarantee, etc., come at the cost of high computational complexity…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…