Related papers: NP-hardness of p-adic linear regression
The reliable fraction of information is an attractive score for quantifying (functional) dependencies in high-dimensional data. In this paper, we systematically explore the algorithmic implications of using this measure for optimization. We…
The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching…
In high-dimensional regression, we attempt to estimate a parameter vector $\beta_0\in\mathbb{R}^p$ from $n\lesssim p$ observations $\{(y_i,x_i)\}_{i\leq n}$ where $x_i\in\mathbb{R}^p$ is a vector of predictors and $y_i$ is a response…
We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…
Given a linear system, we consider the problem of finding a small set of variables to affect with an input so that the resulting system is controllable. We show that this problem is NP-hard; indeed, we show that even approximating the…
The growing amount of applications that generate vast amount of data in short time scales render the problem of partial monitoring, coupled with prediction, a rather fundamental one. We study the aforementioned canonical problem under the…
Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $||x-y||,$ for a specified norm. This paper gives…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
The l1-regularized logistic regression is a widely used statistical model in data classification. This paper proposes a dual Newton method based proximal point algorithm (PPDNA) to solve the l1-regularized logistic regression problem with…
In this paper we obtain improved iteration complexities for solving $\ell_p$ regression. We provide methods which given any full-rank $\mathbf{A} \in \mathbb{R}^{n \times d}$ with $n \geq d$, $b \in \mathbb{R}^n$, and $p \geq 2$ solve…
Decisions are increasingly taken by both humans and machine learning models. However, machine learning models are currently trained for full automation -- they are not aware that some of the decisions may still be taken by humans. In this…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
Minimization of the $L_\infty$ norm, which can be viewed as approximately solving the non-convex least median estimation problem, is a powerful method for outlier removal and hence robust regression. However, current techniques for solving…
The problem of solving linear systems is one of the most fundamental problems in computer science, where given a satisfiable linear system $(A,b)$, for $A \in \mathbb{R}^{n \times n}$ and $b \in \mathbb{R}^n$, we wish to find a vector $x…
State minimization of combinatorial filters is a fundamental problem that arises, for example, in building cheap, resource-efficient robots. But exact minimization is known to be NP-hard. This paper conducts a more nuanced analysis of this…
Many researchers in artificial intelligence are beginning to explore the use of soft constraints to express a set of (possibly conflicting) problem requirements. A soft constraint is a function defined on a collection of variables which…
Robust optimization is a widely studied area in operations research, where the algorithm takes as input a range of values and outputs a single solution that performs well for the entire range. Specifically, a robust algorithm aims to…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
Finding the hedge ratios for a portfolio and risk compression is the same mathematical problem. Traditionally, regression is used for this purpose. However, regression has its own limitations. For example, in a regression model, we can't…