Related papers: Approximation Algorithm Project
In this paper we analyze a class of nonconvex optimization problem from the viewpoint of abstract convexity. Using the respective generalizations of the subgradient we propose an abstract notion proximal operator and derive a number of…
We investigate three related and important problems connected to machine learning: approximating a submodular function everywhere, learning a submodular function (in a PAC-like setting [53]), and constrained minimization of submodular…
First-order optimization algorithms are widely used today. Two standard building blocks in these algorithms are proximal operators (proximals) and gradients. Although gradients can be computed for a wide array of functions, explicit…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
Training a one-node neural network with ReLU activation function (One-Node-ReLU) is a fundamental optimization problem in deep learning. In this paper, we begin with proving the NP-hardness of training One-Node-ReLU. We then present an…
A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit…
An NP-hard combinatorial optimization problem $\Pi$ is said to have an {\em approximation threshold} if there is some $t$ such that the optimal value of $\Pi$ can be approximated in polynomial time within a ratio of $t$, and it is NP-hard…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
We study adaptive approximation algorithms for general multivariate linear problems where the sets of input functions are non-convex cones. While it is known that adaptive algorithms perform essentially no better than non-adaptive…
Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to…
Pattern matching is a fundamental process in almost every scientific domain. The problem involves finding the positions of a given pattern (usually of short length) in a reference stream of data (usually of large length). The matching can…
Approximate computing methods have shown great potential for deep learning. Due to the reduced hardware costs, these methods are especially suitable for inference tasks on battery-operated devices that are constrained by their power budget.…
The Acceptance Probability Estimation Problem (APEP) is to additively approximate the acceptance probability of a Boolean circuit. This problem admits a probabilistic approximation scheme. A central question is whether we can design a…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Automaton learning is a domain in which the target system is inferred by the automaton learning algorithm in the form of an automaton, by synthesizing a finite number of inputs and their corresponding outputs. Automaton learning makes use…
Block Sorting is a well studied problem, motivated by its applications in Optical Character Recognition (OCR), and Computational Biology. Block Sorting has been shown to be NP-Hard, and two separate polynomial time 2-approximation…
To sidestep the curse of dimensionality when computing solutions to Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an algorithm that leverages a neural network to approximate the value function. We show that…
Inexact computing also referred to as approximate computing is a style of designing algorithms and computing systems wherein the accuracy of correctness of algorithms executing on them is deliberately traded for significant resource…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…