Related papers: Solving the LPN problem in cube-root time
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
This paper investigates two related optimal input selection problems for fixed (non-switched) and switched structured systems. More precisely, we consider selecting the minimum cost of inputs from a prior set of inputs, and selecting the…
Solving constrained nonlinear programs (NLPs) is of great importance in various domains such as power systems, robotics, and wireless communication networks. One widely used approach for addressing NLPs is the interior point method (IPM).…
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real…
We study binary classification in the setting where the learner is presented with multiple corrupted training samples, with possibly different sample sizes and degrees of corruption, and introduce an approach based on minimizing a weighted…
Quantum algorithms for solving noisy linear problems are reexamined, under the same assumptions taken from the existing literature. The findings of this work include on the one hand extended applicability of the quantum Fourier transform to…
Demonstrating quantum advantage with less powerful but more realistic devices is of great importance in modern quantum information science. Recently, a significant quantum speedup was achieved in the problem of learning a hidden parity…
Signal detection in environments with unknown signal bandwidth and time intervals is a fundamental problem in adversarial and spectrum-sharing scenarios. This paper addresses the problem of detecting signals occupying unknown degrees of…
We use a combination of analytical and numerical techniques to calculate the noise threshold and resource requirements for a linear optical quantum computing scheme based on parity-state encoding. Parity-state encoding is used at the lowest…
In this work, we show, for the well-studied problem of learning parity under noise, where a learner tries to learn $x=(x_1,\ldots,x_n) \in \{0,1\}^n$ from a stream of random linear equations over $\mathrm{F}_2$ that are correct with…
We first consider the problem of learning $k$-parities in the on-line mistake-bound model: given a hidden vector $x \in \{0,1\}^n$ with $|x|=k$ and a sequence of "questions" $a_1, a_2, ...\in \{0,1\}^n$, where the algorithm must reply to…
We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an…
Correlation Clustering is a fundamental and widely-studied problem in unsupervised learning and data mining. The input is a graph and the goal is to construct a clustering minimizing the number of inter-cluster edges plus the number of…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
Answering a question of Haugland, we show that the pooling problem with one pool and a bounded number of inputs can be solved in polynomial time by solving a polynomial number of linear programs of polynomial size. We also give an overview…
Many consensus string problems are based on Hamming distance. We replace Hamming distance by the more flexible (e.g., easily coping with different input string lengths) dynamic time warping distance, best known from applications in time…
Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range $R$, and these instances can be referred to as the unbounded knapsack problem with bounded…
We study the problem of learning a mixture of two subspaces over $\mathbb{F}_2^n$. The goal is to recover the individual subspaces, given samples from a (weighted) mixture of samples drawn uniformly from the two subspaces $A_0$ and $A_1$.…