Related papers: Quantum Algorithms for the Pathwise Lasso
Quantitative susceptibility mapping (QSM) involves acquisition and reconstruction of a series of images at multi-echo time points to estimate tissue field, which prolongs scan time and requires specific reconstruction technique. In this…
In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave…
Linear regression is a popular machine learning approach to learn and predict real valued outputs or dependent variables from independent variables or features. In many real world problems, its beneficial to perform sparse linear regression…
The least absolute shrinkage and selection operator (lasso) and ridge regression produce usually different estimates although input, loss function and parameterization of the penalty are identical. In this paper we look for ridge and lasso…
Logistic regression, the Support Vector Machine (SVM), and least squares are well-studied methods in the statistical and computer science community, with various practical applications. High-dimensional data arriving on a real-time basis…
We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…
We derive a family of efficient constrained dynamics algorithms by formulating an equivalent linear quadratic regulator (LQR) problem using Gauss principle of least constraint and solving it using dynamic programming. Our approach builds…
We propose an innovative Parallel Quantum Local Search (PQLS) methodology that leverages the capabilities of small-scale quantum computers to efficiently address complex combinatorial optimization problems. Traditional Quantum Local Search…
Following the breakthrough work of Tardos in the bit-complexity model, Vavasis and Ye gave the first exact algorithm for linear programming in the real model of computation with running time depending only on the constraint matrix. For…
We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to…
We achieve a quantum speed-up of fully polynomial randomized approximation schemes (FPRAS) for estimating partition functions that combine simulated annealing with the Monte-Carlo Markov Chain method and use non-adaptive cooling schedules.…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer.…
Continuous-time quantum walks provide a natural framework to tackle the fundamental problem of finding a node among a set of marked nodes in a graph, known as spatial search. Whether spatial search by continuous-time quantum walk provides a…
Over the past few years several quantum machine learning algorithms were proposed that promise quantum speed-ups over their classical counterparts. Most of these learning algorithms either assume quantum access to data -- making it unclear…
Covariance graphical lasso applies a lasso penalty on the elements of the covariance matrix. This method is useful because it not only produces sparse estimation of covariance matrix but also discovers marginal independence structures by…
The classical iteratively reweighted least-squares (IRLS) algorithm aims to recover an unknown signal from linear measurements by performing a sequence of weighted least squares problems, where the weights are recursively updated at each…
Quantum machine learning has the potential for broad industrial applications, and the development of quantum algorithms for improving the performance of neural networks is of particular interest given the central role they play in machine…