Related papers: Linear Regression by Quantum Amplitude Estimation …
As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the…
We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
Sparse linear regression, which entails finding a sparse solution to an underdetermined system of linear equations, can formally be expressed as an $l_0$-constrained least-squares problem. The Orthogonal Least-Squares (OLS) algorithm…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…
Quantum Annealing (QA) is a computational framework where a quantum system's continuous evolution is used to find the global minimum of an objective function over an unstructured search space. It can be seen as a general metaheuristic for…
We previously established that in principle, it is possible to quantum compute using passive linear optics with photo-detectors (quant-ph/0006088). Here we describe techniques based on error detection and correction that greatly improve the…
Penalized quantile regression (QR) is widely used for studying the relationship between a response variable and a set of predictors under data heterogeneity in high-dimensional settings. Compared to penalized least squares, scalable…
This paper considers a distributed stochastic strongly convex optimization, where agents connected over a network aim to cooperatively minimize the average of all agents' local cost functions. Due to the stochasticity of gradient estimation…
Many classical and modern machine learning algorithms require solving optimization tasks under orthogonality constraints. Solving these tasks with feasible methods requires a gradient descent update followed by a retraction operation on the…
There are many practical applications based on the Least Square Error (LSE) approximation. It is based on a square error minimization 'on a vertical' axis. The LSE method is simple and easy also for analytical purposes. However, if data…
We consider the on-line predictive version of the standard problem of linear regression; the goal is to predict each consecutive response given the corresponding explanatory variables and all the previous observations. We are mainly…
We propose a computationally efficient estimator, formulated as a convex program, for a broad class of non-linear regression problems that involve difference of convex (DC) non-linearities. The proposed method can be viewed as a significant…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
Consider a regression problem where the learner is given a large collection of $d$-dimensional data points, but can only query a small subset of the real-valued labels. How many queries are needed to obtain a $1+\epsilon$ relative error…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Hybrid variational quantum algorithms are promising for solving practical problems, such as combinatorial optimization, quantum chemistry simulation, quantum machine learning, and quantum error correction on noisy quantum computers.…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…