Related papers: Average-case analysis of the Gaussian Elimination …
We investigate the quality of space approximation of a class of stochastic integral equations of convolution type with Gaussian noise. Such equations arise, for example, when considering mild solutions of stochastic fractional order partial…
This study investigates the effectiveness of Genetic Algorithms (GAs) in solving both linear and nonlinear systems of equations, comparing their performance to traditional methods such as Gaussian Elimination, Newton's Method, and…
We introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and…
We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar implicit regularization to gradient descent. This implicit…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy…
The Set Cover problem (SCP) and Set Packing problem (SPP) are standard NP-hard combinatorial optimization problems. Their decision problem versions are shown to be NP-Complete in Karp's 1972 paper. We specify a rough guide to constructing…
A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can…
Although machine learning is increasingly applied in control approaches, only few methods guarantee certifiable safety, which is necessary for real world applications. These approaches typically rely on well-understood learning algorithms,…
We revisit the problem of robust linear regression under Gaussian covariates with an unknown covariance matrix of condition number $\kappa$. For this fundamental problem, significant gaps remain in our understanding of the trade-offs among…
Grammatical Evolution (GE) is one of the most popular Genetic Programming (GP) variants, and it has been used with success in several problem domains. Since the original proposal, many enhancements have been proposed to GE in order to…
The graph partitioning problem (GPP) is among the most challenging models in optimization. Because of its NP-hardness, the researchers directed their interest towards approximate methods such as the genetic algorithms (GA). The edge-based…
We study the general scheduling problem (GSP) which generalizes and unifies several well-studied preemptive single-machine scheduling problems, such as weighted flow time, weighted sum of completion time, and minimizing the total weight of…
This article presents a rigorous analysis for efficient statistically accurate algorithms for solving the Fokker-Planck equations associated with high-dimensional nonlinear turbulent dynamical systems with conditional Gaussian structures.…
Grover's search algorithm is the cornerstone of many applications of quantum computing, providing a quadratic speed-up over classical methods. One limitation of the algorithm is that it requires knowledge of the number of solutions to…
This paper deals with a method for solving Poisson Equation (PE) based on genetic algorithms and grammatical evolution. The method forms generations of solutions expressed in an analytical form. Several examples of PE are tested and in most…
In this paper, we consider a classic problem concerning the high excursion probabilities of a Gaussian random field $f$ living on a compact set $T$. We develop efficient computational methods for the tail probabilities $P(\sup_T f(t) > b)$…
Gaussian processes are the gold standard for many real-world modeling problems, especially in cases where a model's success hinges upon its ability to faithfully represent predictive uncertainty. These problems typically exist as parts of…
We study polynomial time algorithms for estimating the mean of a heavy-tailed multivariate random vector. We assume only that the random vector $X$ has finite mean and covariance. In this setting, the radius of confidence intervals achieved…
Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…