Related papers: Parallel cross interpolation for high-precision ca…
Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…
An extremely common bottleneck encountered in statistical learning algorithms is inversion of huge covariance matrices, examples being in evaluating Gaussian likelihoods for a large number of data points. We propose general parallel…
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution…
Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…
In this work, we propose a novel cross Q-learning algorithm, aim at alleviating the well-known overestimation problem in value-based reinforcement learning methods, particularly in the deep Q-networks where the overestimation is exaggerated…
A number of applications require the computation of the trace of a matrix that is implicitly available through a function. A common example of a function is the inverse of a large, sparse matrix, which is the focus of this paper. When the…
The variational quantum Monte Carlo (VQMC) method received significant attention in the recent past because of its ability to overcome the curse of dimensionality inherent in many-body quantum systems. Close parallels exist between VQMC and…
Matrix multiplication is integral to various scientific and engineering disciplines, including machine learning, image processing, and gaming. With the increasing data volumes in areas like machine learning, the demand for efficient…
This article introduces a new fast direct solver for linear systems arising out of wide range of applications, integral equations, multivariate statistics, radial basis interpolation, etc., to name a few. \emph{The highlight of this new…
Monte Carlo methods play a central role in particle physics, where they are indispensable for simulating scattering processes, modeling detector responses, and performing multi-dimensional integrals. However, traditional Monte Carlo methods…
This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…
A fully Bayesian approach is proposed for ultrahigh-dimensional nonparametric additive models in which the number of additive components may be larger than the sample size, though ideally the true model is believed to include only a small…
This paper proposes a new method for estimating sparse precision matrices in the high dimensional setting. It has been popular to study fast computation and adaptive procedures for this problem. We propose a novel approach, called Sparse…
Using detailed exact results on pair-correlation functions of Z-invariant Ising models, we can write and run algorithms of polynomial complexity to obtain wavevector-dependent susceptibilities for a variety of Ising systems. Reviewing…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
Recent advances in meta-optics have enabled diverse functionalities in compact optical devices; however, conventional forward design approaches become inadequate as device complexity and scale grow. Inverse design offers a powerful…
We present a general-purpose algorithm to extrapolate a low rank function of two variables from a small domain to a larger one. It is based on the cross-interpolation formula. We apply it to reconstruct physical quantities in some quantum…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC.…