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Building on the successes of local kernel methods for approximating the solutions to partial differential equations (PDE) and the evaluation of definite integrals (quadrature/cubature), a local estimate of the error in such approximations…

This paper is concerned with the linear/nonlinear Kalman-like filtering problem under binary sensors. Since innovation represents new information in the sensor measurement and serves to correct the prediction for the Kalman-like filter…

The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…

We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…

The robust adjustment of nonlinear models to data is considered in this paper. When data comes from real experiments, it is possible that measurement errors cause the appearance of discrepant values, which should be ignored when adjusting…

Probabilistic Logic Programming (PLP) languages enable programmers to specify systems that combine logical models with statistical knowledge. The inference problem, to determine the probability of query answers in PLP, is intractable in…

We present an efficient approach to simulate real-time quantum dynamics using Projected Variational Quantum Dynamics (PVQD), where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at…

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that $t\to X_t$ is a Markov process and we wish to calculate the measure-valued process…

We investigate the problem of best-policy identification in discounted Markov Decision Processes (MDPs) when the learner has access to a generative model. The objective is to devise a learning algorithm returning the best policy as early as…

Variational quantum algorithms (VQAs) provide a promising approach to achieving quantum advantage for practical problems on near-term noisy intermediate-scale quantum (NISQ) devices. Thus far, most studies on VQAs have focused on…

We investigate the performance of a class of particle filters (PFs) that can automatically tune their computational complexity by evaluating online certain predictive statistics which are invariant for a broad class of state-space models.…

Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…

Filtering and smoothing algorithms for linear discrete-time state-space models with skew-t-distributed measurement noise are proposed. The algorithms use a variational Bayes based posterior approximation with coupled location and skewness…

We study high-dimensional covariance/precision matrix estimation under the assumption that the covariance/precision matrix can be decomposed into a low-rank component L and a diagonal component D. The rank of L can either be chosen to be…

K-fold cross validation (CV) is a popular method for estimating the true performance of machine learning models, allowing model selection and parameter tuning. However, the very process of CV requires random partitioning of the data and so…

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…

A likelihood-based reconstruction algorithm for arbitrary event topologies is introduced and, as an example, applied to the single-lepton decay mode of top-quark pair production. The algorithm comes with several options which further…

We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…