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We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…

In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…

We study the problem of stochastic combinatorial pure exploration (CPE), where an agent sequentially pulls a set of single arms (a.k.a. a super arm) and tries to find the best super arm. Among a variety of problem settings of the CPE, we…

Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…

Recovering a signal (function) from finitely many binary or Fourier samples is one of the core problems in modern medical imaging, and by now there exist a plethora of methods for recovering a signal from such samples. Examples of methods,…

We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…

We present a new algorithm for solving a polynomial program P based on the recent "joint + marginal" approach of the first author for, parametric optimization. The idea is to first consider the variable x1 as a parameter and solve the…

Probabilistic circuits (PCs) such as sum-product networks efficiently represent large multi-variate probability distributions. They are preferred in practice over other probabilistic representations such as Bayesian and Markov networks…

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However for data sets where…

We propose a novel exemplar selection approach based on Principal Component Analysis (PCA) and median sampling, and a neural network training regime in the setting of class-incremental learning. This approach avoids the pitfalls due to…

Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…

Inference in general Markov random fields (MRFs) is NP-hard, though identifying the maximum a posteriori (MAP) configuration of pairwise MRFs with submodular cost functions is efficiently solvable using graph cuts. Marginal inference,…

Network telemetry is a key capability for managing the health and efficiency of a large-scale network. Alternate Marking Performance Measurement (AM-PM) is a recently introduced approach that accurately measures the packet loss and delay in…

A method of prediction is presented to aid compression of sequences of complex-valued samples. The focus is on using prediction to reduce the average magnitude of residual values after prediction (not on the subsequent compression of the…

In-memory associative processor architectures are offered as a great candidate to overcome memory-wall bottleneck and to enable vector/parallel arithmetic operations. In this paper, we extend the functionality of the associative processor…

In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…

We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…

In many high-dimensional problems,polynomial-time algorithms fall short of achieving the statistical limits attainable without computational constraints. A powerful approach to probe the limits of polynomial-time algorithms is to study the…

The POMDP is a powerful framework for reasoning under outcome and information uncertainty, but constructing an accurate POMDP model is difficult. Bayes-Adaptive Partially Observable Markov Decision Processes (BA-POMDPs) extend POMDPs to…