Related papers: Snell envelope with path dependent multiplicative …
Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we…
We propose a global optimization algorithm based on the Sequential Monte Carlo (SMC) sampling framework. In this framework, the objective function is normalized to be a probabilistic density function (pdf), based on which a sequence of…
We propose a semismooth Newton algorithm for pathwise optimization (SNAP) for the LASSO and Enet in sparse, high-dimensional linear regression. SNAP is derived from a suitable formulation of the KKT conditions based on Newton derivatives.…
Since the recent study (Krichene and Rendle 2020) done by Krichene and Rendle on the sampling-based top-k evaluation metric for recommendation, there has been a lot of debates on the validity of using sampling to evaluate recommendation…
The relaxed maximum entropy problem is concerned with finding a probability distribution on a finite set that minimizes the relative entropy to a given prior distribution, while satisfying relaxed max-norm constraints with respect to a…
Approximate inference in probability models is a fundamental task in machine learning. Approximate inference provides powerful tools to Bayesian reasoning, decision making, and Bayesian deep learning. The main goal is to estimate the…
Explaining complex or seemingly simple machine learning models is an important practical problem. We want to explain individual predictions from a complex machine learning model by learning simple, interpretable explanations. Shapley values…
A sampling method by using scattering amplitude is proposed for shape and location reconstruction in inverse acoustic scattering problems. Only matrix multiplication is involved in the computation, thus the novel sampling method is very…
Some of the issues that make sampling parameter spaces of various beyond the Standard Model (BSM) scenarios computationally expensive are the high dimensionality of the input parameter space, complex likelihoods, and stringent experimental…
Dimension reduction is an important tool for analyzing high-dimensional data. The predictor envelope is a method of dimension reduction for regression that assumes certain linear combinations of the predictors are immaterial to the…
In this paper we study the computation of the nonparametric maximum likelihood estimator (NPMLE) in multivariate mixture models. Our first approach discretizes this infinite dimensional convex optimization problem by fixing the support…
This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous…
We study a variant of the median problem for a collection of point sets in high dimensions. This generalizes the geometric median as well as the (probabilistic) smallest enclosing ball (pSEB) problems. Our main objective and motivation is…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
We first review existing sequential methods for estimating a binomial proportion. Afterward, we propose a new family of group sequential sampling schemes for estimating a binomial proportion with prescribed margin of error and confidence…
To tackle massive data, subsampling is a practical approach to select the more informative data points. However, when responses are expensive to measure, developing efficient subsampling schemes is challenging, and an optimal sampling…
We reconsider randomized algorithms for the low-rank approximation of symmetric positive semi-definite (SPSD) matrices such as Laplacian and kernel matrices that arise in data analysis and machine learning applications. Our main results…
We consider the geometric optics problem of finding a system of two reflectors that transform a spherical wavefront into a beam of parallel rays with prescribed intensity distribution. Using techniques from optimal transportation theory, it…
We define a class of reflected backward stochastic differential equation (RBSDE) driven by a marked point process (MPP) and a Brownian motion, where the solution is constrained to stay above a given c\`adl\`ag process. The MPP is only…
This article presents a new search algorithm for the NP-hard problem of optimizing functions of binary variables that decompose according to a graphical model. It can be applied to models of any order and structure. The main novelty is a…