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Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition…
The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Gaussian processes (GPs) are a highly flexible, nonparametric statistical model that are commonly used to fit nonlinear relationships or account for correlation between observations. However, the computational load of fitting a Gaussian…
We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent…
In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori…
Despite empirical risk minimization (ERM) is widely applied in the machine learning community, its performance is limited on data with spurious correlation or subpopulation that is introduced by hidden attributes. Existing literature…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining…
Recent work has explored transforming data sets into smaller, approximate summaries in order to scale Bayesian inference. We examine a related problem in which the parameters of a Bayesian model are very large and expensive to store in…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
We give convergence guarantees for estimating the coefficients of a symmetric mixture of two linear regressions by expectation maximization (EM). In particular, we show that the empirical EM iterates converge to the target parameter vector…
In this contribution, we propose a generic online (also sometimes called adaptive or recursive) version of the Expectation-Maximisation (EM) algorithm applicable to latent variable models of independent observations. Compared to the…
Monte Carlo and Quasi-Monte Carlo methods present a convenient approach for approximating the expected value of a random variable. Algorithms exist to adaptively sample the random variable until a user defined absolute error tolerance is…
The expectation-maximization (EM) algorithm is a well-known iterative method for computing maximum likelihood estimates from incomplete data. Despite its numerous advantages, a main drawback of the EM algorithm is its frequently observed…
The Markov Chain Monte Carlo method is the dominant paradigm for posterior computation in Bayesian analysis. It is common to control computation time by making approximations to the Markov transition kernel. Comparatively little attention…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are objects of different types. One field of application of such models in biology is in studies of cell proliferation. A sampling scheme…
Modern computational advances have enabled easy parallel implementations of Markov chain Monte Carlo (MCMC). However, almost all work in estimating the variance of Monte Carlo averages, including the efficient batch means (BM) estimator,…
While optimizing convex objective (loss) functions has been a powerhouse for machine learning for at least two decades, non-convex loss functions have attracted fast growing interests recently, due to many desirable properties such as…
Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…