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Much recent research has been conducted in the area of Bayesian learning, particularly with regard to the optimization of hyper-parameters via Gaussian process regression. The methodologies rely chiefly on the method of maximizing the…
Comparison of appropriate models to describe observational data is a fundamental task of science. The Bayesian model evidence, or marginal likelihood, is a computationally challenging, yet crucial, quantity to estimate to perform Bayesian…
Computation of the marginal likelihood from a simulated posterior distribution is central to Bayesian model selection but is computationally difficult. I argue that the marginal likelihood can be reliably computed from a posterior sample by…
Hamiltonian Monte Carlo (HMC) is a popular Markov Chain Monte Carlo (MCMC) algorithm to sample from an unnormalized probability distribution. A leapfrog integrator is commonly used to implement HMC in practice, but its performance can be…
Variational inference algorithms have proven successful for Bayesian analysis in large data settings, with recent advances using stochastic variational inference (SVI). However, such methods have largely been studied in independent or…
The task of estimating a matrix given a sample of observed entries is known as the \emph{matrix completion problem}. Most works on matrix completion have focused on recovering an unknown real-valued low-rank matrix from a random sample of…
Automatic algorithms attempt to provide approximate solutions that differ from exact solutions by no more than a user-specified error tolerance. This paper describes an automatic, adaptive algorithm for approximating the solution to a…
This paper studies transfer learning for estimating the mean of random functions based on discretely sampled data, where, in addition to observations from the target distribution, auxiliary samples from similar but distinct source…
A hybrid evolutionary algorithm with importance sampling method is proposed for multi-dimensional optimization problems in this paper. In order to make use of the information provided in the search process, a set of visited solutions is…
In this article we propose a new adaptive numerical quadrature procedure which includes both local subdivision of the integration domain, as well as local variation of the number of quadrature points employed on each subinterval. In this…
To infer the parameters of mechanistic models with intractable likelihoods, techniques such as approximate Bayesian computation (ABC) are increasingly being adopted. One of the main disadvantages of ABC in practical situations, however, is…
In this paper we address the widely-experienced difficulty in tuning Hamiltonian-based Monte Carlo samplers. We develop an algorithm that allows for the adaptation of Hamiltonian and Riemann manifold Hamiltonian Monte Carlo samplers using…
Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling.…
Approximate Bayesian computation performs approximate inference for models where likelihood computations are expensive or impossible. Instead simulations from the model are performed for various parameter values and accepted if they are…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…
Adaptive importance sampling is a powerful tool to sample from complicated target densities, but its success depends sensitively on the initial proposal density. An algorithm is presented to automatically perform the initialization using…
Suppose that a mobile sensor describes a Markovian trajectory in the ambient space. At each time the sensor measures an attribute of interest, e.g., the temperature. Using only the location history of the sensor and the associated…