Related papers: Complexity Analysis of Normalizing Constant Estima…
Importance sampling is a popular technique in Bayesian inference: by reweighting samples drawn from a proposal distribution we are able to obtain samples and moment estimates from a Bayesian posterior over latent variables. Recent work,…
The weighting of critical-point samples in the weighted randomized maximum likelihood method depend on the magnitude of the data mismatch at the critical points and on the Jacobian of the transformation from the prior density to the…
We study the problem of overcoming exponential sample complexity in differential entropy estimation under Gaussian convolutions. Specifically, we consider the estimation of the differential entropy $h(X+Z)$ via $n$ independently and…
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…
Bayesian nonparametric mixture models are widely used to cluster observations. However, one major drawback of the approach is that the estimated partition often presents unbalanced clusters' frequencies with only a few dominating clusters…
Importance sampling has been known as a powerful tool to reduce the variance of Monte Carlo estimator for rare event simulation. Based on the criterion of minimizing the variance of Monte Carlo estimator within a parametric family, we…
In real-world Bayesian inference applications, prior assumptions regarding the parameters of interest may be unrepresentative of their actual values for a given dataset. In particular, if the likelihood is concentrated far out in the wings…
Developing satisfactory methodology for the analysis of Markov random field is a very challenging task. Indeed, due to the Markovian dependence structure, the normalizing constant of the fields cannot be computed using standard analytical…
This paper describes a method for estimating the marginal likelihood or Bayes factors of Bayesian models using non-parametric importance sampling ("arrogance sampling"). This method can also be used to compute the normalizing constant of…
We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
Inference for models with recursively defined likelihoods is computationally demanding, limiting scalability to large datasets. We propose a stabilised weighted subsampling methodology for accelerated inference based on an unbiased…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
There are many models, often called unnormalized models, whose normalizing constants are not calculated in closed form. Maximum likelihood estimation is not directly applicable to unnormalized models. Score matching, contrastive divergence…
We investigate the utility to computational Bayesian analyses of a particular family of recursive marginal likelihood estimators characterized by the (equivalent) algorithms known as "biased sampling" or "reverse logistic regression" in the…
Recently a new algorithm for sampling posteriors of unnormalised probability densities, called ABC Shadow, was proposed in [8]. This talk introduces a global optimisation procedure based on the ABC Shadow simulation dynamics. First the…
The Jarzynski estimator is a powerful tool that uses nonequilibrium statistical physics to numerically obtain partition functions of probability distributions. The estimator reconstructs partition functions with trajectories of the…
The generalized Rosenzweig-Porter model with real (GOE) off-diagonal entries arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first…
Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…
Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, Bayesian model selection requires the computation of the marginal…