Related papers: Fixed-Form Variational Posterior Approximation thr…
In this paper, a Bayesian inference technique based on Taylor series approximation of the logarithm of the likelihood function is presented. The proposed approximation is devised for the case, where the prior distribution belongs to the…
We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…
We propose algorithms to approximate directed information graphs. Directed information graphs are probabilistic graphical models that depict causal dependencies between stochastic processes in a network. The proposed algorithms identify…
This paper concerns the approximation of probability measures on $\mathbf{R}^d$ with respect to the Kullback-Leibler divergence. Given an admissible target measure, we show the existence of the best approximation, with respect to this…
Stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
The PAC-Bayesian approach is a powerful set of techniques to derive non- asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately intractable.…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Bayesian decision theory provides an elegant framework for acting optimally under uncertainty when tractable posterior distributions are available. Modern Bayesian models, however, typically involve intractable posteriors that are…
Bayesian inference allows machine learning models to express uncertainty. Current machine learning models use only a single learnable parameter combination when making predictions, and as a result are highly overconfident when their…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…
This paper deals with a method for the approximation of a spectral density function among the solutions of a generalized moment problem a` la Byrnes/Georgiou/Lindquist. The approximation is pursued with respect to the Kullback-Leibler…
We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear…
An initial screening experiment may lead to ambiguous conclusions regarding the factors which are active in explaining the variation of an outcome variable: thus adding follow-up runs becomes necessary. We propose a fully Bayes objective…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
We empirically evaluate a stochastic annealing strategy for Bayesian posterior optimization with variational inference. Variational inference is a deterministic approach to approximate posterior inference in Bayesian models in which a…
We study Gaussian approximations to the distribution of a diffusion. The approximations are easy to compute: they are defined by two simple ordinary differential equations for the mean and the covariance. Time correlations can also be…