Related papers: Kernel embedding of maps for sequential Bayesian i…
We consider Bayesian inference in sequential latent variable models in general, and in nonlinear state space models in particular (i.e., state smoothing). We work with sequential Monte Carlo (SMC) algorithms, which provide a powerful…
Hamiltonian Monte Carlo is a widely used algorithm for sampling from posterior distributions of complex Bayesian models. It can efficiently explore high-dimensional parameter spaces guided by simulated Hamiltonian flows. However, the…
Optimization in the Bures-Wasserstein space has been gaining popularity in the machine learning community since it draws connections between variational inference and Wasserstein gradient flows. The variational inference objective function…
Particle filters are broadly used to approximate posterior distributions of hidden states in state-space models by means of sets of weighted particles. While the convergence of the filter is guaranteed when the number of particles tends to…
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior…
Sequential Monte Carlo methods are typically not straightforward to implement on parallel architectures. This is because standard resampling schemes involve communication between all particles. The $\alpha$-sequential Monte Carlo method was…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…
The particle filter (PF), also known as sequential Monte Carlo (SMC), approximates high-dimensional probability distributions and their normalizing constants in the discrete-time setting. To reduce the variance of the Monte Carlo…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…
Over the years, sequential Monte Carlo (SMC) and, equivalently, particle filter (PF) theory has gained substantial attention from researchers. However, the performance of the resampling methodology, also known as offspring selection, has…
This work proposed kernel selection approaches for probabilistic classifiers based on features produced by the convolutional encoder of a variational autoencoder. Particularly, the developed methodologies allow the selection of the most…
We consider the generic problem of performing sequential Bayesian inference in a state-space model with observation process y, state process x and fixed parameter theta. An idealized approach would be to apply the iterated batch importance…
Information-theoretic measures such as the entropy, cross-entropy and the Kullback-Leibler divergence between two mixture models is a core primitive in many signal processing tasks. Since the Kullback-Leibler divergence of mixtures provably…
We propose a divide-and-conquer approach to filtering which decomposes the state variable into low-dimensional components to which standard particle filtering tools can be successfully applied and recursively merges them to recover the full…
Sequential Monte Carlo (SMC) algorithms were originally designed for estimating intractable conditional expectations within state-space models, but are now routinely used to generate approximate samples in the context of general-purpose…
We design a sequential Monte Carlo scheme for the dual purpose of Bayesian inference and model selection. We consider the application context of urban mobility, where several modalities of transport and different measurement devices can be…
This study tackles the efficient estimation of Kullback-Leibler (KL) Divergence in Dirichlet Mixture Models (DMM), crucial for clustering compositional data. Despite the significance of DMMs, obtaining an analytically tractable solution for…
In simulation-based inferences for partially observed Markov process models (POMP), the by-product of the Monte Carlo filtering is an approximation of the log likelihood function. Recently, iterated filtering [14, 13] has originally been…
This paper addresses the problem of summarizing the posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with unknown number of components. Such posterior distributions are…