23 accepted papers
Sampling from a distribution $p(x) \propto e^{-\mathcal{E}(x)}$ known up to a normalising constant is an important and challenging problem in statistics. Recent years have seen the rise of a new family of amortised sampling algorithms, commonly referred to as diffusion samplers, that enable fast and…
Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applications. When no ground-truth trajectories are available, but one has only snapshots of data taken at discrete time steps, the problem of modelling the dyna…
This paper proposes a synergy of amortised and particle-based methods for sampling from distributions defined by unnormalised density functions. We state a connection between sequential Monte Carlo (SMC) and neural sequential samplers trained by maximum-entropy reinforcement learning (MaxEnt RL), wh…
State-space models are a statistical framework for modelling temporal phenomena via a hidden state. In this framework, the hidden state is not observed, and instead a series of related observations are obtained. A state-space model is defined by the state dynamics, which is encoded as a distribution…
Mixture variational distributions in black box variational inference (BBVI) have demonstrated impressive results in challenging density estimation tasks. However, currently scaling the number of mixture components can lead to a linear increase in the number of learnable parameters and a quadratic in…
We introduce a new method, named PropMixNN, that uses a neural network to learn the proposal distribution of a particle filter. The optimal proposal distribution is approximated as a multivariate Gaussian mixture, so the proposed method aims at learning the means and covariance matrices of the S com…
State-space models (SSMs) are common tools in time-series analysis for inference and prediction. SSMs are versatile probabilistic models that allow for Bayesian inference by describing a (generally Markovian) latent process. However, the parameters of that latent process are often unknown and must b…
We cast the resampling step in particle filters (PFs) as a variational inference problem, resulting in a new class of resampling schemes: variational resampling. Variational resampling is flexible as it allows for choices of 1) divergence to minimize, 2) target distribution to input to the divergenc…
We introduce the adaptive Gaussian nested filter (AGNesF), the first nested method that adapts the number of samples to estimate both the static parameters and the dynamical variables of a state-space model. The proposed method is based on the nested Gaussian filter (NGF), that combines two layers o…
Simulated annealing is a popular approach to solve nonconvex and black-box optimization problems. It consists in running a non-homogeneous Markov chain to sample from a sequence of Boltzmann probability distributions. This sequence is controlled by a cooling schedule, which governs the concentration…
Bayesian filtering is an approach to the inference problem for state-space models (SSM), arising in many disciplines of science and engineering. The well known Gaussian filters tackle the problem using Gaussian approximations of the distributions of the hidden state in the model. Gaussian filters ho…
In this paper, we show how the mixture components cooperate when they jointly adapt to maximize the ELBO. We build upon recent advances in the multiple and adaptive importance sampling literature. We then model the mixture components using separate encoder networks and show empirically that the ELBO…
State-space models (SSMs) are a common tool for modeling multi-variate discrete-time signals. The linear-Gaussian (LG) SSM is widely applied as it allows for a closed-form solution at inference, if the model parameters are known. However, they are rarely available in real-world problems and must be…
Change-point detection methods are widely used in signal processing, primarily for detecting and locating changes in a considered model. An important family of algorithms for this problem relies on the likelihood ratio (LR) test. In state-space models (SSMs), the time series is modeled through a Mar…
Simulated annealing (SA) is a widely used approach to solve global optimization problems in signal processing. The initial non-convex problem is recast as the exploration of a sequence of Boltzmann probability distributions, which are increasingly harder to sample from. They are parametrized by a te…
Auxiliary particle filters (APFs) are a class of sequential Monte Carlo (SMC) methods for Bayesian inference in state-space models. In their original derivation, APFs operate in an extended state space using an auxiliary variable to improve inference. In this work, we propose
Modeling and inference with multivariate sequences is central in a number of signal processing applications such as acoustics, social network analysis, biomedical, and finance, to name a few. The linear-Gaussian state-space model is a common way to describe a time series through the evolution of a h…
Monte Carlo (MC) algorithms are widely used for Bayesian inference in statistics, signal processing, and machine learning. In this work, we introduce an Markov Chain Monte Carlo (MCMC) technique driven by a particle filter. The resulting scheme is a generalization of the so-called Particle Metropoli…
Population Monte Carlo (PMC) algorithms are a family of adaptive importance sampling (AIS) methods for approximating integrals in Bayesian inference. In this paper, we propose a novel PMC algorithm that combines recent advances in the AIS and the optimization literatures. In such a way, the proposal…
Monte Carlo (MC) methods are widely used in signal processing and machine learning. A well-known class of MC methods is composed of importance sampling and its adaptive extensions (e.g., population Monte Carlo). In this paper, we introduce an adaptive importance sampler using a population of proposa…
We introduce a probabilistic approach to the LMS filter. By means of an efficient approximation, this approach provides an adaptable step-size LMS algorithm together with a measure of uncertainty about the estimation. In addition, the proposed approximation preserves the linear complexity of the sta…
In many practical scenarios, including those dealing with large data sets, calculating global estimators of unknown variables of interest becomes unfeasible. A common solution is obtaining partial estimators and combining them to approximate the global one. In this paper, we focus on minimum mean sq…
Monte Carlo (MC) methods are useful tools for Bayesian inference and stochastic optimization that have been widely applied in signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacti…