Latent variable analysis of causal interactions in atrial fibrillation electrograms

Multi-channel intracardiac electrocardiograms of atrial fibrillation (AF) patients are acquired at the electrophysiology laboratory in order to guide radiofrequency (RF) ablation surgery. Unfortunately, the success rate of RF ablation is still moderate, since the mechanisms underlying AF initiation and maintenance are still not precisely known. In this paper, we use an advanced machine learning model, the Gaussian process latent force model (GP-LFM), to infer the relationship between the observed signals and the unknown (latent or exogenous) sources causing them. The resulting GP-LFM provides valuable information about signal generation and propagation inside the heart, and can then be used to perform causal analysis. Results on realistic synthetic signals, generated using the FitzHugh-Nagumo model, are used to showcase the potential of the proposed approach

An efficient sampling scheme for the eigenvalues of dual wishart matrices

Despite the numerous results in the literature about the eigenvalue distributions of Wishart matrices, the existing closed-form probability density function (pdf) expressions do not allow for efficient sampling schemes from such densities. In this letter, we present a stochastic representation for the eigenvalues of 2×2 complex central uncorrelated Wishart matrices with an arbitrary number of degrees of freedom (referred to as dual Wishart matrices). The draws from the joint pdf of the eigenvalues are generated by means of a simple transformation of a chi-squared random variable and an independent beta random variable. Moreover, this stochastic representation allows a simple derivation, alternative to those already existing in the literature, of some eigenvalue function distributions such as the condition number or the ratio of the maximum eigenvalue to the trace of the matrix. The proposed sampling scheme may be of interest in wireless communications and multivariate statistical analysis, where Wishart matrices play a central role.The work of Ignacio Santamaria was supported in part by the Ministerio de Ciencia e Innovación and AEI/10.13039/501100011033, under Grant PID2019-104958RB-C43 (ADELE). The work of Víctor Elvira was supported in part by the Agence Nationale de la Recherche of France PISCES under Grant ANR-17-CE40-0031-01, and in part by the ARL/ARO under Grant W911NF-20-1-0126

Efficient SER estimation for MIMO detectors via importance sampling schemes

In this paper we propose two importance sampling methods for the efficient symbol error rate (SER) estimation of maximum likelihood (ML) multiple-input multiple-output (MIMO) detectors. Conditioned to a given transmitted symbol, computing the SER requires the evaluation of an integral outside a given polytope in a high-dimensional space, for which a closed-form solution does not exist. Therefore, Monte Carlo (MC) simulation is typically used to estimate the SER, although a naive or raw MC implementation can be very inefficient at high signal-to-noise-ratios or for systems with stringent SER requirements. A reduced variance estimator is provided by the Truncated Hypersphere Importance Sampling (THIS) method, which samples from a proposal density that excludes the largest hypersphere circumscribed within the Voronoi region of the transmitted vector. A much more efficient estimator is provided by the existing ALOE (which stands for "At Least One rare Event") method, which samples conditionally on an error taking place. The paper describes in detail these two IS methods, discussing their advantages and limitations, and comparing their performances.The work of V. Elvira was partially supported by Agence Nationale de la Recherche of France under PISCES project (ANR-17-CE40-0031-01) and the French-American Fulbright Commission. The work of I. Santamaria was partly supported by the Ministerio de Econom´ıa y Competitividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., under grant TEC2016-75067-C4-4-R (CARMEN)

Adapting the number of particles in sequential Monte Carlo methods through an online scheme for convergence assessment

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 infinity, the quality of the approximation is usually unknown but strongly dependent on the number of particles. In this paper, we propose a novel method for assessing the convergence of particle filters in an online manner, as well as a simple scheme for the online adaptation of the number of particles based on the convergence assessment. The method is based on a sequential comparison between the actual observations and their predictive probability distributions approximated by the filter. We provide a rigorous theoretical analysis of the proposed methodology and, as an example of its practical use, we present simulations of a simple algorithm for the dynamic and online adaptation of the number of particles during the operation of a particle filter on a stochastic version of the Lorenz 63 system.This work was supported in part by the Ministerio de Economía y Competitividad of Spain under Grant TEC2013-41718-R OTOSiS, Grant TEC2012-38883-C02-01 COMPREHENSION, and Grant TEC2015-69868-C2-1-R ADVENTURE, in part by the Office of Naval Research Global under Grant N62909-15-1-2011, and in part by the National Science Foundation under Grant CCF-1320626 and Grant CCF-1618999

An adaptive population importance sampler

Monte Carlo (MC) methods are widely used in signal processing, machine learning and communications for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling and its adaptive extensions (e.g., population Monte Carlo). In this work, we introduce an adaptive importance sampler using a population of proposal densities. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples generated. The cloud of proposals is adapted by learning from a subset of previously generated samples, in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error and robustness to initialization

Causality analysis of atrial fibrillation electrograms

Proceeding of 2015 Computing in Cardiology Conference (CinC 2015), September 6-9, 2015, Nice, FranceMulti-channel intracardiac electrocardiograms (electrograms) are sequentially acquired during heart surgery performed on patients with sustained atrial fibrillation (AF) to guide radio frequency catheter ablation. These electrograms are used by cardiologists to determine candidate areas for ablation (e.g., areas corresponding to high dominant frequencies or complex electrograms). In this paper, we introduce a novel hierarchical causality analysis method for the multi-output sequentially acquired electrograms. The causal model obtained provides important information regarding delays among signals as well as the direction and strength of their causal connections. The tool developed may ultimately serve to guide cardiologists towards candidate areas for catheter ablation. Preliminary results on synthetic signals are used to validate the proposed approach.This work has been supported by the Spanish government’s projects ALCIT (TEC2012-38800-C03-01), AGES (S2010/BMD-2422), and OTOSiS (TEC2013-41718-R), and COMPREHENSION (TEC2012-38883-C02-01). D. Luengo has also been funded by the BBVA Foundation’s “I Convocatoria de Ayudas Fundación BBVA a Investigadores, Innovadores y Creadores Culturales”.Publicad

MCMC-driven importance samplers

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of layered adaptive importance sampling algorithms, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of the layered adaptive importance sampling scheme allows for different possible implementations, yielding a variety of different performances and computational costs. In this work, we propose different enhancements of the classical layered adaptive importance sampling setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments show the benefits of the proposed schemes, comparing with benchmark methods presented in the literature, and in several challenging scenarios

Pattern localization in time series through signal-to-model alignment in latent space

In this paper, we study the problem of locating a predefined sequence of patterns in a time series. In particular, the studied scenario assumes a theoretical model is available that contains the expected locations of the patterns. This problem is found in several contexts, and it is commonly solved by first synthesizing a time series from the model, and then aligning it to the true time series through dynamic time warping. We propose a technique that increases the similarity of both time series before aligning them, by mapping them into a latent correlation space. The mapping is learned from the data through a machine-learning setup. Experiments on data from nondestructive testing demonstrate that the proposed approach shows significant improvements over the state of the art.The work of Steven Van Vaerenbergh was supported by the Ministerio de Economía, Industria y Competitividad (MINECO) of Spain under grant TEC2014-57402-JIN (PRISMA). The work of Víctor Elvira was supported by the Agence Nationale de la Recherche of France under PISCES project (ANR-17-CE40-0031-01)

Orthogonal MCMC algorithms

Monte Carlo (MC) methods are widely used in signal processing, machine learning and stochastic optimization. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce a novel parallel interacting MCMC scheme, where the parallel chains share information using another MCMC technique working on the entire population of current states. These parallel ?vertical? chains are led by random-walk proposals, whereas the ?horizontal? MCMC uses a independent proposal, which can be easily adapted by making use of all the generated samples. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error, as well as robustness w.r.t. to initial values and parameter choice