Conditional Deep Gaussian Processes: Empirical Bayes Hyperdata Learning

It is desirable to combine the expressive power of deep learning with Gaussian Process (GP) in one expressive Bayesian learning model. Deep kernel learning showed success as a deep network used for feature extraction. Then, a GP was used as the function model. Recently, it was suggested that, albeit training with marginal likelihood, the deterministic nature of a feature extractor might lead to overfitting, and replacement with a Bayesian network seemed to cure it. Here, we propose the conditional deep Gaussian process (DGP) in which the intermediate GPs in hierarchical composition are supported by the hyperdata and the exposed GP remains zero mean. Motivated by the inducing points in sparse GP, the hyperdata also play the role of function supports, but are hyperparameters rather than random variables. It follows our previous moment matching approach to approximate the marginal prior for conditional DGP with a GP carrying an effective kernel. Thus, as in empirical Bayes, the hyperdata are learned by optimizing the approximate marginal likelihood which implicitly depends on the hyperdata via the kernel. We show the equivalence with the deep kernel learning in the limit of dense hyperdata in latent space. However, the conditional DGP and the corresponding approximate inference enjoy the benefit of being more Bayesian than deep kernel learning. Preliminary extrapolation results demonstrate expressive power from the depth of hierarchy by exploiting the exact covariance and hyperdata learning, in comparison with GP kernel composition, DGP variational inference and deep kernel learning. We also address the non-Gaussian aspect of our model as well as way of upgrading to a full Bayes inference.

EBCR: Empirical Bayes concordance ratio method to improve similarity measurement in memory-based collaborative filtering

Recommender systems aim to provide users with a selection of items, based on predicting their preferences for items they have not yet rated, thus helping them filter out irrelevant ones from a large product catalogue. Collaborative filtering is a widely used mechanism to predict a particular user’s interest in a given item, based on feedback from neighbour users with similar tastes. The way the user’s neighbourhood is identified has a significant impact on prediction accuracy. Most methods estimate user proximity from ratings they assigned to co-rated items, regardless of their number. This paper introduces a similarity adjustment taking into account the number of co-ratings. The proposed method is based on a concordance ratio representing the probability that two users share the same taste for a new item. The probabilities are further adjusted by using the Empirical Bayes inference method before being used to weight similarities. The proposed approach improves existing similarity measures without increasing time complexity and the adjustment can be combined with all existing similarity measures. Experiments conducted on benchmark datasets confirmed that the proposed method systematically improved the recommender system’s prediction accuracy performance for all considered similarity measures.

Oscillatory Biomedical Signals: Frontiers in Mathematical Models and Statistical Analysis

Herein we describe new frontiers in mathematical modeling and statistical analysis of oscillatory biomedical signals, motivated by our recent studies of network formation in the human brain during the early stages of life and studies forty years ago on cardiorespiratory patterns during sleep in infants and animal models. The frontiers involve new nonlinear-type time–frequency analysis of signals with multiple oscillatory components, and efficient particle filters for joint state and parameter estimators together with uncertainty quantification in hidden Markov models and empirical Bayes inference.

Rhinovirus prevalence as indicator for efficacy of measures against SARS-CoV-2

Background Non-pharmaceutical measures to control the spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) should be carefully tuned as they can impose a heavy social and economic burden. To quantify and possibly tune the efficacy of these anti-SARS-CoV-2 measures, we have devised indicators based on the abundant historic and current prevalence data from other respiratory viruses. Methods We obtained incidence data of 17 respiratory viruses from hospitalized patients and outpatients collected by 37 clinics and laboratories between 2010-2020 in Germany. With a probabilistic model for Bayes inference we quantified prevalence changes of the different viruses between months in the pre-pandemic period 2010-2019 and the corresponding months in 2020, the year of the pandemic with noninvasive measures of various degrees of stringency. Results We discovered remarkable reductions δ in rhinovirus (RV) prevalence by about 25% (95% highest density interval (HDI) [−0.35,−0.15]) in the months after the measures against SARS-CoV-2 were introduced in Germany. In the months after the measures began to ease, RV prevalence increased to low pre-pandemic levels, e.g. in August 2020 δ=−0.14 (95% HDI [−0.28,0.12]). Conclusions RV prevalence is negatively correlated with the stringency of anti-SARS-CoV-2 measures with only a short time delay. This result suggests that RV prevalence could possibly be an indicator for the efficiency for these measures. As RV is ubiquitous at higher prevalence than SARS-CoV-2 or other emerging respiratory viruses, it could reflect the efficacy of noninvasive measures better than such emerging viruses themselves with their unevenly spreading clusters.

Multi-Ellipsoidal Extended Target Tracking with Variational Bayes Inference

<div>In this work, we propose a novel extended target tracking algorithm, which is capable of representing a target or a group of targets with multiple ellipses. Each ellipse is modeled by an unknown symmetric positive-definite random matrix. The proposed model requires solving two challenging problems. First, the data association problem between the measurements and the sub-objects. Second, the inference problem that involves non-conjugate priors and likelihoods which needs to be solved within the recursive filtering framework. We utilize the variational Bayes inference method to solve the association problem and to approximate the intractable true posterior. The performance of the proposed solution is demonstrated in simulations and real-data experiments. The results show that our method outperforms the state-of-the-art methods in accuracy with lower computational complexity.</div>

Multi-Ellipsoidal Extended Target Tracking with Variational Bayes Inference

<div>In this work, we propose a novel extended target tracking algorithm, which is capable of representing a target or a group of targets with multiple ellipses. Each ellipse is modeled by an unknown symmetric positive-definite random matrix. The proposed model requires solving two challenging problems. First, the data association problem between the measurements and the sub-objects. Second, the inference problem that involves non-conjugate priors and likelihoods which needs to be solved within the recursive filtering framework. We utilize the variational Bayes inference method to solve the association problem and to approximate the intractable true posterior. The performance of the proposed solution is demonstrated in simulations and real-data experiments. The results show that our method outperforms the state-of-the-art methods in accuracy with lower computational complexity.</div>