Recently there has been an increasing interest in the multivariate Gaussian process (MGP) which extends the Gaussian process (GP) to deal with multiple outputs. One approach to construct the MGP and account for non-trivial commonalities amongst outputs employs a convolution process (CP). The CP is based on the idea of sharing latent functions across several convolutions. Despite the elegance of the CP construction, it provides new challenges that need yet to be tackled. First, even with a moderate number of outputs, model building is extremely prohibitive due to the huge increase in computational demands and number of parameters to be estimated. Second, the negative transfer of knowledge may occur when some outputs do not share commonalities. In this paper we address these issues. We propose a regularized pairwise modeling approach for the MGP established using CP. The key feature of our approach is to distribute the estimation of the full multivariate model into a group of bivariate GPs which are individually built. Interestingly pairwise modeling turns out to possess unique characteristics, which allows us to tackle the challenge of negative transfer through penalizing the latent function that facilitates information sharing in each bivariate model. Predictions are then made through combining predictions from the bivariate models within a Bayesian framework. The proposed method has excellent scalability when the number of outputs is large and minimizes the negative transfer of knowledge between uncorrelated outputs. Statistical guarantees for the proposed method are studied and its advantageous features are demonstrated through numerical studies.

We use self-report and electrodermal activity (EDA) wearable sensor data from 77 nights of sleep on six participants to test the efficacy of EDA data for sleep monitoring. We used factor analysis to find latent factors in the EDA data, and causal model search to find the most probable graphical model accounting for self-reported sleep efficiency (SE), sleep quality (SQ), and the latent EDA factors. Structural equation modeling was used to confirm fit of the extracted graph. Based on the generated graph, logistic regression and naive Bayes models were used to test the efficacy of the EDA data in predicting SE and SQ. Six EDA features extracted from the total signal over a night's sleep could be explained by two latent factors, EDA Magnitude and EDA Storms. EDA Magnitude performed as a strong predictor for SE to aid detection of substantial changes in time asleep. The performance of EDA Magnitured and SE in classifying SQ showed promise for wearable sleep monitoring applications. However, our data suggest that obtaining a more accurate sensor-based measure of SE will be necessary before smaller changes in SQ can be detected from EDA sensor data alone.

Extracting and detecting spike activities from the fluorescence observations is an important step in understanding how neuron systems work. The main challenge lies in that the combination of the ambient noise with dynamic baseline fluctuation, often contaminates the observations, thereby deteriorating the reliability of spike detection. This may be even worse in the face of the nonlinear biological process, the coupling interactions between spikes and baseline, and the unknown critical parameters of an underlying physiological model, in which erroneous estimations of parameters will affect the detection of spikes causing further error propagation. In this paper, we propose a random finite set (RFS) based Bayesian approach. The dynamic behaviors of spike sequence, fluctuated baseline and unknown parameters are formulated as one RFS. This RFS state is capable of distinguishing the hidden active/silent states induced by spike and non-spike activities respectively, thereby \emph{negating the interaction role} played by spikes and other factors. Then, premised on the RFS states, a Bayesian inference scheme is designed to simultaneously estimate the model parameters, baseline, and crucial spike activities. Our results demonstrate that the proposed scheme can gain an extra $12\%$ detection accuracy in comparison with the state-of-the-art MLSpike method.

This paper proposes the divergence triangle as a framework for joint training of generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data. The divergence triangle is a robust training method that can learn from incomplete data.

The symptoms include proximal and axial muscle weakness, distal hyperlaxity, joint contractures, and critical respiratory insufficiency,which requires assisted ventilation and results in a reduced live expectancy. Moreover, the skin and other connective tissues where collagen VI is abundant are also affected [1, 2]. The collagen VI structural defects are related to mutations of three main genes (COL6A1, COL6A2, and COL6A3, OMIM 254090 and 158810). Thus, the new advances in genome editing tools open the possibility to successfully treat these neuromuscular diseases for the first time. This opportunity, though, comes with important challenges. Beyond the challenges of gene editing, this paper focuses on the challenges arising when trying to formally evaluate the efficiency of the therapeutic approaches in the recovery of the collagen VI microfibrillar network.

We introduce a Bayesian nonparametric regression model for data with multiway (tensor) structure, motivated by an application to periodontal disease (PD) data. Our outcome is the number of diseased sites measured over four different tooth types for each subject, with subject-specific covariates available as predictors. The outcomes are not well-characterized by simple parametric models, so we use a nonparametric approach with a binomial likelihood wherein the latent probabilities are drawn from a mixture with an arbitrary number of components, analogous to a Dirichlet Process (DP). We use a flexible probit stick-breaking formulation for the component weights that allows for covariate dependence and clustering structure in the outcomes. The parameter space for this model is large and multiway: patients $\times$ tooth types $\times$ covariates $\times$ components. We reduce its effective dimensionality, and account for the multiway structure, via low-rank assumptions. We illustrate how this can improve performance, and simplify interpretation, while still providing sufficient flexibility. We describe a general and efficient Gibbs sampling algorithm for posterior computation. The resulting fit to the PD data outperforms competitors, and is interpretable and well-calibrated. An interactive visual of the predictive model is available at http://ericfrazerlock.com/toothdata/ToothDisplay.html , and the code is available at https://github.com/lockEF/NonparametricMultiway .

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Recent developments in differentially private (DP) machine learning and DP Bayesian learning have enabled learning under strong privacy guarantees for the training data subjects. In this paper, we further extend the applicability of DP Bayesian learning by presenting the first general DP Markov chain Monte Carlo (MCMC) algorithm whose privacy-guarantees are not subject to unrealistic assumptions on Markov chain convergence and that is applicable to posterior inference in arbitrary models. Our algorithm is based on a decomposition of the Barker acceptance test that allows evaluating the R\'enyi DP privacy cost of the accept-reject choice. We further show how to improve the DP guarantee through data subsampling and approximate acceptance tests.

We present a novel family of deep neural architectures, named partially exchangeable networks (PENs) that leverage probabilistic symmetries. By design, PENs are invariant to block-switch transformations, which characterize the partial exchangeability properties of conditionally Markovian processes. Moreover, we show that any block-switch invariant function has a PEN-like representation. The DeepSets architecture is a special case of PEN and we can therefore also target fully exchangeable data. We employ PENs to learn summary statistics in approximate Bayesian computation (ABC). When comparing PENs to previous deep learning methods for learning summary statistics, our results are highly competitive, both considering time series and static models. Indeed, PENs provide more reliable posterior samples even when using less training data.

Recent studies have shown that imbalance ratio is not the only cause of the performance loss of a classifier in imbalanced data classification. In fact, other data factors, such as small disjuncts, noises and overlapping, also play the roles in tandem with imbalance ratio, which makes the problem difficult. Thus far, the empirical studies have demonstrated the relationship between the imbalance ratio and other data factors only. To the best of our knowledge, there is no any measurement about the extent of influence of class imbalance on the classification performance of imbalanced data. Further, it is also unknown for a dataset which data factor is actually the main barrier for classification. In this paper, we focus on Bayes optimal classifier and study the influence of class imbalance from a theoretical perspective. Accordingly, we propose an instance measure called Individual Bayes Imbalance Impact Index ($IBI^3$) and a data measure called Bayes Imbalance Impact Index ($BI^3$). $IBI^3$ and $BI^3$ reflect the extent of influence purely by the factor of imbalance in terms of each minority class sample and the whole dataset, respectively. Therefore, $IBI^3$ can be used as an instance complexity measure of imbalance and $BI^3$ is a criterion to show the degree of how imbalance deteriorates the classification. As a result, we can therefore use $BI^3$ to judge whether it is worth using imbalance recovery methods like sampling or cost-sensitive methods to recover the performance loss of a classifier. The experiments show that $IBI^3$ is highly consistent with the increase of prediction score made by the imbalance recovery methods and $BI^3$ is highly consistent with the improvement of F1 score made by the imbalance recovery methods on both synthetic and real benchmark datasets.