We propose moment-based variational inference as a flexible framework for approximate smoothing of latent Markov jump processes. The main ingredient of our approach is to partition the set of all transitions of the latent process into classes. This allows to express the Kullback-Leibler divergence between the approximate and the exact posterior process in terms of a set of moment functions that arise naturally from the chosen partition. To illustrate possible choices of the partition, we consider special classes of jump processes that frequently occur in applications. We then extend the results to parameter inference and demonstrate the method on several examples.

Events in the world may be caused by other, unobserved events. We consider sequences of events in continuous time. Given a probability model of complete sequences, we propose particle smoothing---a form of sequential importance sampling---to impute the missing events in an incomplete sequence. We develop a trainable family of proposal distributions based on a type of bidirectional continuous-time LSTM: Bidirectionality lets the proposals condition on future observations, not just on the past as in particle filtering. Our method can sample an ensemble of possible complete sequences (particles), from which we form a single consensus prediction that has low Bayes risk under our chosen loss metric. We experiment in multiple synthetic and real domains, using different missingness mechanisms, and modeling the complete sequences in each domain with a neural Hawkes process (Mei & Eisner 2017). On held-out incomplete sequences, our method is effective at inferring the ground-truth unobserved events, with particle smoothing consistently improving upon particle filtering.

Speech-driven visual speech synthesis involves mapping features extracted from acoustic speech to the corresponding lip animation controls for a face model. This mapping can take many forms, but a powerful approach is to use deep neural networks (DNNs). However, a limitation is the lack of synchronized audio, video, and depth data required to reliably train the DNNs, especially for speaker-independent models. In this paper, we investigate adapting an automatic speech recognition (ASR) acoustic model (AM) for the visual speech synthesis problem. We train the AM on ten thousand hours of audio-only data. The AM is then adapted to the visual speech synthesis domain using ninety hours of synchronized audio-visual speech. Using a subjective assessment test, we compared the performance of the AM-initialized DNN to one with a random initialization. The results show that viewers significantly prefer animations generated from the AM-initialized DNN than the ones generated using the randomly initialized model. We conclude that visual speech synthesis can significantly benefit from the powerful representation of speech in the ASR acoustic models.

It is widely accepted that optimization of medical imaging system performance should be guided by task-based measures of image quality (IQ). Task-based measures of IQ quantify the ability of an observer to perform a specific task such as detection or estimation of a signal (e.g., a tumor). For binary signal detection tasks, the Bayesian Ideal Observer (IO) sets an upper limit of observer performance and has been advocated for use in optimizing medical imaging systems and data-acquisition designs. Except in special cases, determination of the IO test statistic is analytically intractable. Markov-chain Monte Carlo (MCMC) techniques can be employed to approximate IO detection performance, but their reported applications have been limited to relatively simple object models. In cases where the IO test statistic is difficult to compute, the Hotelling Observer (HO) can be employed. To compute the HO test statistic, potentially large covariance matrices must be accurately estimated and subsequently inverted, which can present computational challenges. This work investigates supervised learning-based methodologies for approximating the IO and HO test statistics. Convolutional neural networks (CNNs) and single-layer neural networks (SLNNs) are employed to approximate the IO and HO test statistics, respectively. Numerical simulations were conducted for both signal-known-exactly (SKE) and signal-known-statistically (SKS) signal detection tasks. The performances of the supervised learning methods are assessed via receiver operating characteristic (ROC) analysis and the results are compared to those produced by use of traditional numerical methods or analytical calculations when feasible. The potential advantages of the proposed supervised learning approaches for approximating the IO and HO test statistics are discussed.

Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a quasi-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. In recent years, a number of data discrepancy measures bypassing the construction of summary statistics have been proposed, including the Kullback--Leibler divergence, the Wasserstein distance and maximum mean discrepancies. Here we propose a novel importance-sampling (IS) ABC algorithm relying on the so-called \textit{two-sample energy statistic}. We establish a new asymptotic result for the case where both the observed sample size and the simulated data sample size increase to infinity, which highlights to what extent the data discrepancy measure impacts the asymptotic pseudo-posterior. The result holds in the broad setting of IS-ABC methodologies, thus generalizing previous results that have been established only for rejection ABC algorithms. Furthermore, we propose a consistent V-statistic estimator of the energy statistic, under which we show that the large sample result holds. Our proposed energy statistic based ABC algorithm is demonstrated on a variety of models, including a Gaussian mixture, a moving-average model of order two, a bivariate beta and a multivariate $g$-and-$k$ distribution. We find that our proposed method compares well with alternative discrepancy measures.

Stochastic blockmodels (SBM) and their variants, $e.g.$, mixed-membership and overlapping stochastic blockmodels, are latent variable based generative models for graphs. They have proven to be successful for various tasks, such as discovering the community structure and link prediction on graph-structured data. Recently, graph neural networks, $e.g.$, graph convolutional networks, have also emerged as a promising approach to learn powerful representations (embeddings) for the nodes in the graph, by exploiting graph properties such as locality and invariance. In this work, we unify these two directions by developing a \emph{sparse} variational autoencoder for graphs, that retains the interpretability of SBMs, while also enjoying the excellent predictive performance of graph neural nets. Moreover, our framework is accompanied by a fast recognition model that enables fast inference of the node embeddings (which are of independent interest for inference in SBM and its variants). Although we develop this framework for a particular type of SBM, namely the \emph{overlapping} stochastic blockmodel, the proposed framework can be adapted readily for other types of SBMs. Experimental results on several benchmarks demonstrate encouraging results on link prediction while learning an interpretable latent structure that can be used for community discovery.

This paper deals with estimating model parameters in graphical models. We reformulate it as an information geometric optimization problem and introduce a natural gradient descent strategy that incorporates additional meta parameters. We show that our approach is a strong alternative to the celebrated EM approach for learning in graphical models. Actually, our natural gradient based strategy leads to learning optimal parameters for the final objective function without artificially trying to fit a distribution that may not correspond to the real one. We support our theoretical findings with the question of trend detection in financial markets and show that the learned model performs better than traditional practitioner methods and is less prone to overfitting.

For text analysis, one often resorts to a lossy representation that either completely ignores word order or embeds each word as a low-dimensional dense feature vector. In this paper, we propose convolutional Poisson factor analysis (CPFA) that directly operates on a lossless representation that processes the words in each document as a sequence of high-dimensional one-hot vectors. To boost its performance, we further propose the convolutional Poisson gamma belief network (CPGBN) that couples CPFA with the gamma belief network via a novel probabilistic pooling layer. CPFA forms words into phrases and captures very specific phrase-level topics, and CPGBN further builds a hierarchy of increasingly more general phrase-level topics. For efficient inference, we develop both a Gibbs sampler and a Weibull distribution based convolutional variational auto-encoder. Experimental results demonstrate that CPGBN can extract high-quality text latent representations that capture the word order information, and hence can be leveraged as a building block to enrich a wide variety of existing latent variable models that ignore word order.

Recent studies have explored the use of deep generative models of speech spectra based of variational autoencoders (VAEs), combined with unsupervised noise models, to perform speech enhancement. These studies developed iterative algorithms involving either Gibbs sampling or gradient descent at each step, making them computationally expensive. This paper proposes a variational inference method to iteratively estimate the power spectrogram of the clean speech. Our main contribution is the analytical derivation of the variational steps in which the en-coder of the pre-learned VAE can be used to estimate the varia-tional approximation of the true posterior distribution, using the very same assumption made to train VAEs. Experiments show that the proposed method produces results on par with the afore-mentioned iterative methods using sampling, while decreasing the computational cost by a factor 36 to reach a given performance .

In this paper, we present an experimental study for the classification of perceived human stress using non-invasive physiological signals. These include electroencephalography (EEG), galvanic skin response (GSR), and photoplethysmography (PPG). We conducted experiments consisting of steps including data acquisition, feature extraction, and perceived human stress classification. The physiological data of $28$ participants are acquired in an open eye condition for a duration of three minutes. Four different features are extracted in time domain from EEG, GSR and PPG signals and classification is performed using multiple classifiers including support vector machine, the Naive Bayes, and multi-layer perceptron (MLP). The best classification accuracy of 75% is achieved by using MLP classifier. Our experimental results have shown that our proposed scheme outperforms existing perceived stress classification methods, where no stress inducers are used.