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State space models (SSMs) provide a flexible framework for modeling complex time series via a latent stochastic process. Inference for nonlinear, non-Gaussian SSMs is often tackled with particle methods that do not scale well to long time series. The challenge is two-fold: not only do computations scale linearly with time, as in the linear case, but particle filters additionally suffer from increasing particle degeneracy with longer series. Stochastic gradient MCMC methods have been developed to scale inference for hidden Markov models (HMMs) and linear SSMs using buffered stochastic gradient estimates to account for temporal dependencies. We extend these stochastic gradient estimators to nonlinear SSMs using particle methods. We present error bounds that account for both buffering error and particle error in the case of nonlinear SSMs that are log-concave in the latent process. We evaluate our proposed particle buffered stochastic gradient using SGMCMC for inference on both long sequential synthetic and minute-resolution financial returns data, demonstrating the importance of this class of methods.

The article proposes a new framework for assessment of physical rehabilitation exercises based on a deep learning approach. The objective of the framework is automated quantification of patient performance in completing prescribed rehabilitation exercises, based on captured whole-body joint trajectories. The main components of the framework are metrics for measuring movement performance, scoring functions for mapping the performance metrics into numerical scores of movement quality, and deep neural network models for regressing quality scores of input movements via supervised learning. Furthermore, an overview of the existing methods for modeling and evaluation of rehabilitation movements is presented, encompassing various distance functions, dimensionality-reduction techniques, and movement models employed for this problem in prior studies. To the best of our knowledge, this is the first work that implements deep neural network for assessment of rehabilitation performance. Multiple deep network architectures are repurposed for the task in hand and are validated on a dataset of rehabilitation exercises.

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a model-based approach, whereas, geometric matrix completion models combine the best from both approaches. Existing deep-learning-based geometric models yield good performance, but, in order to operate, they require a fixed structure graph capturing the relationships among the users and items. This graph is typically constructed by evaluating a pre-defined similarity metric on the available observations or by using side information, e.g., user profiles. In contrast, Markov-random-fields-based models do not require a fixed structure graph but rely on handcrafted features to make predictions. When no side information is available and the number of available observations becomes very low, existing solutions are pushed to their limits. In this paper, we propose a geometric matrix completion approach that addresses these challenges. We consider matrix completion as a structured prediction problem in a conditional random field (CRF), which is characterized by a maximum a posterior (MAP) inference, and we propose a deep model that predicts the missing entries by solving the MAP inference problem. The proposed model simultaneously learns the similarities among matrix entries, computes the CRF potentials, and solves the inference problem. Its training is performed in an end-to-end manner, with a method to supervise the learning of entry similarities. Comprehensive experiments demonstrate the superior performance of the proposed model compared to various state-of-the-art models on popular benchmark datasets and underline its superior capacity to deal with highly incomplete matrices.

Recently, some works have suggested methods to combine variational probabilistic inference with Monte Carlo sampling. One promising approach is via local optimal transport. In this approach, a gradient steepest descent method based on local optimal transport principles is formulated to transform deterministically point samples from an intermediate density to a posterior density. The local mappings that transform the intermediate densities are embedded in a reproducing kernel Hilbert space (RKHS). This variational mapping method requires the evaluation of the log-posterior density gradient and therefore the adjoint of the observational operator. In this work, we evaluate nonlinear observational mappings in the variational mapping method using two approximations that avoid the adjoint, an ensemble based approximation in which the gradient is approximated by the particle covariances in the state and observational spaces the so-called ensemble space and an RKHS approximation in which the observational mapping is embedded in an RKHS and the gradient is derived there. The approximations are evaluated for highly nonlinear observational operators and in a low-dimensional chaotic dynamical system. The RKHS approximation is shown to be highly successful and superior to the ensemble approximation.

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.

In this work, we consider the identifiability assumption of Gaussian structural equation models (SEMs) in which each variable is determined by a linear function of its parents plus normally distributed error. It has been shown that linear Gaussian structural equation models are fully identifiable if all error variances are the same or known. Hence, this work proves the identifiability of Gaussian SEMs with both homogeneous and heterogeneous unknown error variances. Our new identifiability assumption exploits not only error variances, but edge weights; hence, it is strictly milder than prior work on the identifiability result. We further provide a structure learning algorithm that is statistically consistent and computationally feasible, based on our new assumption. The proposed algorithm assumes that all relevant variables are observed, while it does not assume causal minimality and faithfulness. We verify our theoretical findings through simulations, and compare our algorithm to state-of-the-art PC, GES and GDS algorithms.

Crowdsourcing has become widely used in supervised scenarios where training sets are scarce and difficult to obtain. Most crowdsourcing models in the literature assume labelers can provide answers to full questions. In classification contexts, full questions require a labeler to discern among all possible classes. Unfortunately, discernment is not always easy in realistic scenarios. Labelers may not be experts in differentiating all classes. In this work, we provide a full probabilistic model for a shorter type of queries. Our shorter queries only require "yes" or "no" responses. Our model estimates a joint posterior distribution of matrices related to labelers' confusions and the posterior probability of the class of every object. We developed an approximate inference approach, using Monte Carlo Sampling and Black Box Variational Inference, which provides the derivation of the necessary gradients. We built two realistic crowdsourcing scenarios to test our model. The first scenario queries for irregular astronomical time-series. The second scenario relies on the image classification of animals. We achieved results that are comparable with those of full query crowdsourcing. Furthermore, we show that modeling labelers' failures plays an important role in estimating true classes. Finally, we provide the community with two real datasets obtained from our crowdsourcing experiments. All our code is publicly available.