Neural language models have been widely used in various NLP tasks, including machine translation, next word prediction and conversational agents. However, it is challenging to deploy these models on mobile devices due to their slow prediction speed, where the bottleneck is to compute top candidates in the softmax layer. In this paper, we introduce a novel softmax layer approximation algorithm by exploiting the clustering structure of context vectors. Our algorithm uses a light-weight screening model to predict a much smaller set of candidate words based on the given context, and then conducts an exact softmax only within that subset. Training such a procedure end-to-end is challenging as traditional clustering methods are discrete and non-differentiable, and thus unable to be used with back-propagation in the training process. Using the Gumbel softmax, we are able to train the screening model end-to-end on the training set to exploit data distribution. The algorithm achieves an order of magnitude faster inference than the original softmax layer for predicting top-$k$ words in various tasks such as beam search in machine translation or next words prediction. For example, for machine translation task on German to English dataset with around 25K vocabulary, we can achieve 20.4 times speed up with 98.9\% precision@1 and 99.3\% precision@5 with the original softmax layer prediction, while state-of-the-art ~\citep{MSRprediction} only achieves 6.7x speedup with 98.7\% precision@1 and 98.1\% precision@5 for the same task.

The world is witnessing an unprecedented growth of cyber-physical systems (CPS), which are foreseen to revolutionize our world {via} creating new services and applications in a variety of sectors such as environmental monitoring, mobile-health systems, intelligent transportation systems and so on. The {information and communication technology }(ICT) sector is experiencing a significant growth in { data} traffic, driven by the widespread usage of smartphones, tablets and video streaming, along with the significant growth of sensors deployments that are anticipated in the near future. {It} is expected to outstandingly increase the growth rate of raw sensed data. In this paper, we present the CPS taxonomy {via} providing a broad overview of data collection, storage, access, processing and analysis. Compared with other survey papers, this is the first panoramic survey on big data for CPS, where our objective is to provide a panoramic summary of different CPS aspects. Furthermore, CPS {require} cybersecurity to protect {them} against malicious attacks and unauthorized intrusion, which {become} a challenge with the enormous amount of data that is continuously being generated in the network. {Thus, we also} provide an overview of the different security solutions proposed for CPS big data storage, access and analytics. We also discuss big data meeting green challenges in the contexts of CPS.

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian inference in Hilbert spaces. We investigate the link between QGMs and HSEs and show that the sum rule and Bayes rule for QGMs are equivalent to the kernel sum rule in HSEs and a special case of Nadaraya-Watson kernel regression, respectively. We show that these operations can be kernelized, and use these insights to propose a Hilbert Space Embedding of Hidden Quantum Markov Models (HSE-HQMM) to model dynamics. We present experimental results showing that HSE-HQMMs are competitive with state-of-the-art models like LSTMs and PSRNNs on several datasets, while also providing a nonparametric method for maintaining a probability distribution over continuous-valued features.

An Euler discretization of the Langevin diffusion is known to converge to the global minimizers of certain convex and non-convex optimization problems. We show that this property holds for any suitably smooth diffusion and that different diffusions are suitable for optimizing different classes of convex and non-convex functions. This allows us to design diffusions suitable for globally optimizing convex and non-convex functions not covered by the existing Langevin theory. Our non-asymptotic analysis delivers computable optimization and integration error bounds based on easily accessed properties of the objective and chosen diffusion. Central to our approach are new explicit Stein factor bounds on the solutions of Poisson equations. We complement these results with improved optimization guarantees for targets other than the standard Gibbs measure.

Gaussian Processes (GPs) are a generic modelling tool for supervised learning. While they have been successfully applied on large datasets, their use in safety-critical applications is hindered by the lack of good performance guarantees. To this end, we propose a method to learn GPs and their sparse approximations by directly optimizing a PAC-Bayesian bound on their generalization performance, instead of maximizing the marginal likelihood. Besides its theoretical appeal, we find in our evaluation that our learning method is robust and yields significantly better generalization guarantees than other common GP approaches on several regression benchmark datasets.

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model discrepancy term using Gaussian processes; inference is then carried out using MCMC. These choices pose computational and statistical challenges and limitations, which we overcome by proposing the use of approximate Deep Gaussian processes and variational inference techniques. The result is a practical and scalable framework for calibration, which obtains competitive performance compared to the state-of-the-art.

Mixture of Experts (MoE) are successful models for modeling heterogeneous data in many statistical learning problems including regression, clustering and classification. Generally fitted by maximum likelihood estimation via the well-known EM algorithm, their application to high-dimensional problems is still therefore challenging. We consider the problem of fitting and feature selection in MoE models, and propose a regularized maximum likelihood estimation approach that encourages sparse solutions for heterogeneous regression data models with potentially high-dimensional predictors. Unlike state-of-the art regularized MLE for MoE, the proposed modelings do not require an approximate of the penalty function. We develop two hybrid EM algorithms: an Expectation-Majorization-Maximization (EM/MM) algorithm, and an EM algorithm with coordinate ascent algorithm. The proposed algorithms allow to automatically obtaining sparse solutions without thresholding, and avoid matrix inversion by allowing univariate parameter updates. An experimental study shows the good performance of the algorithms in terms of recovering the actual sparse solutions, parameter estimation, and clustering of heterogeneous regression data.

We consider the semi-supervised clustering problem where crowdsourcing provides noisy information about the pairwise comparisons on a small subset of data, i.e., whether a sample pair is in the same cluster. We propose a new approach that includes a deep generative model (DGM) to characterize low-level features of the data, and a statistical relational model for noisy pairwise annotations on its subset. The two parts share the latent variables. To make the model automatically trade-off between its complexity and fitting data, we also develop its fully Bayesian variant. The challenge of inference is addressed by fast (natural-gradient) stochastic variational inference algorithms, where we effectively combine variational message passing for the relational part and amortized learning of the DGM under a unified framework. Empirical results on synthetic and real-world datasets show that our model outperforms previous crowdsourced clustering methods.

We might hope that when faced with unexpected inputs, well-designed software systems would fire off warnings. Machine learning (ML) systems, however, which depend strongly on properties of their inputs (e.g. the i.i.d. assumption), tend to fail silently. This paper explores the problem of building ML systems that fail loudly, investigating methods for detecting dataset shift and identifying exemplars that most typify the shift. We focus on several datasets and various perturbations to both covariates and label distributions with varying magnitudes and fractions of data affected. Interestingly, we show that while classifier-based methods perform well in high-data settings, they perform poorly in low-data settings. Moreover, across the dataset shifts that we explore, a two-sample-testing-based approach, using pretrained classifiers for dimensionality reduction performs best.

Despite advances in scalable models, the inference tools used for Gaussian processes (GPs) have yet to fully capitalize on developments in computing hardware. We present an efficient and general approach to GP inference based on Blackbox Matrix-Matrix multiplication (BBMM). BBMM inference uses a modified batched version of the conjugate gradients algorithm to derive all terms for training and inference in a single call. BBMM reduces the asymptotic complexity of exact GP inference from $O(n^3)$ to $O(n^2)$. Adapting this algorithm to scalable approximations and complex GP models simply requires a routine for efficient matrix-matrix multiplication with the kernel and its derivative. In addition, BBMM uses a specialized preconditioner to substantially speed up convergence. In experiments we show that BBMM effectively uses GPU hardware to dramatically accelerate both exact GP inference and scalable approximations. Additionally, we provide GPyTorch, a software platform for scalable GP inference via BBMM, built on PyTorch.