With the rapid development of manufacturing industry, machine fault diagnosis has become increasingly significant to ensure safe equipment operation and production. Consequently, multifarious approaches have been explored and developed in the past years, of which intelligent algorithms develop particularly rapidly. Convolutional neural network, as a typical representative of intelligent diagnostic models, has been extensively studied and applied in recent five years, and a large amount of literature has been published in academic journals and conference proceedings. However, there has not been a systematic review to cover these studies and make a prospect for the further research. To fill in this gap, this work attempts to review and summarize the development of the Convolutional Network based Fault Diagnosis (CNFD) approaches comprehensively. Generally, a typical CNFD framework is composed of the following steps, namely, data collection, model construction, and feature learning and decision making, thus this paper is organized by following this stream. Firstly, data collection process is described, in which several popular datasets are introduced. Then, the fundamental theory from the basic convolutional neural network to its variants is elaborated. After that, the applications of CNFD are reviewed in terms of three mainstream directions, i.e. classification, prediction and transfer diagnosis. Finally, conclusions and prospects are presented to point out the characteristics of current development, facing challenges and future trends. Last but not least, it is expected that this work would provide convenience and inspire further exploration for researchers in this field.

This paper studies the optimal rate of estimation in a finite Gaussian location mixture model in high dimensions without separation conditions. We assume that the number of components $k$ is bounded and that the centers lie in a ball of bounded radius, while allowing the dimension $d$ to be as large as the sample size $n$. Extending the one-dimensional result of Heinrich and Kahn \cite{HK2015}, we show that the minimax rate of estimating the mixing distribution in Wasserstein distance is $\Theta((d/n)^{1/4} + n^{-1/(4k-2)})$, achieved by an estimator computable in time $O(nd^2+n^{5/4})$. Furthermore, we show that the mixture density can be estimated at the optimal parametric rate $\Theta(\sqrt{d/n})$ in Hellinger distance; however, no computationally efficient algorithm is known to achieve the optimal rate. Both the theoretical and methodological development rely on a careful application of the method of moments. Central to our results is the observation that the information geometry of finite Gaussian mixtures is characterized by the moment tensors of the mixing distribution, whose low-rank structure can be exploited to obtain a sharp local entropy bound.

Hidden Markov Models (HMMs) are a powerful generative approach for modeling sequential data and time-series in general. However, the commonly employed assumption of the dependence of the current time frame to a single or multiple immediately preceding frames is unrealistic; more complicated dynamics potentially exist in real world scenarios. Human Action Recognition constitutes such a scenario, and has attracted increased attention with the advent of low-cost 3D sensors. The naturally arising variations and complex temporal dependencies have established this task as a challenging problem in the community. This paper revisits conventional sequential modeling approaches, aiming to address the problem of capturing time-varying temporal dependency patterns. To this end, we propose a different formulation of HMMs, whereby the dependence on past frames is dynamically inferred from the data. Specifically, we introduce a hierarchical extension by postulating an additional latent variable layer; therein, the (time-varying) temporal dependence patterns are treated as latent variables over which inference is performed. We leverage solid arguments from the Variational Bayes framework and derive a tractable inference algorithm based on the forward-backward algorithm. As we experimentally show using benchmark datasets, our approach yields competitive recognition accuracy and can effectively handle data with missing values.

In this paper, we study the problem of sampling from distributions of the form p(x) \propto e^{-\beta f(x)} for some function f whose values and gradients we can query. This mode of access to f is natural in the scenarios in which such problems arise, for instance sampling from posteriors in parametric Bayesian models. Classical results show that a natural random walk, Langevin diffusion, mixes rapidly when f is convex. Unfortunately, even in simple examples, the applications listed above will entail working with functions f that are nonconvex -- for which sampling from p may in general require an exponential number of queries. In this paper, we study one aspect of nonconvexity relevant for modern machine learning applications: existence of invariances (symmetries) in the function f, as a result of which the distribution p will have manifolds of points with equal probability. We give a recipe for proving mixing time bounds of Langevin dynamics in order to sample from manifolds of local optima of the function f in settings where the distribution is well-concentrated around them. We specialize our arguments to classic matrix factorization-like Bayesian inference problems where we get noisy measurements A(XX^T), X \in R^{d \times k} of a low-rank matrix, i.e. f(X) = \|A(XX^T) - b\|^2_2, X \in R^{d \times k}, and \beta the inverse of the variance of the noise. Such functions f are invariant under orthogonal transformations, and include problems like matrix factorization, sensing, completion. Beyond sampling, Langevin dynamics is a popular toy model for studying stochastic gradient descent. Along these lines, we believe that our work is an important first step towards understanding how SGD behaves when there is a high degree of symmetry in the space of parameters the produce the same output.

Meta-learning can successfully acquire useful inductive biases from data, especially when a large number of meta-tasks are available. Yet, its generalization properties to unseen tasks are poorly understood. Particularly if the number of meta-tasks is small, this raises concerns for potential overfitting. We provide a theoretical analysis using the PAC-Bayesian framework and derive novel generalization bounds for meta-learning with unbounded loss functions and Bayesian base learners. Using these bounds, we develop a class of PAC-optimal meta-learning algorithms with performance guarantees and a principled meta-regularization. When instantiating our PAC-optimal hyper-posterior (PACOH) with Gaussian processes as base learners, the resulting approach consistently outperforms several popular meta-learning methods, both in terms of predictive accuracy and the quality of its uncertainty estimates.

Recurrent neural networks (RNNs) have emerged as an effective representation of control policies in sequential decision-making problems. However, a major drawback in the application of RNN-based policies is the difficulty in providing formal guarantees on the satisfaction of behavioral specifications, e.g. safety and/or reachability. By integrating techniques from formal methods and machine learning, we propose an approach to automatically extract a finite-state controller (FSC) from an RNN, which, when composed with a finite-state system model, is amenable to existing formal verification tools. Specifically, we introduce an iterative modification to the so-called quantized bottleneck insertion technique to create an FSC as a randomized policy with memory. For the cases in which the resulting FSC fails to satisfy the specification, verification generates diagnostic information. We utilize this information to either adjust the amount of memory in the extracted FSC or perform focused retraining of the RNN. While generally applicable, we detail the resulting iterative procedure in the context of policy synthesis for partially observable Markov decision processes (POMDPs), which is known to be notoriously hard. The numerical experiments show that the proposed approach outperforms traditional POMDP synthesis methods by 3 orders of magnitude within 2% of optimal benchmark values.

Deep Learning (DL) techniques for Natural Language Processing have been evolving remarkably fast. Recently, the DL advances in language modeling, machine translation and paragraph understanding are so prominent that the potential of DL in Software Engineering cannot be overlooked, especially in the field of program learning. To facilitate further research and applications of DL in this field, we provide a comprehensive review to categorize and investigate existing DL methods for source code modeling and generation. To address the limitations of the traditional source code models, we formulate common program learning tasks under an encoder-decoder framework. After that, we introduce recent DL mechanisms suitable to solve such problems. Then, we present the state-of-the-art practices and discuss their challenges with some recommendations for practitioners and researchers as well.

Companies may be achieving only a third of the value they could be getting from data science in industry applications. In this paper, we propose a methodology for categorizing and answering 'The Big Three' questions (what is going on, what is causing it, and what actions can I take that will optimize what I care about) using data science. The applications of data science seem to be nearly endless in today's modern landscape, with each company jockeying for position in the new data and insights economy. Yet, data scientists seem to be solely focused on using classification, regression, and clustering methods to answer the question 'what is going on'. Answering questions about why things are happening or how to take optimal actions to improve metrics are relegated to niche fields of research and generally neglected in industry data science analysis. We survey technical methods to answer these other important questions, describe areas in which some of these methods are being applied, and provide a practical example of how to apply our methodology and selected methods to a real business use case.

Causal models could increase interpretability, robustness to distributional shift and sample efficiency of RL agents. In this vein, we address the question of learning a causal model of an RL environment. This problem is known to be difficult due to spurious correlations. We overcome this difficulty by rewarding an RL agent for designing and executing interventions to discover the true model. We compare rewarding the agent for disproving uncertain edges in the causal graph, rewarding the agent for activating a certain node, or rewarding the agent for increasing the causal graph loss. We show that our methods result in a better causal graph than one generated by following the random policy, or a policy trained on the environment's reward. We find that rewarding for the causal graph loss works the best.

Effective decision making requires understanding the uncertainty inherent in a prediction. To estimate uncertainty in regression, one could modify a deep neural network to predict coverage intervals, such as by predicting the mean and standard deviation. Unfortunately, in our empirical evaluations the predicted coverage from existing approaches is either overconfident or lacks sharpness (gives imprecise intervals). To address this challenge, we propose a novel method to estimate uncertainty based on two distinct neural networks with two distinct loss functions in a similar vein to Generative Adversarial Networks. Specifically, one network tries to learn the cumulative distribution function, and the second network tries to learn its inverse. Theoretical analysis demonstrates that the idealized solution is a fixed point and that under certain conditions the approach is asymptotically consistent to ground truth. We benchmark the approach on one synthetic and five real-world datasets, including forecasting A1c values in diabetic patients from electronic health records, where uncertainty is critical. In synthetic data, the proposed approach essentially matches the theoretically optimal solution in all aspects. In the real datasets, the proposed approach is empirically more faithful in its coverage estimates and typically gives sharper intervals than competing methods.