In this survey paper, we systematically summarize the current literature on studies that apply machine learning (ML) and data mining techniques to bearing fault diagnostics. Conventional ML methods, including artificial neural network (ANN), principal component analysis (PCA), support vector machines (SVM), etc., have been successfully applied to detecting and categorizing bearing faults since the last decade, while the application of deep learning (DL) methods has sparked great interest in both the industry and academia in the last five years. In this paper, we will first review the conventional ML methods, before taking a deep dive into the latest developments in DL algorithms for bearing fault applications. Specifically, the superiority of the DL based methods over the conventional ML methods are analyzed in terms of metrics directly related to fault feature extraction and classifier performances; the new functionalities offered by DL techniques that cannot be accomplished before are also summarized. In addition, to obtain a more intuitive insight, a comparative study is performed on the classifier performance and accuracy for a number of papers utilizing the open source Case Western Reserve University (CWRU) bearing data set. Finally, based on the nature of the time-series 1-D data obtained from sensors monitoring the bearing conditions, recommendations and suggestions are provided to applying DL algorithms on bearing fault diagnostics based on specific applications, as well as future research directions to further improve its performance.

We study the problem of sparsity constrained $M$-estimation with arbitrary corruptions to both {\em explanatory and response} variables in the high-dimensional regime, where the number of variables $d$ is larger than the sample size $n$. Our main contribution is a highly efficient gradient-based optimization algorithm that we call Trimmed Hard Thresholding -- a robust variant of Iterative Hard Thresholding (IHT) by using trimmed mean in gradient computations. Our algorithm can deal with a wide class of sparsity constrained $M$-estimation problems, and we can tolerate a nearly dimension independent fraction of arbitrarily corrupted samples. More specifically, when the corrupted fraction satisfies $\epsilon \lesssim {1} /\left({\sqrt{k} \log (nd)}\right)$, where $k$ is the sparsity of the parameter, we obtain accurate estimation and model selection guarantees with optimal sample complexity. Furthermore, we extend our algorithm to sparse Gaussian graphical model (precision matrix) estimation via a neighborhood selection approach. We demonstrate the effectiveness of robust estimation in sparse linear, logistic regression, and sparse precision matrix estimation on synthetic and real-world US equities data.

We report on an empirical study of the main strategies for conditional quantile estimation in the context of stochastic computer experiments. To ensure adequate diversity, six metamodels are presented, divided into three categories based on order statistics, functional approaches, and those of Bayesian inspiration. The metamodels are tested on several problems characterized by the size of the training set, the input dimension, the quantile order and the value of the probability density function in the neighborhood of the quantile. The metamodels studied reveal good contrasts in our set of 480 experiments, enabling several patterns to be extracted. Based on our results, guidelines are proposed to allow users to select the best method for a given problem.

Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used estimation approach. We present an algorithmic framework for efficiently testing, constructing, and enumerating $m$-separators in ancestral graphs (AGs), a class of graphical causal models that can represent uncertainty about the presence of latent confounders. Furthermore, we prove a reduction from causal effect identification by covariate adjustment to $m$-separation in a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs). Jointly, these results yield constructive criteria that characterize all adjustment sets as well as all minimal and minimum adjustment sets for identification of a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results extend several existing solutions for special cases of these problems. Our efficient algorithms allowed us to empirically quantify the identifiability gap between covariate adjustment and the do-calculus in random DAGs and MAGs, covering a wide range of scenarios. Implementations of our algorithms are provided in the R package dagitty.

We propose Bayesian Deep Q-Networks (BDQN), a Thompson sampling approach for Deep Reinforcement Learning (DRL) in Markov decision processes (MDP). BDQN is an efficient exploration-exploitation algorithm which combines Thompson sampling with deep-Q networks (DQN) and directly incorporates uncertainty over the Q-value in the last layer of the DQN, on the feature representation layer. This allows us to efficiently carry out Thompson sampling through Gaussian sampling and Bayesian Linear Regression (BLR), which has fast closed-form updates. We apply our method to a wide range of Atari games and compare BDQN to a powerful baseline: the double deep Q-network (DDQN). Since BDQN carries out more efficient exploration, it is able to reach higher rewards substantially faster: in less than 5M-+1M interactions for almost half of the games to reach DDQN scores. We also establish theoretical guarantees for the special case when the feature representation is d-dimensional and fixed. We provide the Bayesian regret of posterior sampling RL (PSRL) and frequentist regret of the optimism in the face of uncertainty (OFU) for episodic MDPs.

By achieving their purposes through interactions with the physical world, Cyber Physical Systems (CPS) pose new challenges. Indeed, the evolution of the physical systems they control with transducers can be affected by surrounding physical processes over which they have no control and which may potentially hamper the achievement of their purposes. While it is illusory to hope for a comprehensive model of the physical environment at design time to anticipate and remove faults that may occur once these systems are deployed, it becomes necessary to evaluate their degree of effectiveness in vivo.In this paper, the degree of effectiveness is formally defined and generalized in the context of the measure theory and the mathematical properties it has to comply with are detailed. The measure is developed in the context of the Transferable Belief Model (TBM), an elaboration on the Dempster Shafer Theory (DST) of evidence so as to handle epistemic and aleatory uncertainties respectively pertaining the users expectations and the natural variability of the physical environment. This theoretical framework has several advantages over the probability and the possibility theories. (1) It is built on the Open World Assumption (OWA), (2) it allows to cope with dependent and possibly unreliable sources of information. The TBM is used in conjunction with the Input Output Hidden Markov Modeling framework (IOHMM) to specify the expected evolution of the physical system controlled by the CPS and the tolerances towards uncertainties. The measure of effectiveness is obtained from the forward algorithm, leveraging the conflict entailed by the successive combinations of the beliefs obtained from observations of the physical system and the beliefs corresponding to its expected evolution. The conflict, inherent to OWA, is meant to quantify the inability of the model at explaining observations.

We consider a two-agent MDP framework where agents repeatedly solve a task in a collaborative setting. We study the problem of designing a learning algorithm for the first agent (A1) that facilitates a successful collaboration even in cases when the second agent (A2) is adapting its policy in an unknown way. The key challenge in our setting is that the presence of the second agent leads to non-stationarity and non-obliviousness of rewards and transitions for the first agent. We design novel online learning algorithms for agent A1 whose regret decays as $O(T^{1-\frac{3}{7} \cdot \alpha})$ with $T$ learning episodes provided that the magnitude of agent A2's policy changes between any two consecutive episodes are upper bounded by $O(T^{-\alpha})$. Here, the parameter $\alpha$ is assumed to be strictly greater than $0$, and we show that this assumption is necessary provided that the {\em learning parity with noise} problem is computationally hard. We show that sub-linear regret of agent A1 further implies near-optimality of the agents' joint return for MDPs that manifest the properties of a {\em smooth} game.

Next-generation wireless networks (NGWN) have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of machine learning by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning, respectively. Furthermore, we investigate their employment in the compelling applications of NGWNs, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various machine learning algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.

We report a scalable hybrid quantum-classical machine learning framework to build Bayesian networks (BN) that captures the conditional dependence and causal relationships of random variables. The generation of a BN consists of finding a directed acyclic graph (DAG) and the associated joint probability distribution of the nodes consistent with a given dataset. This is a combinatorial problem of structural learning of the underlying graph, starting from a single node and building one arc at a time, that fits a given ensemble using maximum likelihood estimators (MLE). It is cast as an optimization problem that consists of a scoring step performed on a classical computer, penalties for acyclicity and number of parents allowed constraints, and a search step implemented using a quantum annealer. We have assumed uniform priors in deriving the Bayesian network that can be relaxed by formulating the problem as an estimation Dirichlet parameters. We demonstrate the utility of the framework by applying to the problem of elucidating the gene regulatory network for the MAPK/Raf pathway in human T-cells using proteomics data where the concentration of proteins, nodes of the BN, are interpreted as probabilities.

Autoencoders are a deep learning model for representation learning. When trained to minimize the Euclidean distance between the data and its reconstruction, linear autoencoders (LAEs) learn the subspace spanned by the top principal directions but cannot learn the principal directions themselves. In this paper, we prove that $L_2$-regularized LAEs learn the principal directions as the left singular vectors of the decoder, providing an extremely simple and scalable algorithm for rank-$k$ SVD. More generally, we consider LAEs with (i) no regularization, (ii) regularization of the composition of the encoder and decoder, and (iii) regularization of the encoder and decoder separately. We relate the minimum of (iii) to the MAP estimate of probabilistic PCA and show that for all critical points the encoder and decoder are transposes. Building on topological intuition, we smoothly parameterize the critical manifolds for all three losses via a novel unified framework and illustrate these results empirically. Overall, this work clarifies the relationship between autoencoders and Bayesian models and between regularization and orthogonality.