A great deal of attention has been recently given to Machine Learning (ML) techniques in many different application fields. This paper provides a vision of what ML can do in Power Line Communications (PLC). We firstly and briefly describe classical formulations of ML, and distinguish deterministic problems from statistical problems with relevance to communications. We then discuss ML applications in PLC for each layer, namely, for characterization and modeling, for physical layer algorithms, for media access control and networking algorithms. Finally, other applications of PLC that can benefit from the usage of ML, as grid diagnostics, are analyzed. Illustrative numerical examples are reported to serve the purpose of validating the ideas and motivate future research endeavors in this stimulating signal/data processing field.

Contributions: Prior studies on education have mostly followed the model of the cross sectional study, namely, examining the pretest and the posttest scores. This paper shows that students' knowledge throughout the intervention can be estimated by time series analysis using a hidden Markov model. Background: Analyzing time series and the interaction between the students and the game data can result in valuable information that cannot be gained by only cross sectional studies of the exams. Research Questions: Can a hidden Markov model be used to analyze the educational games? Can a hidden Markov model be used to make a prediction of the students' performance? Methodology: The study was conducted on (N=854) students who played the Save Patch game. Students were divided into class 1 and class 2. Class 1 students are those who scored lower in the test than class 2 students. The analysis is done by choosing various features of the game as the observations. Findings: The state trajectories can predict the students' performance accurately for both class 1 and class 2.

There are three quite distinct ways to train a machine learning model on recommender system logs. The first method is to model the reward prediction for each possible recommendation to the user, at the scoring time the best recommendation is found by computing an argmax over the personalized recommendations. This method obeys principles such as the conditionality principle and the likelihood principle. A second method is useful when the model does not fit reality and underfits. In this case, we can use the fact that we know the distribution of historical recommendations (concentrated on previously identified good actions with some exploration) to adjust the errors in the fit to be evenly distributed over all actions. Finally, the inverse propensity score can be used to produce an estimate of the decision rules expected performance. The latter two methods violate the conditionality and likelihood principle but are shown to have good performance in certain settings. In this paper we review the literature around this fundamental, yet often overlooked choice and do some experiments using the RecoGym simulation environment.

Recursive stochastic algorithms have gained significant attention in the recent past due to data driven applications. Examples include stochastic gradient descent for solving large-scale optimization problems and empirical dynamic programming algorithms for solving Markov decision problems. These recursive stochastic algorithms approximates certain contraction operators and can be viewed within the framework of iterated random maps. Accordingly, we consider iterated random maps over a Polish space that simulates a contraction operator over that Polish space. Assume that the iterated maps are indexed by $n$ such that as $n\rightarrow\infty$, each realization of the random map converges (in some sense) to the contraction map it is simulating. We show that starting from the same initial condition, the distribution of the random sequence generated by the iterated random maps converge weakly to the trajectory generated by the contraction operator. We further show that under certain conditions, the time average of the random sequence converge to the spatial mean of the invariant distribution. We then apply these results to logistic regression, empirical value iteration, empirical Q value iteration, and empirical relative value iteration for finite state finite action MDPs.

In an episodic Markov Decision Process (MDP) problem, an online algorithm chooses from a set of actions in a sequence of $H$ trials, where $H$ is the episode length, in order to maximize the total payoff of the chosen actions. Q-learning, as the most popular model-free reinforcement learning (RL) algorithm, directly parameterizes and updates value functions without explicitly modeling the environment. Recently, [Jin et al. 2018] studies the sample complexity of Q-learning with finite states and actions. Their algorithm achieves nearly optimal regret, which shows that Q-learning can be made sample efficient. However, MDPs with large discrete states and actions [Silver et al. 2016] or continuous spaces [Mnih et al. 2013] cannot learn efficiently in this way. Hence, it is critical to develop new algorithms to solve this dilemma with provable guarantee on the sample complexity. With this motivation, we propose a novel algorithm that works for MDPs with a more general setting, which has infinitely many states and actions and assumes that the payoff function and transition kernel are Lipschitz continuous. We also provide corresponding theory justification for our algorithm. It achieves the regret $\tilde{\mathcal{O}}(K^{\frac{d+1}{d+2}}\sqrt{H^3}),$ where $K$ denotes the number of episodes and $d$ denotes the dimension of the joint space. To the best of our knowledge, this is the first analysis in the model-free setting whose established regret matches the lower bound up to a logarithmic factor.

Continual learning aims to enable machine learning models to learn a general solution space for past and future tasks in a sequential manner. Conventional models tend to forget the knowledge of previous tasks while learning a new task, a phenomenon known as catastrophic forgetting. When using Bayesian models in continual learning, knowledge from previous tasks can be retained in two ways: (i) posterior distributions over the parameters, containing the knowledge gained from inference in previous tasks, which then serve as the priors for the following task; (ii) coresets, containing knowledge of data distributions of previous tasks. Here, we show that Bayesian continual learning can be facilitated in terms of these two means through the use of natural gradients and Stein gradients respectively.

Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes. In this paper, we study the problem of learning an optimal DAG from continuous observational data. We cast this problem in the form of a mathematical programming model which can naturally incorporate a super-structure in order to reduce the set of possible candidate DAGs. We use the penalized negative log-likelihood score function with both $\ell_0$ and $\ell_1$ regularizations and propose a new mixed-integer quadratic optimization (MIQO) model, referred to as a layered network (LN) formulation. The LN formulation is a compact model, which enjoys as tight an optimal continuous relaxation value as the stronger but larger formulations under a mild condition. Computational results indicate that the proposed formulation outperforms existing mathematical formulations and scales better than available algorithms that can solve the same problem with only $\ell_1$ regularization. In particular, the LN formulation clearly outperforms existing methods in terms of computational time needed to find an optimal DAG in the presence of a sparse super-structure.

Multimodal learning has been lacking principled ways of combining information from different modalities and learning a low-dimensional manifold of meaningful representations. We study multimodal learning and sensor fusion from a latent variable perspective. We first present a regularized recurrent attention filter for sensor fusion. This algorithm can dynamically combine information from different types of sensors in a sequential decision making task. Each sensor is bonded with a modular neural network to maximize utility of its own information. A gating modular neural network dynamically generates a set of mixing weights for outputs from sensor networks by balancing utility of all sensors' information. We design a co-learning mechanism to encourage co-adaption and independent learning of each sensor at the same time, and propose a regularization based co-learning method. In the second part, we focus on recovering the manifold of latent representation. We propose a co-learning approach using probabilistic graphical model which imposes a structural prior on the generative model: multimodal variational RNN (MVRNN) model, and derive a variational lower bound for its objective functions. In the third part, we extend the siamese structure to sensor fusion for robust acoustic event detection. We perform experiments to investigate the latent representations that are extracted; works will be done in the following months. Our experiments show that the recurrent attention filter can dynamically combine different sensor inputs according to the information carried in the inputs. We consider MVRNN can identify latent representations that are useful for many downstream tasks such as speech synthesis, activity recognition, and control and planning. Both algorithms are general frameworks which can be applied to other tasks where different types of sensors are jointly used for decision making.

Graph learning from data represents a canonical problem that has received substantial attention in the literature. However, insufficient work has been done in incorporating prior structural knowledge onto the learning of underlying graphical models from data. Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. Useful structured graphs include the multi-component graph, bipartite graph, connected graph, sparse graph, and regular graph. In general, structured graph learning is an NP-hard combinatorial problem, therefore, designing a general tractable optimization method is extremely challenging. In this paper, we introduce a unified graph learning framework lying at the integration of Gaussian graphical models and spectral graph theory. To impose a particular structure on a graph, we first show how to formulate the combinatorial constraints as an analytical property of the graph matrix. Then we develop an optimization framework that leverages graph learning with specific structures via spectral constraints on graph matrices. The proposed algorithms are provably convergent, computationally efficient, and practically amenable for numerous graph-based tasks. Extensive numerical experiments with both synthetic and real data sets illustrate the effectiveness of the proposed algorithms. The code for all the simulations is made available as an open source repository.

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model, with the initial image serving as the latent variables, and discard the learned EBM. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. Moreover, unlike traditional EBM or MCMC, the learned short-run MCMC is also capable of reconstructing observed images and interpolating different images, like generator model or flow model. The code can be found in the Appendix.