Today, the amount of data that can be retrieved from communications networks is extremely high and diverse (e.g., data regarding users behavior, traffic traces, network alarms, signal quality indicators, etc.). Advanced mathematical tools are required to extract useful information from this large set of network data. In particular, Machine Learning (ML) is regarded as a promising methodological area to perform network-data analysis and enable, e.g., automatized network self-configuration and fault management. In this survey we classify and describe relevant studies dealing with the applications of ML to optical communications and networking. Optical networks and system are facing an unprecedented growth in terms of complexity due to the introduction of a huge number of adjustable parameters (such as routing configurations, modulation format, symbol rate, coding schemes, etc.), mainly due to the adoption of, among the others, coherent transmission/reception technology, advanced digital signal processing and to the presence of nonlinear effects in optical fiber systems. Although a good number of research papers have appeared in the last years, the application of ML to optical networks is still in its early stage. In this survey we provide an introductory reference for researchers and practitioners interested in this field. To stimulate further work in this area, we conclude the paper proposing new possible research directions.

Anomalies in the ambient magnetic field can be used as features in indoor positioning and navigation. By using Maxwell's equations, we derive and present a Bayesian non-parametric probabilistic modeling approach for interpolation and extrapolation of the magnetic field. We model the magnetic field components jointly by imposing a Gaussian process (GP) prior on the latent scalar potential of the magnetic field. By rewriting the GP model in terms of a Hilbert space representation, we circumvent the computational pitfalls associated with GP modeling and provide a computationally efficient and physically justified modeling tool for the ambient magnetic field. The model allows for sequential updating of the estimate and time-dependent changes in the magnetic field. The model is shown to work well in practice in different applications: we demonstrate mapping of the magnetic field both with an inexpensive Raspberry Pi powered robot and on foot using a standard smartphone.

Intelligent robots frequently need to explore the objects in their working environments. Modern sensors have enabled robots to learn object properties via perception of multiple modalities. However, object exploration in the real world poses a challenging trade-off between information gains and exploration action costs. Mixed observability Markov decision process (MOMDP) is a framework for planning under uncertainty, while accounting for both fully and partially observable components of the state. Robot perception frequently has to face such mixed observability. This work enables a robot equipped with an arm to dynamically construct query-oriented MOMDPs for object exploration. The robot’s behavioral policy is learned from two datasets collected using real robots. Our approach enables a robot to explore object properties in a way that is significantly faster while improving accuracies in comparison to existing methods that rely on hand-coded exploration strategies.

Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

Editor: Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks. Efforts have focussed on two fronts: constraint based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. Here we synthesise these two fields in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint based method. Individual steps in the MCMC scheme only require simple table lookups so that very long chains can be efficiently obtained. Furthermore, the scheme includes an iterative procedure to correct for errors from the conditional independence tests. The algorithm not only offers markedly superior performance to alternatives, but DAGs can also be sampled from the posterior distribution enabling full Bayesian modelling averaging for much larger Bayesian networks.

We introduce a dynamic mechanism for the solution of analytically-tractable substructure in probabilistic programs, using conjugate priors and affine transformations to reduce variance in Monte Carlo estimators. For inference with Sequential Monte Carlo, this automatically yields improvements such as locally-optimal proposals and Rao-Blackwellization. The mechanism maintains a directed graph alongside the running program that evolves dynamically as operations are triggered upon it. Nodes of the graph represent random variables, edges the analytically-tractable relationships between them. Random variables remain in the graph for as long as possible, to be sampled only when they are used by the program in a way that cannot be resolved analytically. In the meantime, they are conditioned on as many observations as possible. We demonstrate the mechanism with a few pedagogical examples, as well as a linear-nonlinear state-space model with simulated data, and an epidemiological model with real data of a dengue outbreak in Micronesia. In all cases one or more variables are automatically marginalized out to significantly reduce variance in estimates of the marginal likelihood, in the final case facilitating a random-weight or pseudo-marginal-type importance sampler for parameter estimation. We have implemented the approach in Anglican and a new probabilistic programming language called Birch.

There has recently been a steadily increase in the iterative approaches to boosted density estimation and sampling, usually proceeding by adding candidate "iterate" densities to a model that gets more accurate with iterations. The relative accompanying burst of formal convergence results has not yet changed a striking picture: all results essentially pay the price of heavy assumptions on iterates, often unrealistic or hard to check, and offer a blatant contrast with the original boosting theory where such assumptions would be the weakest possible. In this paper, we show that all that suffices to achieve boosting for \textit{density estimation} is a \emph{weak learner} in the original boosting theory sense, that is, an oracle that supplies \textit{classifiers}. We provide converge rates that comply with boosting requirements, being better and / or relying on substantially weaker assumptions than the state of the art. One of our rates is to our knowledge the first to rely on not just weak but also \textit{empirically testable} assumptions. We show that the model fit belongs to exponential families, and obtain in the course of our results a variational characterization of $f$-divergences better than $f$-GAN's. Experimental results on several simulated problems display significantly better results than AdaGAN during early boosting rounds, in particular for mode capture, and using architectures less than the fifth's of AdaGAN's size.

In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization from a non-Gaussian random vector. The manifold structure is learned using diffusion manifolds and the statistical sample generation is accomplished using a projected Ito stochastic differential equation. This probabilistic learning approach has been extended to polynomial chaos representation of databases on manifolds and to probabilistic nonconvex constrained optimization with a fixed budget of function evaluations. The methodology introduces an isotropic-diffusion kernel with hyperparameter {\epsilon}. Currently, {\epsilon} is more or less arbitrarily chosen. In this paper, we propose a selection criterion for identifying an optimal value of {\epsilon}, based on a maximum entropy argument. The result is a comprehensive, closed, probabilistic model for characterizing data sets with hidden constraints. This entropy argument ensures that out of all possible models, this is the one that is the most uncertain beyond any specified constraints, which is selected. Applications are presented for several databases.

The Madrid ASDM summer school is in its thirteenth edition this year, with hundreds of students from all over the world having attended so far. It comprises 12 intensive (15 lecture hours) week-long courses, and a student may attend from one up to six courses. The courses cover topics such as Neural Networks and Deep Learning, Bayesian Networks, Big Data with Apache Spark, Bayesian Inference, Text Mining and Time Series. Each course has theoretical and practical classes, the latter done with R or python. While the summer school is mainly attended by people from academia - PhD students and researchers-, people from the industry also assist.

Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable, leading to extensive study of approximation methods. Iterative variational methods are a popular and successful family of approaches. However, even state of the art variational methods can return poor results or fail to converge on difficult instances. In this paper, we instead consider computing the partition function via sequential summation over variables. We develop robust approximate algorithms by combining ideas from mini-bucket elimination with tensor network and renormalization group methods from statistical physics. The resulting "convergence-free" methods show good empirical performance on both synthetic and real-world benchmark models, even for difficult instances.