Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is formed by projecting the problem onto a set of approximate eigenfunctions derived from the prior covariance structure. Learning under this family of models can be conducted using a carefully crafted particle MCMC algorithm. This scheme is computationally efficient and yet allows for a fully Bayesian treatment of the problem. Compared to conventional system identification tools or existing learning methods, we show competitive performance and reliable quantification of uncertainties in the model.

I was a physicist with an almost nil education in bayesian inference and machine learning, and his book was the first contact I had with those things. It was the first book on this topic that I read cover-to-cover when I decided to my a phd in Bayesian models instead of Semiconductor Physics (my M.Sc. It was so recently that I congratulated him on twitter on him being knighted by the Queen, and I was so happy that he responded. I never knew him, only through his book.

Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit matrix completion problem. Our approach relies on tools from machine learning theory: empirical risk minimization and its convex relaxations. We propose an algorithm to compute a variational approximation of the pseudo-posterior. Thanks to the convex relaxation, the corresponding minimization problem is bi-convex, and thus the method behaves well in practice. We also study the performance of this variational approximation through PAC-Bayesian learning bounds. On the contrary to previous works that focused on upper bounds on the estimation error of M with various matrix norms, we are able to derive from this analysis a PAC bound on the prediction error of our algorithm. We focus essentially on convex relaxation through the hinge loss, for which we present the complete analysis, a complete simulation study and a test on the MovieLens data set. However, we also discuss a variational approximation to deal with the logistic loss.

We focus on the problem of estimating and quantifying uncertainties on the excursion set of a function under a limited evaluation budget. We adopt a Bayesian approach where the objective function is assumed to be a realization of a Gaussian random field. In this setting, the posterior distribution on the objective function gives rise to a posterior distribution on excursion sets. Several approaches exist to summarize the distribution of such sets based on random closed set theory. While the recently proposed Vorob'ev approach exploits analytical formulae, further notions of variability require Monte Carlo estimators relying on Gaussian random field conditional simulations. In the present work we propose a method to choose Monte Carlo simulation points and obtain quasi-realizations of the conditional field at fine designs through affine predictors. The points are chosen optimally in the sense that they minimize the posterior expected distance in measure between the excursion set and its reconstruction. The proposed method reduces the computational costs due to Monte Carlo simulations and enables the computation of quasi-realizations on fine designs in large dimensions. We apply this reconstruction approach to obtain realizations of an excursion set on a fine grid which allow us to give a new measure of uncertainty based on the distance transform of the excursion set. Finally we present a safety engineering test case where the simulation method is employed to compute a Monte Carlo estimate of a contour line.

Noname manuscript No. (will be inserted by the editor) Abstract Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the sourcespecific data models are complex, or if the number of sources is very large. To facilitate computation, we propose an approach, where inference is first made independently for the parameters of each data set, whereupon the obtained posterior samples are used as observed data in a substitute hierarchical model, based on a scaled likelihood function. Compared to direct inference in a full hierarchical model, the approach has the advantage of being able to speed up convergenceby breaking down the initial large inference problem into smaller individual subproblems with better convergence properties. Moreover it enables parallel processing of the possibly complex inferences of the source-specific parameters, which may otherwise create a computational bottleneck if processed jointly as part of a hierarchical model.

Is there a reason these are not employed more often in Machine Learning problems and more often in scientific computing?

Wireless sensor networks play a major role in smart grids and smart buildings. They are not just used for sensing, but they are also used as actuating. In terms of sensing they are used to measure temperature, humidity, light, to detect motion, etc. Sensors are often operated on a battery and hence we often face a trade-off between obtaining frequent sensor readings versus maximizing their battery life. There have been several approaches to maximizing their battery life from hardware level to software level such as reducing components energy consumption, limiting node operation capabilities, using power-aware routing protocols, and adding solar energy support. In this paper, we introduce a novel approach: we model the sensor readings in a wireless network using a dynamic Gaussian Bayesian network (dGBn) whose structure is automatically learned from data. dGBn allows us to integrate information across sensors and infer missing readings more accurately. Through active inference for dGBns, we are able to actively choose which sensors should be pulled for a reading and which ones can stay in a power-saving mode at each time step, maximizing prediction accuracy while staying within the budgetary constraints on battery consumption.

The paper focuses on finding the m best solutions to combinatorial optimization problems using best-first or depth-first branch and bound search. Specifically, we present a new algorithm m-A*, extending the well-known A* to the m-best task, and for the first time prove that all its desirable properties, including soundness, completeness and optimal efficiency, are maintained. Since best-first algorithms require extensive memory, we also extend the memory-efficient depth-first branch and bound to the m-best task. We adapt both algorithms to optimization tasks over graphical models (e.g., Weighted CSP and MPE in Bayesian networks), provide complexity analysis and an empirical evaluation. Our experiments confirm theory that the best-first approach is largely superior when memory is available, but depth-first branch and bound is more robust. We also show that our algorithms are competitive with related schemes recently developed for the m-best task.

Malware phylogenetics help cybersecurity experts to quickly understand a new malware sample by placing the new sample in the context of similar samples that have been previously reverse engineered. Recently, researchers have begun using malware code as data to infer directed acyclic graphs (DAG) that model the evolutionary relationships among samples of malware. A DAG is the ideal model for a phylogenetic graph because it includes the merges and branches that are often present in malware evolution. We present a novel Bayesian network discovery algorithm for learning a DAG via statistical inference of conditional dependencies from observed data with an informative prior on the partial ordering of variables. Our approach leverages the information on edge direction that a human can provide and the edge presence inference which data can provide. We give an efficient implementation of the partial-order prior in a Bayesian structure discovery learning algorithm, as well as a related structure prior, showing that both priors meet the local modularity requirement necessary for the efficient Bayesian discovery algorithm. We apply our algorithm to learn phylogenetic graphs on three malicious families and two benign families where the ground truth is known; and show that compared to competing algorithms, our algorithm more accurately identifies directed edges.

In many situations, agents are required to use a set of strategies (behaviors) and switch among them during the course of an interaction. This work focuses on the problem of recognizing the strategy used by an agent within a small number of interactions. We propose using a Bayesian framework to address this problem. Bayesian policy reuse (BPR) has been empirically shown to be efficient at correctly detecting the best policy to use from a library in sequential decision tasks. In this paper we extend BPR to adversarial settings, in particular, to opponents that switch from one stationary strategy to another. Our proposed extension enables learning new models in an online fashion when the learning agent detects that the current policies are not performing optimally. Experiments presented in repeated games show that our approach is capable of efficiently detecting opponent strategies and reacting quickly to behavior switches, thereby yielding better performance than state-of-the-art approaches in terms of average rewards.