We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered local and pairwise Markov properties for the new models. We show the equivalence of these properties for strictly positive probability distributions. We also show that when the random variables are continuous, the new models can be interpreted as systems of structural equations with correlated errors. This enables us to adapt Pearl's do-calculus to them. Finally, we describe an exact algorithm for learning the new models from observational and interventional data via answer set programming.

Sampling with replacement occurs in many settings in machine learning, notably in the bagging ensemble technique and the .632+ validation scheme. The number of unique original items in a bootstrap sample can have an important role in the behaviour of prediction models learned on it. Indeed, there are uncontrived examples where duplicate items have no effect. The purpose of this report is to present the distribution of the number of unique original items in a bootstrap sample clearly and concisely, with a view to enabling other machine learning researchers to understand and control this quantity in existing and future resampling techniques. We describe the key characteristics of this distribution along with the generalisation for the case where items come from distinct categories, as in classification. In both cases we discuss the normal limit, and conduct an empirical investigation to derive a heuristic for when a normal approximation is permissible.

This paper considers the classification of linear subspaces with mismatched classifiers. In particular, we assume a model where one observes signals in the presence of isotropic Gaussian noise and the distribution of the signals conditioned on a given class is Gaussian with a zero mean and a low-rank covariance matrix. We also assume that the classifier knows only a mismatched version of the parameters of input distribution in lieu of the true parameters. By constructing an asymptotic low-noise expansion of an upper bound to the error probability of such a mismatched classifier, we provide sufficient conditions for reliable classification in the low-noise regime that are able to sharply predict the absence of a classification error floor. Such conditions are a function of the geometry of the true signal distribution, the geometry of the mismatched signal distributions as well as the interplay between such geometries, namely, the principal angles and the overlap between the true and the mismatched signal subspaces. Numerical results demonstrate that our conditions for reliable classification can sharply predict the behavior of a mismatched classifier both with synthetic data and in a motion segmentation and a hand-written digit classification applications.

The paper considers the problem of global optimization in the setup of stochastic process bandits. We introduce an UCB algorithm which builds a cascade of discretization trees based on generic chaining in order to render possible his operability over a continuous domain. The theoretical framework applies to functions under weak probabilistic smoothness assumptions and also extends significantly the spectrum of application of UCB strategies. Moreover generic regret bounds are derived which are then specialized to Gaussian processes indexed on infinite-dimensional spaces as well as to quadratic forms of Gaussian processes. Lower bounds are also proved in the case of Gaussian processes to assess the optimality of the proposed algorithm.

Driven by the opportunity to harvest the flexibility related to building climate control for demand response applications, this work presents a data-driven control approach building upon recent advancements in reinforcement learning. More specifically, model assisted batch reinforcement learning is applied to the setting of building climate control subjected to a dynamic pricing. The underlying sequential decision making problem is cast on a markov decision problem, after which the control algorithm is detailed. In this work, fitted Q-iteration is used to construct a policy from a batch of experimental tuples. In those regions of the state space where the experimental sample density is low, virtual support samples are added using an artificial neural network. Finally, the resulting policy is shaped using domain knowledge. The control approach has been evaluated quantitatively using a simulation and qualitatively in a living lab. From the quantitative analysis it has been found that the control approach converges in approximately 20 days to obtain a control policy with a performance within 90% of the mathematical optimum. The experimental analysis confirms that within 10 to 20 days sensible policies are obtained that can be used for different outside temperature regimes.

We study an original problem of pure exploration in a strategic bandit model motivated by Monte Carlo Tree Search. It consists in identifying the best action in a game, when the player may sample random outcomes of sequentially chosen pairs of actions. We propose two strategies for the fixed-confidence setting: Maximin-LUCB, based on lower-and upper-confidence bounds; and Maximin-Racing, which operates by successively eliminating the sub-optimal actions. We discuss the sample complexity of both methods and compare their performance empirically.

Privacy concern has been increasingly important in many machine learning (ML) problems. We study empirical risk minimization (ERM) problems under secure multi-party computation (MPC) frameworks. Main technical tools for MPC have been developed based on cryptography. One of limitations in current cryptographically private ML is that it is computationally intractable to evaluate non-linear functions such as logarithmic functions or exponential functions. Therefore, for a class of ERM problems such as logistic regression in which non-linear function evaluations are required, one can only obtain approximate solutions. In this paper, we introduce a novel cryptographically private tool called secure approximation guarantee (SAG) method. The key property of SAG method is that, given an arbitrary approximate solution, it can provide a non-probabilistic assumption-free bound on the approximation quality under cryptographically secure computation framework. We demonstrate the benefit of the SAG method by applying it to several problems including a practical privacy-preserving data analysis task on genomic and clinical information.

The recent availability of complex and high-dimensional datasets has spurred the need for new data analysis methods. One prominent research direction in signal processing has been the focus on data supported over graphs [1]. Graph signals, i.e., signals taking values on the nodes of combinatorial graphs, represent a convenient solution to model data exhibiting complex and nonuniform properties, such as those found in social, biological, and transportation networks, among others. Arguably, the most fundamental tool in the analysis of graph signals is the graph Fourier transform (GFT) [1]-[3]. In an analogous manner to the discrete Fourier transform (DFT), using GFT one may examine graph signals in the graph frequency domain, and, for instance, remove noise by attenuating high graph-frequencies. GFT has also lead to significant new insights in problems such as smoothing and denoising [4]-[6], segmentation [7], sampling and approximation [8]-[10], and classification [11]-[13] of graph data.

Adaptive Filter for Automatic Identification of Multiple Faults in a Noisy OTDR Profile Jean Pierre von der Weid, Mario H. Souto, Joaquim D. Garcia, and Gustavo C. Amaral November 7, 2018 Abstract We present a novel methodology able to distinguish meaningful level shifts from typical signal fluctuations. A two-stage regularization filtering can accurately identify the location of the significant level-shifts with an efficient parameter-free algorithm. The developed methodology demands low computational effort and can easily be embedded in a dedicated processing unit. Our case studies compare the new methodology with current available ones and show that it is the most adequate technique for fast detection of multiple unknown level-shifts in a noisy OTDR profile. 1 Introduction The central problem in fiber monitoring is the detection of small faults or losses most commonly performed by inspecting the trace of an Optical Time Domain Reflectometer (OTDR) [1]. These faults appear as small level shifts in a slowly varying backscattered optical power, eventually masked by the detector noise. Averaging over many OTDR shots is usually required to get access to the information needed. However, measurement time is of paramount importance in network monitoring, so that signal processing and filtering is a fundamental tool to improve time and sensitivity of the overall process. Moreover, in the case of wavelength multiplexed optical networks (WDM-PON) the problem is still worse because coherent backscattered power fluctuations (CRN) cannot be averaged out by summing up many OTDR shots [2].

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. This paper develops a new approximate Bayesian learning scheme that enables DGPs to be applied to a range of medium to large scale regression problems for the first time. The new method uses an approximate Expectation Propagation procedure and a novel and efficient extension of the probabilistic backpropagation algorithm for learning. We evaluate the new method for non-linear regression on eleven real-world datasets, showing that it always outperforms GP regression and is almost always better than state-of-the-art deterministic and sampling-based approximate inference methods for Bayesian neural networks. As a by-product, this work provides a comprehensive analysis of six approximate Bayesian methods for training neural networks.