The challenge of taking many variables into account in optimization problems may be overcome under the hypothesis of low effective dimensionality. Then, the search of solutions can be reduced to the random embedding of a low dimensional space into the original one, resulting in a more manageable optimization problem. Specifically, in the case of time consuming black-box functions and when the budget of evaluations is severely limited, global optimization with random embeddings appears as a sound alternative to random search. Yet, in the case of box constraints on the native variables, defining suitable bounds on a low dimensional domain appears to be complex. Indeed, a small search domain does not guarantee to find a solution even under restrictive hypotheses about the function, while a larger one may slow down convergence dramatically. Here we tackle the issue of low-dimensional domain selection based on a detailed study of the properties of the random embedding, giving insight on the aforementioned difficulties. In particular, we describe a minimal low-dimensional set in correspondence with the embedded search space. We additionally show that an alternative equivalent embedding procedure yields simultaneously a simpler definition of the low-dimensional minimal set and better properties in practice. Finally, the performance and robustness gains of the proposed enhancements for Bayesian optimization are illustrated on three examples.

The Monty Hall problem was first featured on the classic game show "Let's make a Deal". In the final segment of the show, contestants were presented with a choice of three different doors. Behind two of the doors would be a goat, and behind the third would be an extravagant prize such as a car. The contestant begins the game by picking one door. The host, Monty Hall, would then open one of the remaining doors.

We introduce a novel Bayesian hybrid matrix factorisation model (HMF) for data integration, based on combining multiple matrix factorisation methods, that can be used for in- and out-of-matrix prediction of missing values. The model is very general and can be used to integrate many datasets across different entity types, including repeated experiments, similarity matrices, and very sparse datasets. We apply our method on two biological applications, and extensively compare it to state-of-the-art machine learning and matrix factorisation models. For in-matrix predictions on drug sensitivity datasets we obtain consistently better performances than existing methods. This is especially the case when we increase the sparsity of the datasets. Furthermore, we perform out-of-matrix predictions on methylation and gene expression datasets, and obtain the best results on two of the three datasets, especially when the predictivity of datasets is high.

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their overall accuracy and computational efficiency. This marriage of fast evaluation and flexible approximation provides a promising means of designing scalable Bayesian inference methods. In this paper, we explore the possibility of incorporating variational approximation into a state-of-the-art MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient computation in the simulation of Hamiltonian flow, which is the bottleneck for many applications of HMC in big data problems. To this end, we use a {\it free-form} approximation induced by a fast and flexible surrogate function based on single-hidden layer feedforward neural networks. The surrogate provides sufficiently accurate approximation while allowing for fast exploration of parameter space, resulting in an efficient approximate inference algorithm. We demonstrate the advantages of our method on both synthetic and real data problems.

For big data analysis, high computational cost for Bayesian methods often limits their applications in practice. In recent years, there have been many attempts to improve computational efficiency of Bayesian inference. Here we propose an efficient and scalable computational technique for a state-of-the-art Markov Chain Monte Carlo (MCMC) methods, namely, Hamiltonian Monte Carlo (HMC). The key idea is to explore and exploit the structure and regularity in parameter space for the underlying probabilistic model to construct an effective approximation of its geometric properties. To this end, we build a surrogate function to approximate the target distribution using properly chosen random bases and an efficient optimization process. The resulting method provides a flexible, scalable, and efficient sampling algorithm, which converges to the correct target distribution. We show that by choosing the basis functions and optimization process differently, our method can be related to other approaches for the construction of surrogate functions such as generalized additive models or Gaussian process models. Experiments based on simulated and real data show that our approach leads to substantially more efficient sampling algorithms compared to existing state-of-the art methods.

Since the 2016 presidential election, one topic dominating political discourse is the issue of "Fake News". A number of political pundits claim that the rise of significantly biased and/or untrue news influenced the election, though a study by researchers from Stanford and New York University concluded otherwise. Nonetheless, fake news posts have exploited Facebook users' feeds to propagate throughout the internet. Obviously, a deliberately misleading story is "fake news" but lately blathering social media discourse, is changing its definition. Some now use the term to dismiss facts counter to their preferred viewpoints, the most prominent example being President Trump.

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.

It is not death that a man should fear but he should fear never beginning to live.

In this paper, we consider a new low-quality label learning problem: learning time series detection models from temporally imprecise labels. In this problem, the data consist of a set of input time series, and supervision is provided by a sequence of noisy time stamps corresponding to the occurrence of positive class events. Such temporally imprecise labels commonly occur in areas like mobile health research where human annotators are tasked with labeling the occurrence of very short duration events. We propose a general learning framework for this problem that can accommodate different base classifiers and noise models. We present results on real mobile health data showing that the proposed framework significantly outperforms a number of alternatives including assuming that the label time stamps are noise-free, transforming the problem into the multiple instance learning framework, and learning on labels that were manually re-aligned.

Bayesian network structure learning is often performed in a Bayesian setting, evaluating candidate structures using their posterior probabilities for a given data set. Score-based algorithms then use those posterior probabilities as an objective function and return the maximum a posteriori network as the learned model. For discrete Bayesian networks, the canonical choice for a posterior score is the Bayesian Dirichlet equivalent uniform (BDeu) marginal likelihood with a uniform (U) graph prior, which assumes a uniform prior both on the network structures and on the parameters of the networks. In this paper, we investigate the problems arising from these assumptions, focusing on those caused by small sample sizes and sparse data. We then propose an alternative posterior score: the Bayesian Dirichlet sparse (BDs) marginal likelihood with a marginal uniform (MU) graph prior. Like U BDeu, MU BDs does not require any prior information on the probabilistic structure of the data and can be used as a replacement noninformative score. We study its theoretical properties and we evaluate its performance in an extensive simulation study, showing that MU BDs is both more accurate than U BDeu in learning the structure of the network and competitive in predicting power, while not being computationally more complex to estimate.