Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.

Many of the current scientific advances in the life sciences have their origin in the intensive use of data for knowledge discovery. In no area this is so clear as in bioinformatics, led by technological breakthroughs in data acquisition technologies. It has been argued that bioinformatics could quickly become the field of research generating the largest data repositories, beating other data-intensive areas such as high-energy physics or astroinformatics. Over the last decade, deep learning has become a disruptive advance in machine learning, giving new live to the long-standing connectionist paradigm in artificial intelligence. Deep learning methods are ideally suited to large-scale data and, therefore, they should be ideally suited to knowledge discovery in bioinformatics and biomedicine at large. In this brief paper, we review key aspects of the application of deep learning in bioinformatics and medicine, drawing from the themes covered by the contributions to an ESANN 2018 special session devoted to this topic.

This Chapter, "High-dimensional ABC", is to appear in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind extending ABC methods to higher dimensions, with supporting examples and illustrations.

This Chapter, "Overview of Approximate Bayesian Computation", is to appear as the first chapter in the forthcoming Handbook of Approximate Bayesian Computation (2018). It details the main ideas and concepts behind ABC methods with many examples and illustrations.

We present pomegranate, an open source machine learning package for probabilistic modeling in Python. Probabilistic modeling encompasses a wide range of methods that explicitly describe uncertainty using probability distributions. Three widely used probabilistic models implemented in pomegranate are general mixture models, hidden Markov models, and Bayesian networks. A primary focus of pomegranate is to abstract away the complexities of training models from their definition. This allows users to focus on specifying the correct model for their application instead of being limited by their understanding of the underlying algorithms. An aspect of this focus involves the collection of additive sufficient statistics from data sets as a strategy for training models. This approach trivially enables many useful learning strategies, such as out-of-core learning, minibatch learning, and semi-supervised learning, without requiring the user to consider how to partition data or modify the algorithms to handle these tasks themselves. pomegranate is written in Cython to speed up calculations and releases the global interpreter lock to allow for built-in multithreaded parallelism, making it competitive with---or outperform---other implementations of similar algorithms. This paper presents an overview of the design choices in pomegranate, and how they have enabled complex features to be supported by simple code.

Classifying samples into categories becomes intractable when a single sample can have millions to billions of features, such as in genetics or imaging data. Principal Components Analysis (PCA) is widely used to identify a low-dimensional representation of such features for further analysis. However, PCA ignores class labels, such as whether or not a subject has cancer, thereby discarding information that could substantially improve downstream classification performance. We describe an approach, "Linear Optimal Low-rank" projection (LOL), which extends PCA by incorporating the class labels in a fashion that is advantageous over existing supervised dimensionality reduction techniques. We prove, and substantiate with synthetic experiments, that LOL leads to a better representation of the data for subsequent classification than other linear approaches, while adding negligible computational cost. We then demonstrate that LOL substantially outperforms PCA in differentiating cancer patients from healthy controls using genetic data, and in differentiating gender using magnetic resonance imaging data with $>$500 million features and 400 gigabytes of data. LOL therefore allows the solution of previous intractable problems, yet requires only a few minutes to run on a desktop computer.

The Contrastive Divergence (CD) algorithm has achieved notable success in training energy-based models including Restricted Boltzmann Machines and played a key role in the emergence of deep learning. The idea of this algorithm is to approximate the intractable term in the exact gradient of the log-likelihood function by using short Markov chain Monte Carlo (MCMC) runs. The approximate gradient is computationally-cheap but biased. Whether and why the CD algorithm provides an asymptotically consistent estimate are still open questions. This paper studies the asymptotic properties of the CD algorithm in canonical exponential families, which are special cases of the energy-based model. Suppose the CD algorithm runs $m$ MCMC transition steps at each iteration $t$ and iteratively generates a sequence of parameter estimates $\{\theta_t\}_{t \ge 0}$ given an i.i.d. data sample $\{X_i\}_{i=1}^n \sim p_{\theta_\star}$. Under conditions which are commonly obeyed by the CD algorithm in practice, we prove the existence of some bounded $m$ such that any limit point of the time average $\left. \sum_{s=0}^{t-1} \theta_s \right/ t$ as $t \to \infty$ is a consistent estimate for the true parameter $\theta_\star$. Our proof is based on the fact that $\{\theta_t\}_{t \ge 0}$ is a homogenous Markov chain conditional on the data sample $\{X_i\}_{i=1}^n$. This chain meets the Foster-Lyapunov drift criterion and converges to a random walk around the Maximum Likelihood Estimate. The range of the random walk shrinks to zero at rate $\mathcal{O}(1/\sqrt[3]{n})$ as the sample size $n \to \infty$.

We study the problem of allocating impressions to sellers in e-commerce websites, such as Amazon, eBay or Taobao, aiming to maximize the total revenue generated by the platform. We employ a general framework of reinforcement mechanism design, which uses deep reinforcement learning to design efficient algorithms, taking the strategic behaviour of the sellers into account. Specifically, we model the impression allocation problem as a Markov decision process, where the states encode the history of impressions, prices, transactions and generated revenue and the actions are the possible impression allocations in each round. To tackle the problem of continuity and high-dimensionality of states and actions, we adopt the ideas of the DDPG algorithm to design an actor-critic policy gradient algorithm which takes advantage of the problem domain in order to achieve convergence and stability. We evaluate our proposed algorithm, coined IA(GRU), by comparing it against DDPG, as well as several natural heuristics, under different rationality models for the sellers - we assume that sellers follow well-known no-regret type strategies which may vary in their degree of sophistication. We find that IA(GRU) outperforms all algorithms in terms of the total revenue.

We study planning problems where autonomous agents operate inside environments that are subject to uncertainties and not fully observable. Partially observable Markov decision processes (POMDPs) are a natural formal model to capture such problems. Because of the potentially huge or even infinite belief space in POMDPs, synthesis with safety guarantees is, in general, computationally intractable. We propose an approach that aims to circumvent this difficulty: in scenarios that can be partially or fully simulated in a virtual environment, we actively integrate a human user to control an agent. While the user repeatedly tries to safely guide the agent in the simulation, we collect data from the human input. Via behavior cloning, we translate the data into a strategy for the POMDP. The strategy resolves all nondeterminism and non-observability of the POMDP, resulting in a discrete-time Markov chain (MC). The efficient verification of this MC gives quantitative insights into the quality of the inferred human strategy by proving or disproving given system specifications. For the case that the quality of the strategy is not sufficient, we propose a refinement method using counterexamples presented to the human. Experiments show that by including humans into the POMDP verification loop we improve the state of the art by orders of magnitude in terms of scalability.

The changes in user preferences can originate from substantial reasons, like personality shift, or transient and circumstantial ones, like seasonal changes in item popularities. Disregarding these temporal drifts in modelling user preferences can result in unhelpful recommendations. Moreover, different temporal patterns can be associated with various preference domains, and preference components and their combinations. These components comprise preferences over features, preferences over feature values, conditional dependencies between features, socially-influenced preferences, and bias. For example, in the movies domain, the user can change his rating behaviour (bias shift), her preference for genre over language (feature preference shift), or start favouring drama over comedy (feature value preference shift). In this paper, we first propose a novel latent factor model to capture the domain-dependent component-specific temporal patterns in preferences. The component-based approach followed in modelling the aspects of preferences and their temporal effects enables us to arbitrarily switch components on and off. We evaluate the proposed method on three popular recommendation datasets and show that it significantly outperforms the most accurate state-of-the-art static models. The experiments also demonstrate the greater robustness and stability of the proposed dynamic model in comparison with the most successful models to date. We also analyse the temporal behaviour of different preference components and their combinations and show that the dynamic behaviour of preference components is highly dependent on the preference dataset and domain. Therefore, the results also highlight the importance of modelling temporal effects but also underline the advantages of a component-based architecture that is better suited to capture domain-specific balances in the contributions of the aspects.