Reinforcement learning is a body of theory and techniques for optimal sequential decision making developed in the last thirty years primarily within the machine learning and operations research communities, and which has separately become important in psychology and neuroscience. This tutorial will develop an intuitive understanding of the underlying formal problem (Markov decision processes) and its core solution methods, including dynamic programming, Monte Carlo methods, and temporal-difference learning. It will focus on how these methods have been combined with parametric function approximation, including deep learning, to find good approximate solutions to problems that are otherwise too large to be addressed at all.

Remarkably general method for bounding the statistical risk of penalized likelihood estimators comes from work on two-part coding, one of the minimum description length (MDL) approaches to statistical inference. Two-part coding MDL prescribes assigning codelengths to a model (or model class) then selecting the distribution that provides the most efficient description of one's data [1]. The total description length has two parts: the part that specifies a distribution within the model (as well as a model within the model class if necessary) and the part that specifies the data with reference to the specified distribution. If the codelengths are exactly Kraft-valid, this approach is equivalent to Bayesian maximum a posteriori (MAP) estimation, in that the two parts correspond to log reciprocal of prior and log reciprocal of likelihood respectively. More generally, one can call the part of the codelength specifying the distribution a penalty term; it is called the complexity in MDL literature. Let (Θ, L) denote a discrete set indexing distributions along with a complexity function. With X P, the (pointwise) redundancy of any θ Θ is its two-part codelength minus log(1/p(X)), the codelength one gets by using P as the coding distribution.

Artificial intelligence (AI) generally and machine learning (ML) specifically demonstrate impressive practical success in many different application domains, e.g. in autonomous driving, speech recognition, or recommender systems. Deep learning approaches, trained on extremely large data sets or using reinforcement learning methods have even exceeded human performance in visual tasks, particularly on playing games such as Atari, or mastering the game of Go. Even in the medical domain there are remarkable results. The central problem of such models is that they are regarded as black-box models and even if we understand the underlying mathematical principles, they lack an explicit declarative knowledge representation, hence have difficulty in generating the underlying explanatory structures. This calls for systems enabling to make decisions transparent, understandable and explainable. A huge motivation for our approach are rising legal and privacy aspects. The new European General Data Protection Regulation entering into force on May 25th 2018, will make black-box approaches difficult to use in business. This does not imply a ban on automatic learning approaches or an obligation to explain everything all the time, however, there must be a possibility to make the results re-traceable on demand. In this paper we outline some of our research topics in the context of the relatively new area of explainable-AI with a focus on the application in medicine, which is a very special domain. This is due to the fact that medical professionals are working mostly with distributed heterogeneous and complex sources of data. In this paper we concentrate on three sources: images, *omics data and text. We argue that research in explainable-AI would generally help to facilitate the implementation of AI/ML in the medical domain, and specifically help to facilitate transparency and trust.

In X-ray binary star systems consisting of a compact object that accretes material from an orbiting secondary star, there is no straightforward means to decide if the compact object is a black hole or a neutron star. To assist this classification, we develop a Bayesian statistical model that makes use of the fact that X-ray binary systems appear to cluster based on their compact object type when viewed from a 3-dimensional coordinate system derived from X-ray spectral data. The first coordinate of this data is the ratio of counts in mid to low energy band (color 1), the second coordinate is the ratio of counts in high to low energy band (color 2), and the third coordinate is the sum of counts in all three bands. We use this model to estimate the probabilities that an X-ray binary system contains a black hole, non-pulsing neutron star, or pulsing neutron star. In particular, we utilize a latent variable model in which the latent variables follow a Gaussian process prior distribution, and hence we are able to induce the spatial correlation we believe exists between systems of the same type. The utility of this approach is evidenced by the accurate prediction of system types using Rossi X-ray Timing Explorer All Sky Monitor data, but it is not flawless. In particular, non-pulsing neutron systems containing "bursters" that are close to the boundary demarcating systems containing black holes tend to be classified as black hole systems. As a byproduct of our analyses, we provide the astronomer with public R code that can be used to predict the compact object type of X-ray binaries given training data.

In this work we introduce declarative statistics, a suite of declarative modelling tools for statistical analysis. Statistical constraints represent the key building block of declarative statistics. First, we introduce a range of relevant counting and matrix constraints and associated decompositions, some of which novel, that are instrumental in the design of statistical constraints. Second, we introduce a selection of novel statistical constraints and associated decompositions, which constitute a self-contained toolbox that can be used to tackle a wide range of problems typically encountered by statisticians. Finally, we deploy these statistical constraints to a wide range of application areas drawn from classical statistics and we contrast our framework against established practices.

Many machine learning tasks are interested in recognizing or identifying an individual instance within a large set of possible candidates. These problems are usually modeled as multi-class classification problems, with a large and possibly complex label set. Leading examples include detecting the speaker from his voice patterns (Togneri and Pullella, 2011), identifying the author from her written text (Stamatatos et al., 2014), or labeling the object category from its image (Duygulu et al., 2002, Deng et al., 2010, Oquab et al., 2014). In all these examples, the algorithm observes an input x, and uses the classifier function h to guess the label y from a large label set S. 1 There are multiple practical challenges in developing classifiers for large label sets. Collecting high quality training data is perhaps the main obstacle, as the costs scale with the number of classes. It can be affordable to first collect data for a small set of classes, even if the long-term goal is to generalize to a larger set. Furthermore, classifier development can be accelerated by training first on fewer classes, as each training cycle may require substantially less resources. Indeed, due to interest in how small-set performance generalizes to larger sets, such comparisons can found in the literature (Oquab et al., 2014, Griffin et al., 2007). A natural question is: how does changing the size of the label set affect the classification accuracy?

Significant success has been realized recently on applying machine learning to real-world applications. There have also been corresponding concerns on the privacy of training data, which relates to data security and confidentiality issues. Differential privacy provides a principled and rigorous privacy guarantee on machine learning models. While it is common to design a model satisfying a required differential-privacy property by injecting noise, it is generally hard to balance the trade-off between privacy and utility. We show that stochastic gradient Markov chain Monte Carlo (SG-MCMC) -- a class of scalable Bayesian posterior sampling algorithms proposed recently -- satisfies strong differential privacy with carefully chosen step sizes. We develop theory on the performance of the proposed differentially-private SG-MCMC method. We conduct experiments to support our analysis and show that a standard SG-MCMC sampler without any modification (under a default setting) can reach state-of-the-art performance in terms of both privacy and utility on Bayesian learning.

Bayesian Computational Analyses with R is an introductory course on the use and implementation of Bayesian modeling using R software. The Bayesian approach is an alternative to the "frequentist" approach where one simply takes a sample of data and makes inferences about the likely parameters of the population. In contrast, the Bayesian approach uses both likelihood functions and a sample of observed data (the'prior') to estimate the most likely values and distributions for the estimated population parameters (the'posterior'). The course is useful to anyone who wishes to learn about Bayesian concepts and is suited to both novice and intermediate Bayesian students and Bayesian practitioners. It is both a practical, "hands-on" course with many examples using R scripts and software, and is conceptual, as the course explains the Bayesian concepts. All materials, software, R scripts, slides, exercises and solutions are included with the course materials.

Variational inference [25, 7, 40] is now a well-established tool to approximate intractable posterior distributions in hierarchical multi-layered Bayesian models. The traditional Markov chain Monte Carlo (MCMC; [17]) approach of approximating distributions with intractable normalizing constants draws (correlated) samples according to a discrete-time Markov chain whose stationary distribution is the target distribution. Despite their success and popularity, MCMC methods can be slow to converge and lack scalability in big data problems and/or problems involving very many latent variables, which has fueled search for alternatives. In contrast to the sampling approach of MCMC, variational inference approaches the problem from an optimization viewpoint. First, a class of analytically tractable distributions, referred to as the variational family, is identified for the problem at hand. For example, in mean-field approximation, the set of parameters and latent variables is divided into blocks and the variational distribution is assumed to be independent across blocks.

Abstract--Long Short-T erm Memory networks trained with gradient descent and back-propagation have received great success in various applications. However, point estimation of the weights of the networks is prone to over-fitting problems and lacks important uncertainty information associated with the estimation. However, exact Bayesian neural network methods are intractable and non-applicable for real-world applications. In this study, we propose an approximate estimation of the weights uncertainty using Ensemble Kalman Filter, which is easily scalable to a large number of weights. T o assess the proposed algorithm, we apply it to outlier detection in five real-world events retrieved from the Twitter platform. I NTRODUCTION The recent resurgence of neural network trained with back-propagation has established state-of-art results in a wide range of domains. However, backpropagation-based neural networks (NN) are associated with many disadvantages, including but not limited to, the lack of uncertainty estimation, tendency of overfitting small data, and tuning of many hyper-parameters.