We propose a new framework of XGBoost that predicts the entire conditional distribution of a univariate response variable. In particular, XGBoostLSS models all moments of a parametric distribution, i.e., mean, location, scale and shape (LSS), instead of the conditional mean only. Choosing from a wide range of continuous, discrete and mixed discrete-continuous distribution, modelling and predicting the entire conditional distribution greatly enhances the flexibility of XGBoost, as it allows to gain additional insight into the data generating process, as well as to create probabilistic forecasts from which prediction intervals and quantiles of interest can be derived. We present both a simulation study and real world examples that demonstrate the benefits of our approach.

Many methods for machine learning rely on approximate inference from intractable probability distributions. Variational inference approximates such distributions by tractable models that can be subsequently used for approximate inference. Learning sufficiently accurate approximations requires a rich model family and careful exploration of the relevant modes of the target distribution. We propose a method for learning accurate GMM approximations of intractable probability distributions based on insights from policy search by establishing information-geometric trust regions for principled exploration. For efficient improvement of the GMM approximation, we derive a lower bound on the corresponding optimization objective enabling us to update the components independently. The use of the lower bound ensures convergence to a local optimum of the original objective. The number of components is adapted online by adding new components in promising regions and by deleting components with negligible weight. We demonstrate on several domains that we can learn approximations of complex, multi-modal distributions with a quality that is unmet by previous variational inference methods, and that the GMM approximation can be used for drawing samples that are on par with samples created by state-of-the-art MCMC samplers while requiring up to three orders of magnitude less computational resources.

Studies on massive open online courses (MOOCs) users discuss the existence of typical profiles and their impact on the learning process of the students. However defining the typical behaviors as well as classifying the users accordingly is a difficult task. In this paper we suggest two methods to model MOOC users behaviour given their log data. We mold their behavior into a Markov Decision Process framework. We associate the user's intentions with the MDP reward and argue that this allows us to classify them.

We derive the functional form of mutual information (MI) from a set of design criteria and a principle of maximal sufficiency. The (MI) between two sets of propositions is a global quantifier of correlations and is implemented as a tool for ranking joint probability distributions with respect to said correlations. The derivation parallels the derivations of relative entropy with an emphasis on the behavior of independent variables. By constraining the functional $I$ according to special cases, we arrive at its general functional form and hence establish a clear meaning behind its definition. We also discuss the notion of sufficiency and offer a new definition which broadens its applicability.

The time series cluster kernel (TCK) provides a powerful tool for analysing multivariate time series subject to missing data. TCK is designed using an ensemble learning approach in which Bayesian mixture models form the base models. Because of the Bayesian approach, TCK can naturally deal with missing values without resorting to imputation and the ensemble strategy ensures robustness to hyperparameters, making it particularly well suited for unsupervised learning. However, TCK assumes missing at random and that the underlying missingness mechanism is ignorable, i.e. uninformative, an assumption that does not hold in many real-world applications, such as e.g. medicine. To overcome this limitation, we present a kernel capable of exploiting the potentially rich information in the missing values and patterns, as well as the information from the observed data. In our approach, we create a representation of the missing pattern, which is incorporated into mixed mode mixture models in such a way that the information provided by the missing patterns is effectively exploited. Moreover, we also propose a semi-supervised kernel, capable of taking advantage of incomplete label information to learn more accurate similarities. Experiments on benchmark data, as well as a real-world case study of patients described by longitudinal electronic health record data who potentially suffer from hospital-acquired infections, demonstrate the effectiveness of the proposed methods.

The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to a simple transformation, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.

Dynamic Bayesian networks (DBNs) are a general model for stochastic processes with partially observed states. Belief filtering in DBNs is the task of inferring the belief state (i.e. the probability distribution over process states) based on incomplete and uncertain observations. In this article, we explore the idea of accelerating the filtering task by automatically exploiting causality in the process. We consider a specific type of causal relation, called passivity, which pertains to how state variables cause changes in other variables. We present the Passivity-based Selective Belief Filtering (PSBF) method, which maintains a factored belief representation and exploits passivity to perform selective updates over the belief factors. PSBF is evaluated in both synthetic processes and a simulated multi-robot warehouse, where it outperformed alternative filtering methods by exploiting passivity.

Language modelling has been an integral part of providing an understanding of the nature of language to capture its meaning. In order to improve the machine understanding of language using sequential models, we seek to explore two prominent areas of statistical language models, the Hidden Markov Model (HMM), and a Recurrent Neural Network (RNN) architecture, known commonly as Long Short-Term Memory (LSTM). Under a discrete stochastic modelling framework, HMM's were first introduced in Rabiner [1] to classify speech signals. First used to automate AT&T's voice activated call center, the revolutionary technology allowed computers to robustly characterise speech, and form a basic understanding of spoken words. HMM's have since become a definitive benchmark for the state-of-the-art for speech recognition, and text recognition. Around the same period, RNN's were introduced by Rumelhart et al. [2], however, the training complexity of the model was far too high and not commensurate with the hardware capabilities at the time. In the 21st century, With the introduction of more advanced hardware for deep learning model training, came a wave of applications for the RNN for both voice, text recognition, [3], [4], [5] and machine translation [6]. In parallel, an early form of neural language model was developed in Bengio et al. [7], displaying promising results in statistical language modelling. LSTM's were the first introduced in Hochreiter and Schmidhuber [8], specifically to combat the vanishing gradient problem, which will be further addressed in Section 1.2.

We tackle the problem of acting in an unknown finite and discrete Markov Decision Process (MDP) for which the expected shortest path from any state to any other state is bounded by a finite number $D$. An MDP consists of $S$ states and $A$ possible actions per state. Upon choosing an action $a_t$ at state $s_t$, one receives a real value reward $r_t$, then one transits to a next state $s_{t+1}$. The reward $r_t$ is generated from a fixed reward distribution depending only on $(s_t, a_t)$ and similarly, the next state $s_{t+1}$ is generated from a fixed transition distribution depending only on $(s_t, a_t)$. The objective is to maximize the accumulated rewards after $T$ interactions. In this paper, we consider the case where the reward distributions, the transitions, $T$ and $D$ are all unknown. We derive the first polynomial time Bayesian algorithm, BUCRL{} that achieves up to logarithm factors, a regret (i.e the difference between the accumulated rewards of the optimal policy and our algorithm) of the optimal order $\tilde{\mathcal{O}}(\sqrt{DSAT})$. Importantly, our result holds with high probability for the worst-case (frequentist) regret and not the weaker notion of Bayesian regret. We perform experiments in a variety of environments that demonstrate the superiority of our algorithm over previous techniques. Our work also illustrates several results that will be of independent interest. In particular, we derive a sharper upper bound for the KL-divergence of Bernoulli random variables. We also derive sharper upper and lower bounds for Beta and Binomial quantiles. All the bound are very simple and only use elementary functions.

Reduced models are simplified versions of a given domain, designed to accelerate the planning process. Interest in reduced models has grown since the surprising success of determinization in the first international probabilistic planning competition, leading to the development of several enhanced determinization techniques. To address the drawbacks of previous determinization methods, we introduce a family of reduced models in which probabilistic outcomes are classified as one of two types: primary and exceptional. In each model that belongs to this family of reductions, primary outcomes can occur an unbounded number of times per trajectory, while exceptions can occur at most a finite number of times, specified by a parameter. Distinct reduced models are characterized by two parameters: the maximum number of primary outcomes per action, and the maximum number of occurrences of exceptions per trajectory. This family of reductions generalizes the well-known most-likely-outcome determinization approach, which includes one primary outcome per action and zero exceptional outcomes per plan. We present a framework to determine the benefits of planning with reduced models, and develop a continual planning approach that handles situations where the number of exceptions exceeds the specified bound during plan execution. Using this framework, we compare the performance of various reduced models and consider the challenge of generating good ones automatically. We show that each one of the dimensions---allowing more than one primary outcome or planning for some limited number of exceptions---could improve performance relative to standard determinization. The results place previous work on determinization in a broader context and lay the foundation for a systematic exploration of the space of model reductions.