This is an up-to-date introduction to and overview of the Minimum Description Length (MDL) Principle, a theory of inductive inference that can be applied to general problems in statistics, machine learning and pattern recognition. While MDL was originally based on data compression ideas, this introduction can be read without any knowledge thereof. It takes into account all major developments since 2007, the last time an extensive overview was written. These include new methods for model selection and averaging and hypothesis testing, as well as the first completely general definition of {\em MDL estimators}. Incorporating these developments, MDL can be seen as a powerful extension of both penalized likelihood and Bayesian approaches, in which penalization functions and prior distributions are replaced by more general luckiness functions, average-case methodology is replaced by a more robust worst-case approach, and in which methods classically viewed as highly distinct, such as AIC vs BIC and cross-validation vs Bayes can, to a large extent, be viewed from a unified perspective.

Items in modern recommender systems are often organized in hierarchical structures. These hierarchical structures and the data within them provide valuable information for building personalized recommendation systems. In this paper, we propose a general hierarchical Bayesian learning framework, i.e., \emph{HBayes}, to learn both the structures and associated latent factors. Furthermore, we develop a variational inference algorithm that is able to learn model parameters with fast empirical convergence rate. The proposed HBayes is evaluated on two real-world datasets from different domains. The results demonstrate the benefits of our approach on item recommendation tasks, and show that it can outperform the state-of-the-art models in terms of precision, recall, and normalized discounted cumulative gain. To encourage the reproducible results, we make our code public on a git repo: \url{https://tinyurl.com/ycruhk4t}.

The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend this bridge between Rademacher complexity and state-of-the-art PAC-Bayesian theory. We first demonstrate that one can match the fast rate of Catoni's PAC-Bayes bounds (Catoni, 2007) using shifted Rademacher processes (Wegkamp, 2003; Lecu\'{e} and Mitchell, 2012; Zhivotovskiy and Hanneke, 2018). We then derive a new fast-rate PAC-Bayes bound in terms of the "flatness" of the empirical risk surface on which the posterior concentrates. Our analysis establishes a new framework for deriving fast-rate PAC-Bayes bounds and yields new insights on PAC-Bayesian theory.

--The problem of missing values in multivariable time series is a key challenge in many applications such as clinical data mining. Although many imputation methods show their effectiveness in many applications, few of them are designed to accommodate clinical multivariable time series. In this work, we propose a multiple imputation model that capture both cross-sectional information and temporal correlations. We integrate Gaussian processes with mixture models and introduce individualized mixing weights to handle the variance of predictive confidence of Gaussian process models. The proposed model is compared with several state-of-the-art imputation algorithms on both real-world and synthetic datasets. Experiments show that our best model can provide more accurate imputation than the benchmarks on all of our datasets. I NTRODUCTION The computational modeling in clinical applications attracts growing interest with the realization that the quantitative understanding of patient pathophysiological progression is crucial to clinical studies [1]. With a comprehensive and precise modeling, we can have a better understanding of a patient's state, offer more precise diagnosis and provide better individualized therapies [2]. Researchers are increasingly motivated to build more accurate computational models from multiple types of clinical data. However, missing values in clinical data challenge researchers using analytic techniques for modeling, as many of the techniques are designed for complete data. Traditional strategies used in clinical studies to handle missing values include deleting records with missing values and imputing missing entries by mean values. However, deleting records with missing values and some other filtering strategies can introduce biases [3] that can impact modeling in many ways, thus limiting its generalizability. Mean imputation is widely used by researchers to handle missing values. However, it is shown to yield less effective estimates than many other modern imputation techniques [4]-[7], such as maximum likelihood approaches and multiple imputation methods (e.g.

-- As deep learning applications are becoming more and more pervasive in robotics, the question of evaluating the reliability of inferences becomes a central question in the robotics community. This domain, known as predictive uncertainty, has come under the scrutiny of research groups developing Bayesian approaches adapted to deep learning such as Monte Carlo Dropout. Unfortunately, for the time being, the real goal of predictive uncertainty has been swept under the rug. Indeed, these approaches are solely evaluated in terms of raw performance of the network prediction, while the quality of their estimated uncertainty is not assessed. Evaluating such uncertainty prediction quality is especially important in robotics, as actions shall depend on the confidence in perceived information. In this context, the main contribution of this article is to propose a novel metric that is adapted to the evaluation of relative uncertainty assessment and directly applicable to regression with deep neural networks. T o experimentally validate this metric, we evaluate it on a toy dataset and then apply it to the task of monocular depth estimation. The outcome of deep learning these past few years - capable of reaching and even sometimes surpass human performances, e.g. for vision tasks [1], [2] - offers novel avenues in robotics, but also raises some novel questions: as pointed out by [3], how much trust can we put in the predictions of a deep learning system?

This paper utilizes the hierarchical model structure from the Bayesian Lasso in the Sparse Bayesian Learning process to develop a new type of probabilistic supervised learning approach. This approach has several performance advantages, such as being fast, sparse and especially robust to the variance in random noise. The hierarchical model structure in this Bayesian framework is designed in such a way that the priors do not only penalize the unnecessary complexity of the model but also depend on the variance of the random noise in the data. The hyperparameters in the model are estimated by the Fast Marginal Likelihood Maximization algorithm and can achieve low computational cost and faster learning process. We compare our methodology with two other popular Sparse Bayesian Learning models: The Relevance Vector Machine and a sparse Bayesian model that has been used for signal reconstruction in compressive sensing. We show that our method will generally provide more sparse solutions and be more flexible and stable when data is polluted by high variance noise.

Can an arbitrarily intelligent reinforcement learning agent be kept under control by a human user? Or do agents with sufficient intelligence inevitably find ways to shortcut their reward signal? This question impacts how far reinforcement learning can be scaled, and whether alternative paradigms must be developed in order to build safe artificial general intelligence. In this paper, we use an intuitive yet precise graphical model called causal influence diagrams to formalize reward tampering problems. We also describe a number of modifications to the reinforcement learning objective that prevent incentives for reward tampering. We verify the solutions using recently developed graphical criteria for inferring agent incentives from causal influence diagrams. Along the way, we also compare corrigibility and self-preservation properties of the various solutions, and discuss how they can be combined into a single agent without reward tampering incentives.

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It is also the algorithm of choice to fit mixture models: generative models that represent unlabelled points originating from $k$ different processes, as samples from $k$ multivariate distributions. In this work we define and use a quantum version of EM to fit a Gaussian Mixture Model. Given quantum access to a dataset of $n$ vectors of dimension $d$, our algorithm has convergence and precision guarantees similar to the classical algorithm, but the runtime is only polylogarithmic in the number of elements in the training set, and is polynomial in other parameters - as the dimension of the feature space, and the number of components in the mixture. We generalize further the algorithm in two directions. First, we show how to fit any mixture model of probability distributions in the exponential family. Then, we show how to use this algorithm to compute the Maximum a Posteriori (MAP) estimate of a mixture model: the Bayesian approach to likelihood estimation problems. We discuss the performance of the algorithm on datasets that are expected to be classified successfully by those algorithms, arguing that on those cases we can give strong guarantees on the runtime.

Learning with label proportions(LLP), which seeks an instance-level classifier merely based on bag-level label proportions, is a new paradigm in machine learning that addresses the classification of instances [1, 2, 3]. In LLP, we only know the proportions of examples belonging to different classes in each bag; however the labels of the instances are unknown. From the binary classification perspective, the task of LLP is to learn a classifier to classify the unknown label instance as either positive class or negative class. The formulation that learning with label proportions has been first proposed by Kuck et al. in [1], which can be used for political elections analysis. In the case of politician polls, each candidate may have a group of loyal voters and some swing voters. They may know the vague proportion of votes cast in each district; however, they usually do not know the vote of each person. Since the candidates have limited resources, they have to analyze political elections and consider which kind of voters they should focus on so as to maximize their interests. To date, LLP has been applied to forecasting revenue [4], image classification [5, 6], video event detection [7], demographics mining [8] and privacy protection [9]. Figure 1 illustrates the binary classification problem in LLP.

Despite numerous research work in reinforcement learning (RL) and the recent successes obtained by combining it with deep learning, deep reinforcement learning (DRL) is still facing many challenges. Some of them, like the ability to abstract actions or the difficulty to explore the environment with sparse rewards, can be addressed by the use of intrinsic motivation. In this article, we provide a survey on the role of intrinsic motivation in DRL. We categorize the different kinds of intrinsic motivations and detail their interests and limitations. Our investigation shows that the combination of DRL and intrinsic motivation enables to learn more complicated and more generalisable behaviours than standard DRL. We provide an in-depth analysis describing learning modules through an unifying scheme composed of information theory, compression theory and reinforcement learning. We then explain how these modules could serve as building blocks over a complete developmental architecture, highlighting the numerous outlooks of the domain.