Advertisers that engage in real-time bidding (RTB) to display their ads commonly have two goals: learning their optimal bidding policy and estimating the expected effect of exposing users to their ads. Typical strategies to accomplish one of these goals tend to ignore the other, creating an apparent tension between the two. This paper exploits the economic structure of the bid optimization problem faced by advertisers to show that these two objectives can actually be perfectly aligned. By framing the advertiser's problem as a multi-armed bandit (MAB) problem, we propose a modified Thompson Sampling (TS) algorithm that concurrently learns the optimal bidding policy and estimates the expected effect of displaying the ad while minimizing economic losses from potential sub-optimal bidding. Simulations show that not only the proposed method successfully accomplishes the advertiser's goals, but also does so at a much lower cost than more conventional experimentation policies aimed at performing causal inference.

In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable functions, multiresolution analysis enables us to construct a wavelet system from which the basis functions are selected adaptively, resulting in a tree structure. Furthermore, we present the convergence rate of our multiscale approximation which does not depend on the regularity of basis functions.

In [1], we have explored the theoretical aspects of feature selection and evolutionary algorithms. In this chapter, we focus on optimization algorithms for enhancing data analytic process, i.e., we propose to explore applications of nature-inspired algorithms in data science. Feature selection optimization is a hybrid approach leveraging feature selection techniques and evolutionary algorithms process to optimize the selected features. Prior works solve this problem iteratively to converge to an optimal feature subset. Feature selection optimization is a non-specific domain approach. Data scientists mainly attempt to find an advanced way to analyze data n with high computational efficiency and low time complexity, leading to efficient data analytics. Thus, by increasing generated/measured/sensed data from various sources, analysis, manipulation and illustration of data grow exponentially. Due to the large scale data sets, Curse of dimensionality (CoD) is one of the NP-hard problems in data science. Hence, several efforts have been focused on leveraging evolutionary algorithms (EAs) to address the complex issues in large scale data analytics problems. Dimension reduction, together with EAs, lends itself to solve CoD and solve complex problems, in terms of time complexity, efficiently. In this chapter, we first provide a brief overview of previous studies that focused on solving CoD using feature extraction optimization process. We then discuss practical examples of research studies are successfully tackled some application domains, such as image processing, sentiment analysis, network traffics / anomalies analysis, credit score analysis and other benchmark functions/data sets analysis.

In this paper, we address the problem of measuring and analysing sensation, the subjective magnitude of one's experience. We do this in the context of the method of triads: the sensation of the stimulus is evaluated via relative judgments of the form: "Is stimulus S_i more similar to stimulus S_j or to stimulus S_k?". We propose to use ordinal embedding methods from machine learning to estimate the scaling function from the relative judgments. We review two relevant and well-known methods in psychophysics which are partially applicable in our setting: non-metric multi-dimensional scaling (NMDS) and the method of maximum likelihood difference scaling (MLDS). We perform an extensive set of simulations, considering various scaling functions, to demonstrate the performance of the ordinal embedding methods. We show that in contrast to existing approaches our ordinal embedding approach allows, first, to obtain reasonable scaling function from comparatively few relative judgments, second, the estimation of non-monotonous scaling functions, and, third, multi-dimensional perceptual scales. In addition to the simulations, we analyse data from two real psychophysics experiments using ordinal embedding methods. Our results show that in the one-dimensional, monotonically increasing perceptual scale our ordinal embedding approach works as well as MLDS, while in higher dimensions, only our ordinal embedding methods can produce a desirable scaling function. To make our methods widely accessible, we provide an R-implementation and general rules of thumb on how to use ordinal embedding in the context of psychophysics.

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.

Self-reinforcing feedback loops in personalization systems are typically caused by users choosing from a limited set of alternatives presented systematically based on previous choices. We propose a Bayesian choice model built on Luce axioms that explicitly accounts for users' limited exposure to alternatives. Our model is fair---it does not impose negative bias towards unpresented alternatives, and practical---preference estimates are accurately inferred upon observing a small number of interactions. It also allows efficient sampling, leading to a straightforward online presentation mechanism based on Thompson sampling. Our approach achieves low regret in learning to present upon exploration of only a small fraction of possible presentations. The proposed structure can be reused as a building block in interactive systems, e.g., recommender systems, free of feedback loops.

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.

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.