Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods that use unlabeled data rely on certain assumptions about the data distribution. When those assumptions are not met in reality, including unlabeled data may actually decrease performance. Studying such methods, it therefore is particularly important to have an understanding of the underlying theory. In this review we gather results about the possible gains one can achieve when using semi-supervised learning as well as results about the limits of such methods. More precisely, this review collects the answers to the following questions: What are, in terms of improving supervised methods, the limits of semi-supervised learning? What are the assumptions of different methods? What can we achieve if the assumptions are true? Finally, we also discuss the biggest bottleneck of semi-supervised learning, namely the assumptions they make.

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the literature around the construction and use of Normalizing Flows for distribution learning. We aim to provide context and explanation of the models, review current state-of-the-art literature, and identify open questions and promising future directions.

Language identification ("LI") is the problem of determining the natural language that a document or part thereof is written in. Automatic LI has been extensively researched for over fifty years. Today, LI is a key part of many text processing pipelines, as text processing techniques generally assume that the language of the input text is known. Research in this area has recently been especially active. This article provides a brief history of LI research, and an extensive survey of the features and methods used in the LI literature. We describe the features and methods using a unified notation, to make the relationships between methods clearer. We discuss evaluation methods, applications of LI, as well as off-the-shelf LI systems that do not require training by the end user. Finally, we identify open issues, survey the work to date on each issue, and propose future directions for research in LI.

Blood glucose value prediction is an important task in diabetes management. While it is reported that glucose concentration is sensitive to social context such as mood, physical activity, stress, diet, alongside the influence of diabetes pathologies, we need more research on data and methodologies to incorporate and evaluate signals about such temporal context into prediction models. Person-generated data sources, such as actively contributed surveys as well as passively mined data from social media offer opportunity to capture such context, however the self-reported nature and sparsity of such data mean that such data are noisier and less specific than physiological measures such as blood glucose values themselves. Therefore, here we propose a Gaussian Process model to both address these data challenges and combine blood glucose and latent feature representations of contextual data for a novel multi-signal blood glucose prediction task. We find this approach outperforms common methods for multi-variate data, as well as using the blood glucose values in isolation. Given a robust evaluation across two blood glucose datasets with different forms of contextual information, we conclude that multi-signal Gaussian Processes can improve blood glucose prediction by using contextual information and may provide a significant shift in blood glucose prediction research and practice.

Although GAN-based methods have received many achievements in the last few years, they have not been such successful in generating discrete data. The most important challenge of these methods is the difficulty of passing the gradient from the discriminator to the generator when the generator outputs are discrete. Despite several attempts done to alleviate this problem, none of the existing GAN-based methods has improved the performance of text generation (using measures that evaluate both the quality and the diversity of generated samples) compared to a generative RNN that is simply trained by the maximum likelihood approach. In this paper, we propose a new framework for generating discrete data by an adversarial approach in which we do not need to pass the gradient to the generator. In the proposed method, the update of either the generator or the discriminator can be accomplished straightforwardly. Moreover, we leverage the discreteness of data to explicitly model the data distribution and ensure the normalization of the generated distribution and consequently the convergence properties of the proposed method. Experimental results generally show the superiority of the proposed DGSAN method compared to the other GAN-based approaches for generating discrete sequential data.

Submitted to the Annals of Applied Statistics SCALABLE MODELING OF SPATIOTEMPORAL DATA USING THE VARIATIONAL AUTOENCODER: AN APPLICATION IN GLAUCOMA By Samuel I. Berchuck, Felipe A. Medeiros and Sayan Mukherjee Duke University As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational autoencoder (V AE), an unsupervised generative model based on deep learning and approximate Bayesian inference, fills this void using a latent variable specification that is inferred jointly across the large number of samples. In this manuscript, we compare the performance of the V AE with a more classical ST method when analyzing longitudinal visual fields from a large cohort of patients in a prospective glaucoma study. Through simulation and a case study, we demonstrate that the V AE is a scalable method for analyzing ST data, when the goal is to obtain accurate predictions. R code to implement the V AE can be found on GitHub: https://github.com/berchuck/vaeST. 1. Introduction. As high-speed computing and medical imaging become increasingly inexpensive, massive amounts of data are generated that have to be analyzed and are often spatial in nature (Bearden and Thompson, 2017; Smith and Nichols, 2018). In the case of medical imaging, the number of patients that can be imaged has skyrocketed in recent years, allowing for studies that include images from many thousands of patients (Van Essen et al., 2013; Miller et al., 2016). The current spatial statistics literature focuses heavily on scalability in terms of the number of spatial locations (Banerjee, 2017), however largely ignores the setting where a joint model is needed for spatiotemporal (ST) data that are generated from a large cohort. Historically, learning an appropriate generating process in this setting was untenable, typically leading to simplifying assumptions, such as point-wise (PW) modeling of locations across time (Fitzke et al., 1996). In particular, generative models using deep learning have shown great promise in modeling complex distributions, p( x), for x x 1: M in some potentially high-dimensional space X . Sampling from X is often intractable, so instead generative modeling learns a distribution q (x) that can be sampled from and is close to p (x) (Doersch, 2016). As such, generative modeling can be viewed as an approximate method for performing inference in high-dimensional contexts, when there is an overwhelming availability of observations x . Generative modeling, and in particular the variational auto-encoder (V AE), are well-suited for modeling large cohorts of ST data, because they can characterize variability in a spatial data source through joint modeling (Kingma and Welling, 2013).

Why Partnership Strategy, not Technology, drives Digital Transformation? Known from the 17th century (Blaise Pascal invoked it in his famous wager, which is contained in his Pensées, published in 1670), the idea of expected value is that, when faced with a number of actions, each of which could give rise to more than one possible outcome with different probabilities, the rational procedure is to identify all possible outcomes, determine their values (positive or negative) and the probabilities that will result from each course of action, and multiply the two to give an "expected value", or the average expectation for an outcome; the action to be chosen should be the one that gives rise to the highest total expected value. Decision theory (or the theory of choice) is closely related to the field of game theory and is an interdisciplinary topic, studied by economists, statisticians, psychologists, biologists, political and other social scientists, philosophers, and computer scientists. The need for decision under uncertainty has never been stronger. Although the digital realm is evolving fast, the partnership strategical choice remains a human prerogative and a key driver of the digital ecosystem evolution.

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test samples are drawn from the same distribution---especially if the dimension of the uncertainty is large relative to the training sample size. Wasserstein distributionally robust optimization seeks data-driven decisions that perform well under the most adverse distribution within a certain Wasserstein distance from a nominal distribution constructed from the training samples. In this tutorial we will argue that this approach has many conceptual and computational benefits. Most prominently, the optimal decisions can often be computed by solving tractable convex optimization problems, and they enjoy rigorous out-of-sample and asymptotic consistency guarantees. We will also show that Wasserstein distributionally robust optimization has interesting ramifications for statistical learning and motivates new approaches for fundamental learning tasks such as classification, regression, maximum likelihood estimation or minimum mean square error estimation, among others.

As a subfield of machine learning, \emph{reinforcement learning} (RL) aims at empowering one's capabilities in behavioural decision making by using interaction experience with the world and an evaluative feedback. Unlike traditional supervised learning methods that usually rely on one-shot, exhaustive and supervised reward signals, RL tackles with sequential decision making problems with sampled, evaluative and delayed feedback simultaneously. Such distinctive features make RL technique a suitable candidate for developing powerful solutions in a variety of healthcare domains, where diagnosing decisions or treatment regimes are usually characterized by a prolonged and sequential procedure. This survey will discuss the broad applications of RL techniques in healthcare domains, in order to provide the research community with systematic understanding of theoretical foundations, enabling methods and techniques, existing challenges, and new insights of this emerging paradigm. By first briefly examining theoretical foundations and key techniques in RL research from efficient and representational directions, we then provide an overview of RL applications in a variety of healthcare domains, ranging from dynamic treatment regimes in chronic diseases and critical care, automated medical diagnosis from both unstructured and structured clinical data, as well as many other control or scheduling domains that have infiltrated many aspects of a healthcare system. Finally, we summarize the challenges and open issues in current research, and point out some potential solutions and directions for future research.

In several reinforcement learning (RL) scenarios such as security settings, there may be adversaries trying to interfere with the reward generating process for their own benefit. We introduce Threatened Markov Decision Processes (TMDPs) as a framework to support an agent against potential opponents in a RL context. We also propose a level-k thinking scheme resulting in a novel learning approach to deal with TMDPs. After introducing our framework and deriving theoretical results, relevant empirical evidence is given via extensive experiments, showing the benefits of accounting for adversaries in RL while the agent learns