The prevalence of high-dimensional signals in modern scientific investigation has inspired an influx of research on recovering structural information from noisy data. These problems arise across a variety of scientific and engineering disciplines; for example identifying cluster structure in communication or social networks, multiple hypothesis testing in genomics, or anomaly detection in sensor networking. Specific structural assumptions include sparsity [13], low-rankedness [11], cluster structure [15], and many others [8]. The literature in this direction focuses on three inference goals: detection, localization or recovery, and estimation or denoising. Detection tasks involve deciding whether an observation contains some meaningful information or is simply ambient noise, while recovery and estimation tasks involve more precisely characterizing the information contained in a signal. These problems are closely related, but also exhibit important differences, and this paper focuses on the recovery problem, where the goal is to identify, from a finite collection of signals, which signal produced the observed data. One frustration among researchers is that algorithmic and analytic techniques for these problems differ significantly for different structural assumptions. This issue was recently resolved in the context of the estimation, where the atomic norm [8] has provided a unifying algorithmic and analytical framework, but no such theory is available for detection and recovery problems. In this paper, we provide a unification for the recovery problem, leading to deeper understanding of how signal structure affects statistical performance.

The first ever human vs. computer no-limit Texas hold 'em competition took place from April 24-May 8, 2015 at River's Casino in Pittsburgh, PA. In this article I present my thoughts on the competition design, agent architecture, and lessons learned.

Linear independence testing is a fundamental information-theoretic and statistical problem that can be posed as follows: given $n$ points $\{(X_i,Y_i)\}^n_{i=1}$ from a $p+q$ dimensional multivariate distribution where $X_i \in \mathbb{R}^p$ and $Y_i \in\mathbb{R}^q$, determine whether $a^T X$ and $b^T Y$ are uncorrelated for every $a \in \mathbb{R}^p, b\in \mathbb{R}^q$ or not. We give minimax lower bound for this problem (when $p+q,n \to \infty$, $(p+q)/n \leq \kappa < \infty$, without sparsity assumptions). In summary, our results imply that $n$ must be at least as large as $\sqrt {pq}/\|\Sigma_{XY}\|_F^2$ for any procedure (test) to have non-trivial power, where $\Sigma_{XY}$ is the cross-covariance matrix of $X,Y$. We also provide some evidence that the lower bound is tight, by connections to two-sample testing and regression in specific settings.

We present a system for online monitoring of maritime activity over streaming positions from numerous vessels sailing at sea. It employs an online tracking module for detecting important changes in the evolving trajectory of each vessel across time, and thus can incrementally retain concise, yet reliable summaries of its recent movement. In addition, thanks to its complex event recognition module, this system can also offer instant notification to marine authorities regarding emergency situations, such as risk of collisions, suspicious moves in protected zones, or package picking at open sea. Not only did our extensive tests validate the performance, efficiency, and robustness of the system against scalable volumes of real-world and synthetically enlarged datasets, but its deployment against online feeds from vessels has also confirmed its capabilities for effective, real-time maritime surveillance.

Physicists use quantum models to describe the behavior of physical systems. Quantum models owe their success to their interpretability, to their relation to probabilistic models (quantization of classical models) and to their high predictive power. Beyond physics, these properties are valuable in general data science. This motivates the use of quantum models to analyze general nonphysical datasets. Here we provide both empirical and theoretical insights into the application of quantum models in data science. In the theoretical part of this paper, we firstly show that quantum models can be exponentially more efficient than probabilistic models because there exist datasets that admit low-dimensional quantum models and only exponentially high-dimensional probabilistic models. Secondly, we explain in what sense quantum models realize a useful relaxation of compressed probabilistic models. Thirdly, we show that sparse datasets admit low-dimensional quantum models and finally, we introduce a method to compute hierarchical orderings of properties of users (e.g., personality traits) and items (e.g., genres of movies). In the empirical part of the paper, we evaluate quantum models in item recommendation and observe that the predictive power of quantum-inspired recommender systems can compete with state-of-the-art recommender systems like SVD++ and PureSVD. Furthermore, we make use of the interpretability of quantum models by computing hierarchical orderings of properties of users and items. This work establishes a connection between data science (item recommendation), information theory (communication complexity), mathematical programming (positive semidefinite factorizations) and physics (quantum models).

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

For many complex diseases, there is a wide variety of ways in which an individual can manifest the disease. The challenge of personalized medicine is to develop tools that can accurately predict the trajectory of an individual's disease, which can in turn enable clinicians to optimize treatments. We represent an individual's disease trajectory as a continuous-valued continuous-time function describing the severity of the disease over time. We propose a hierarchical latent variable model that individualizes predictions of disease trajectories. This model shares statistical strength across observations at different resolutions--the population, subpopulation and the individual level. We describe an algorithm for learning population and subpopulation parameters offline, and an online procedure for dynamically learning individual-specific parameters. Finally, we validate our model on the task of predicting the course of interstitial lung disease, a leading cause of death among patients with the autoimmune disease scleroderma. We compare our approach against state-of-the-art and demonstrate significant improvements in predictive accuracy.

Technology and collaboration enable dramatic increases in the size of psychological and psychiatric data collections, but finding structure in these large data sets with many collected variables is challenging. Decision tree ensembles like random forests (Strobl, Malley, and Tutz, 2009) are a useful tool for finding structure, but are difficult to interpret with multiple outcome variables which are often of interest in psychology. To find and interpret structure in data sets with multiple outcomes and many predictors (possibly exceeding the sample size), we introduce a multivariate extension to a decision tree ensemble method called Gradient Boosted Regression Trees (Friedman, 2001). Our method, multivariate tree boosting, can be used for identifying important predictors, detecting predictors with non-linear effects and interactions without specification of such effects, and for identifying predictors that cause two or more outcome variables to covary without parametric assumptions. We provide the R package 'mvtboost' to estimate, tune, and interpret the resulting model, which extends the implementation of univariate boosting in the R package 'gbm' (Ridgeway, 2013) to continuous, multivariate outcomes. To illustrate the approach, we analyze predictors of psychological well-being (Ryff and Keyes, 1995). Simulations verify that our approach identifies predictors with non-linear effects and achieves high prediction accuracy, exceeding or matching the performance of (penalized) multivariate multiple regression and multivariate decision trees over a wide range of conditions.

In recent years there has been an increased interest in statistical analysis of data with multiple types of relations among a set of entities. Such multi-relational data can be represented as multi-layer graphs where the set of vertices represents the entities and multiple types of edges represent the different relations among them. For community detection in multi-layer graphs, we consider two random graph models, the multi-layer stochastic blockmodel (MLSBM) and a model with a restricted parameter space, the restricted multi-layer stochastic blockmodel (RMLSBM). We derive consistency results for community assignments of the maximum likelihood estimators (MLEs) in both models where MLSBM is assumed to be the true model, and either the number of nodes or the number of types of edges or both grow. We compare MLEs in the two models with other baseline approaches, such as separate modeling of layers, aggregating the layers and majority voting. RMLSBM is shown to have advantage over MLSBM when either the growth rate of the number of communities is high or the growth rate of the average degree of the component graphs in the multi-graph is low. We also derive minimax rates of error and sharp thresholds for achieving consistency of community detection in both models, which are then used to compare the multi-layer models with a baseline model, the aggregate stochastic block model. The simulation studies and real data applications confirm the superior performance of the multi-layer approaches in comparison to the baseline procedures.

Domain Adaptation (DA) techniques aim at enabling machine learning methods learn effective classifiers for a "target'' domain when the only available training data belongs to a different "source'' domain. In this paper we present the Distributional Correspondence Indexing (DCI) method for domain adaptation in sentiment classification. DCI derives term representations in a vector space common to both domains where each dimension reflects its distributional correspondence to a pivot, i.e., to a highly predictive term that behaves similarly across domains. Term correspondence is quantified by means of a distributional correspondence function (DCF). We propose a number of efficient DCFs that are motivated by the distributional hypothesis, i.e., the hypothesis according to which terms with similar meaning tend to have similar distributions in text. Experiments show that DCI obtains better performance than current state-of-the-art techniques for cross-lingual and cross-domain sentiment classification. DCI also brings about a significantly reduced computational cost, and requires a smaller amount of human intervention. As a final contribution, we discuss a more challenging formulation of the domain adaptation problem, in which both the cross-domain and cross-lingual dimensions are tackled simultaneously.