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.

We propose a non-parametric anomaly detection algorithm for high dimensional data. We first rank scores derived from nearest neighbor graphs on $n$-point nominal training data. We then train limited complexity models to imitate these scores based on the max-margin learning-to-rank framework. A test-point is declared as an anomaly at $\alpha$-false alarm level if the predicted score is in the $\alpha$-percentile. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate $\alpha$, its decision region converges to the $\alpha$-percentile minimum volume level set of the unknown underlying density. In addition, we test both the statistical performance and computational efficiency of our algorithm on a number of synthetic and real-data experiments. Our results demonstrate the superiority of our algorithm over existing $K$-NN based anomaly detection algorithms, with significant computational savings.

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.

In this paper, we recover sparse signals from their noisy linear measurements by solving nonlinear differential inclusions, which is based on the notion of inverse scale space (ISS) developed in applied mathematics. Our goal here is to bring this idea to address a challenging problem in statistics, \emph{i.e.} finding the oracle estimator which is unbiased and sign-consistent using dynamics. We call our dynamics \emph{Bregman ISS} and \emph{Linearized Bregman ISS}. A well-known shortcoming of LASSO and any convex regularization approaches lies in the bias of estimators. However, we show that under proper conditions, there exists a bias-free and sign-consistent point on the solution paths of such dynamics, which corresponds to a signal that is the unbiased estimate of the true signal and whose entries have the same signs as those of the true signs, \emph{i.e.} the oracle estimator. Therefore, their solution paths are regularization paths better than the LASSO regularization path, since the points on the latter path are biased when sign-consistency is reached. We also show how to efficiently compute their solution paths in both continuous and discretized settings: the full solution paths can be exactly computed piece by piece, and a discretization leads to \emph{Linearized Bregman iteration}, which is a simple iterative thresholding rule and easy to parallelize. Theoretical guarantees such as sign-consistency and minimax optimal $l_2$-error bounds are established in both continuous and discrete settings for specific points on the paths. Early-stopping rules for identifying these points are given. The key treatment relies on the development of differential inequalities for differential inclusions and their discretizations, which extends the previous results and leads to exponentially fast recovering of sparse signals before selecting wrong ones.

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.

Models for which the likelihood function can be evaluated only up to a parameter-dependent unknown normalising constant, such as Markov random field models, are used widely in computer science, statistical physics, spatial statistics, and network analysis. However, Bayesian analysis of these models using standard Monte Carlo methods is not possible due to the intractability of their likelihood functions. Several methods that permit exact, or close to exact, simulation from the posterior distribution have recently been developed. However, estimating the evidence and Bayes' factors (BFs) for these models remains challenging in general. This paper describes new random weight importance sampling and sequential Monte Carlo methods for estimating BFs that use simulation to circumvent the evaluation of the intractable likelihood, and compares them to existing methods. In some cases we observe an advantage in the use of biased weight estimates. An initial investigation into the theoretical and empirical properties of this class of methods is presented. Some support for the use of biased estimates is presented, but we advocate caution in the use of such estimates.

The stochastic block model (SBM) is a popular framework for studying community detection in networks. This model is limited by the assumption that all nodes in the same community are statistically equivalent and have equal expected degrees. The degree-corrected stochastic block model (DCSBM) is a natural extension of SBM that allows for degree heterogeneity within communities. This paper proposes a convexified modularity maximization approach for estimating the hidden communities under DCSBM. Our approach is based on a convex programming relaxation of the classical (generalized) modularity maximization formulation, followed by a novel doubly-weighted $ \ell_1 $-norm $ k $-median procedure. We establish non-asymptotic theoretical guarantees for both approximate clustering and perfect clustering. Our approximate clustering results are insensitive to the minimum degree, and hold even in sparse regime with bounded average degrees. In the special case of SBM, these theoretical results match the best-known performance guarantees of computationally feasible algorithms. Numerically, we provide an efficient implementation of our algorithm, which is applied to both synthetic and real-world networks. Experiment results show that our method enjoys competitive performance compared to the state of the art in the literature.

It is well known that speaker verification systems are subject to spoofing attacks. The Automatic Speaker Verification Spoofing and Countermeasures Challenge -- ASVSpoof2015 -- provides a standard spoofing database, containing attacks based on synthetic speech, along with a protocol for experiments. This paper describes CPqD's systems submitted to the ASVSpoof2015 Challenge, based on deep neural networks, working both as a classifier and as a feature extraction module for a GMM and a SVM classifier. Results show the validity of this approach, achieving less than 0.5\% EER for known attacks.