We study the problem of detecting an abrupt change to the signal covariance matrix. In particular, the covariance changes from a "white" identity matrix to an unknown spiked or low-rank matrix. Two sequential change-point detection procedures are presented, based on the largest and the smallest eigenvalues of the sample covariance matrix. To control false-alarm-rate, we present an accurate theoretical approximation to the average-run-length (ARL) and expected detection delay (EDD) of the detection, leveraging the extreme eigenvalue distributions from random matrix theory and by capturing a non-negligible temporal correlation in the sequence of scan statistics due to the sliding window approach. Real data examples demonstrate the good performance of our method for detecting behavior change of a swarm.

Developing efficient numerical algorithms for high dimensional (say, hundreds of dimensions) partial differential equations (PDEs) has been one of the most challenging tasks in applied mathematics. As is well-known, the difficulty lies in the "curse of dimensionality" [1], namely, as the dimensionality grows, the complexity of the algorithms grows exponentially. For this reason, there are only a limited number of cases where practical 2 high dimensional algorithms have been developed. For linear parabolic PDEs, one can use the Feynman-Kac formula and Monte Carlo methods to develop efficient algorithms to evaluate solutions at any given space-time locations. For a class of inviscid Hamilton-Jacobi equations, Darbon & Osher have recently developed an algorithm which performs numerically well in the case of such high dimensional inviscid Hamilton-Jacobi equations; see [9]. Darbon & Osher's algorithm is based on results from compressed sensing and on the Hopf formulas for the Hamilton-Jacobi equations. A general algorithm for (nonlinear) parabolic PDEs based on the Feynman-Kac and Bismut-Elworthy-Li formula and a multilevel decomposition of Picard iteration was developed in [11] and has been shown to be quite efficient on a number examples in finance and physics.

Peer effects, in which the behavior of an individual is affected by the behavior of their peers, are posited by multiple theories in the social sciences. Other processes can also produce behaviors that are correlated in networks and groups, thereby generating debate about the credibility of observational (i.e. nonexperimental) studies of peer effects. Randomized field experiments that identify peer effects, however, are often expensive or infeasible. Thus, many studies of peer effects use observational data, and prior evaluations of causal inference methods for adjusting observational data to estimate peer effects have lacked an experimental "gold standard" for comparison. Here we show, in the context of information and media diffusion on Facebook, that high-dimensional adjustment of a nonexperimental control group (677 million observations) using propensity score models produces estimates of peer effects statistically indistinguishable from those from using a large randomized experiment (220 million observations). Naive observational estimators overstate peer effects by 320% and commonly used variables (e.g., demographics) offer little bias reduction, but adjusting for a measure of prior behaviors closely related to the focal behavior reduces bias by 91%. High-dimensional models adjusting for over 3,700 past behaviors provide additional bias reduction, such that the full model reduces bias by over 97%. This experimental evaluation demonstrates that detailed records of individuals' past behavior can improve studies of social influence, information diffusion, and imitation; these results are encouraging for the credibility of some studies but also cautionary for studies of rare or new behaviors. More generally, these results show how large, high-dimensional data sets and statistical learning techniques can be used to improve causal inference in the behavioral sciences.

We investigate the problem of learning discrete, undirected graphical models in a differentially private way. We show that the approach of releasing noisy sufficient statistics using the Laplace mechanism achieves a good trade-off between privacy, utility, and practicality. A naive learning algorithm that uses the noisy sufficient statistics "as is" outperforms general-purpose differentially private learning algorithms. However, it has three limitations: it ignores knowledge about the data generating process, rests on uncertain theoretical foundations, and exhibits certain pathologies. We develop a more principled approach that applies the formalism of collective graphical models to perform inference over the true sufficient statistics within an expectation-maximization framework. We show that this learns better models than competing approaches on both synthetic data and on real human mobility data used as a case study.

Stochastic gradient MCMC (SG-MCMC) algorithms have proven useful in scaling Bayesian inference to large datasets under an assumption of i.i.d data. We instead develop an SG-MCMC algorithm to learn the parameters of hidden Markov models (HMMs) for time-dependent data. There are two challenges to applying SG-MCMC in this setting: The latent discrete states, and needing to break dependencies when considering minibatches. We consider a marginal likelihood representation of the HMM and propose an algorithm that harnesses the inherent memory decay of the process. We demonstrate the effectiveness of our algorithm on synthetic experiments and an ion channel recording data, with runtimes significantly outperforming batch MCMC.

There is general consensus that learning representations is useful for a variety of reasons, e.g. efficient use of labeled data (semi-supervised learning), transfer learning and understanding hidden structure of data. Popular techniques for representation learning include clustering, manifold learning, kernel-learning, autoencoders, Boltzmann machines, etc. To study the relative merits of these techniques, it's essential to formalize the definition and goals of representation learning, so that they are all become instances of the same definition. This paper introduces such a formal framework that also formalizes the utility of learning the representation. It is related to previous Bayesian notions, but with some new twists. We show the usefulness of our framework by exhibiting simple and natural settings -- linear mixture models and loglinear models, where the power of representation learning can be formally shown. In these examples, representation learning can be performed provably and efficiently under plausible assumptions (despite being NP-hard), and furthermore: (i) it greatly reduces the need for labeled data (semi-supervised learning) and (ii) it allows solving classification tasks when simpler approaches like nearest neighbors require too much data (iii) it is more powerful than manifold learning methods.

We present a solution to "Google Cloud and YouTube-8M Video Understanding Challenge" that ranked 5th place. The proposed model is an ensemble of three model families, two frame level and one video level. The training was performed on augmented dataset, with cross validation.

We study the problem of throughput maximization by predicting spectrum opportunities using reinforcement learning. Our kernel-based reinforcement learning approach is coupled with a sparsification technique that efficiently captures the environment states to control dimensionality and finds the best possible channel access actions based on the current state. This approach allows learning and planning over the intrinsic state-action space and extends well to large state and action spaces. For stationary Markov environments, we derive the optimal policy for channel access, its associated limiting throughput, and propose a fast online algorithm for achieving the optimal throughput. We then show that the maximum-likelihood channel prediction and access algorithm is suboptimal in general, and derive conditions under which the two algorithms are equivalent. For reactive Markov environments, we derive kernel variants of Q-learning, R-learning and propose an accelerated R-learning algorithm that achieves faster convergence. We finally test our algorithms against a generic reactive network. Simulation results are shown to validate the theory and show the performance gains over current state-of-the-art techniques.

The ratio of normalizing constants for the G-Wishart distribution, for two graphs differing by an edge e, has long been a bottleneck in the search for efficient model selection in the class of graphical Gaussian models. We give an accurate approximation to this ratio under two assumptions: first, we assume that the scale of the prior is the identity, second we assume that the set of paths between the two ends of e are disjoint. The first approximation does not represent a restriction since this is what statisticians use. The second assumption is a real restriction but we conjecture that similar results are also true without this second assumption. We shall prove it in subsequent work. This approximation is simply a ratio of Gamma functions and thus need no simulation. We illustrate the efficiency and practical impact of our result by comparing model selection in the class of graphical Gaussian models using this approximation and using current Metropolis-Hastings methods. We work both with simulated data and a complex high-dimensional real data set. In the numerical examples, we do not assume that the paths between the two endpoints of edge e are disjoint.

Background: Cardiac MRI derived biventricular mass and function parameters, such as end-systolic volume (ESV), end-diastolic volume (EDV), ejection fraction (EF), stroke volume (SV), and ventricular mass (VM) are clinically well established. Image segmentation can be challenging and time-consuming, due to the complex anatomy of the human heart. Objectives: This study introduces $\nu$-net (/nju:n$\varepsilon$t/) -- a deep learning approach allowing for fully-automated high quality segmentation of right (RV) and left ventricular (LV) endocardium and epicardium for extraction of cardiac function parameters. Methods: A set consisting of 253 manually segmented cases has been used to train a deep neural network. Subsequently, the network has been evaluated on 4 different multicenter data sets with a total of over 1000 cases. Results: For LV EF the intraclass correlation coefficient (ICC) is 98, 95, and 80 % (95 %), and for RV EF 96, and 87 % (80 %) on the respective data sets (human expert ICCs reported in parenthesis). The LV VM ICC is 95, and 94 % (84 %), and the RV VM ICC is 83, and 83 % (54 %). This study proposes a simple adjustment procedure, allowing for the adaptation to distinct segmentation philosophies. $\nu$-net exhibits state of-the-art performance in terms of dice coefficient. Conclusions: Biventricular mass and function parameters can be determined reliably in high quality by applying a deep neural network for cardiac MRI segmentation, especially in the anatomically complex right ventricle. Adaption to individual segmentation styles by applying a simple adjustment procedure is viable, allowing for the processing of novel data without time-consuming additional training.