Lazy stochastic principal component analysis

Stochastic principal component analysis (SPCA) has become a popular dimensionality reduction strategy for large, high-dimensional datasets. We derive a simplified algorithm, called Lazy SPCA, which has reduced computational complexity and is better suited for large-scale distributed computation. We prove that SPCA and Lazy SPCA find the same approximations to the principal subspace, and that the pairwise distances between samples in the lower-dimensional space is invariant to whether SPCA is executed lazily or not. Empirical studies find downstream predictive performance to be identical for both methods, and superior to random projections, across a range of predictive models (linear regression, logistic lasso, and random forests). In our largest experiment with 4.6 million samples, Lazy SPCA reduced 43.7 hours of computation to 9.9 hours. Overall, Lazy SPCA relies exclusively on matrix multiplications, besides an operation on a small square matrix whose size depends only on the target dimensionality.Comment: To be published in: 2017 IEEE International Conference on Data Mining Workshops (ICDMW

Discovering group dynamics in synchronous time series via hierarchical recurrent switching-state models

We seek to model a collection of time series arising from multiple entities interacting over the same time period. Recent work focused on modeling individual time series is inadequate for our intended applications, where collective system-level behavior influences the trajectories of individual entities. To address such problems, we present a new hierarchical switching-state model that can be trained in an unsupervised fashion to simultaneously explain both system-level and individual-level dynamics. We employ a latent system-level discrete state Markov chain that drives latent entity-level chains which in turn govern the dynamics of each observed time series. Feedback from the observations to the chains at both the entity and system levels improves flexibility via context-dependent state transitions. Our hierarchical switching recurrent dynamical models can be learned via closed-form variational coordinate ascent updates to all latent chains that scale linearly in the number of individual time series. This is asymptotically no more costly than fitting separate models for each entity. Experiments on synthetic and real datasets show that our model can produce better forecasts of future entity behavior than existing methods. Moreover, the availability of latent state chains at both the entity and system level enables interpretation of group dynamics

The Psychological Control Of Implicit Biases: A Dynamical Systems Perspective

Much of social psychological theorizing is entrenched in a dualism between two distinctive mental systems - one associative, the other rule-based. In particular, in the field of evaluations, the contemporary dual systems approach emphasizes the separated existence of distinct implicit and explicit attitudes. However, in recent times, theoreticians have been seeking an understanding of social psychological topics through models that can handle real-time interactivity between component parts. Thus, this dissertation applies the framework of dynamical systems towards key social psychological topics typically construed through dual systems theory. In Chapter 2, we provide evidence that explicit evaluations are gradually unfolding from the self-organization of multiple biases. By analyzing hand-movement trajectories in an explicit attitude report task, we show that while our participants are about equally likely to report liking white people and black people, their formations of these two responses show qualitatively distinct processing dynamics. These findings support the notion that the mind hosts a continuously evolving blend of evaluative decisions from which the eventual explicit decision emerges. In Chapter 3, we provide preliminary evidence that the dynamics of formulating an explicit evaluative judgment is even biased by subliminal evaluative conditioning. These findings would challenge the notion that explicit and implicit attitudes partake in two distinct psychological "channels," suggesting instead that a dynamically interactive mind underlies the preparation of an eventual explicit decision. Finally, in Chapter 4, we sketch out a dynamical systems approach to motivated control. We provide dynamical systems interpretations for three constituent aspects of control - selection, goal pursuit, and top-down flexibility, and thereby craft a perspective on motivated control which respects the existence of specialized neurobiological systems, but creates space for more than two of them, and allows them to continually interact

A Simple Bayesian Approach To Detecting Changepoints Across Multiple Samples

Changepoints are abrupt changes in sequential data. The presence of multiple samples should, in theory, help to reveal subtle changepoints within noisy data. However, multi-sample changepoint detection methods are rarely used in practice because existing inference methods are complex and inefficient. In this talk, we present a simple yet effective approach to detecting changepoints across multiple samples. By transforming Bayesian multi-sample changepoint models into unconventional Hidden Markov Models, we achieve fast, closed-form approximations to the posterior distributions on changepoint indictors, segmentations, and local parameters. We present promising initial results on simulated data, and consider the problem of identifying copy number alterations in cancer biopsy samples with low tumor fractions

The Ornstein-Uhlenbeck Process In Neural Decision-Making: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence

Thesis (Master's)--University of Washington, 2012