Discriminative Nonparametric Latent Feature Relational Models with Data Augmentation

We present a discriminative nonparametric latent feature relational model (LFRM) for link prediction to automatically infer the dimensionality of latent features. Under the generic RegBayes (regularized Bayesian inference) framework, we handily incorporate the prediction loss with probabilistic inference of a Bayesian model; set distinct regularization parameters for different types of links to handle the imbalance issue in real networks; and unify the analysis of both the smooth logistic log-loss and the piecewise linear hinge loss. For the nonconjugate posterior inference, we present a simple Gibbs sampler via data augmentation, without making restricting assumptions as done in variational methods. We further develop an approximate sampler using stochastic gradient Langevin dynamics to handle large networks with hundreds of thousands of entities and millions of links, orders of magnitude larger than what existing LFRM models can process. Extensive studies on various real networks show promising performance.Comment: Accepted by AAAI 201

Statistical Analysis of Spherical Data: Clustering, Feature Selection and Applications

In the light of interdisciplinary applications, data to be studied and analyzed have witnessed a growth in volume and change in their intrinsic structure and type. In other words, in practice the diversity of resources generating objects have imposed several challenges for decision maker to determine informative data in terms of time, model capability, scalability and knowledge discovery. Thus, it is highly desirable to be able to extract patterns of interest that support the decision of data management. Clustering, among other machine learning approaches, is an important data engineering technique that empowers the automatic discovery of similar object’s clusters and the consequent assignment of new unseen objects to appropriate clusters. In this context, the majority of current research does not completely address the true structure and nature of data for particular application at hand. In contrast to most previous research, our proposed work focuses on the modeling and classification of spherical data that are naturally generated in many data mining and knowledge discovery applications. Thus, in this thesis we propose several estimation and feature selection frameworks based on Langevin distribution which are devoted to spherical patterns in offline and online settings. In this thesis, we first formulate a unified probabilistic framework, where we build probabilistic kernels based on Fisher score and information divergences from finite Langevin mixture for Support Vector Machine. We are motivated by the fact that the blending of generative and discriminative approaches has prevailed by exploring and adopting distinct characteristic of each approach toward constructing a complementary system combining the best of both. Due to the high demand to construct compact and accurate statistical models that are automatically adjustable to dynamic changes, next in this thesis, we propose probabilistic frameworks for high-dimensional spherical data modeling based on finite Langevin mixtures that allow simultaneous clustering and feature selection in offline and online settings. To this end, we adopted finite mixture models which have long been heavily relied on deterministic learning approaches such as maximum likelihood estimation. Despite their successful utilization in wide spectrum of areas, these approaches have several drawbacks as we will discuss in this thesis. An alternative approach is the adoption of Bayesian inference that naturally addresses data uncertainty while ensuring good generalization. To address this issue, we also propose a Bayesian approach for finite Langevin mixture model estimation and selection. When data change dynamically and grow drastically, finite mixture is not always a feasible solution. In contrast with previous approaches, which suppose an unknown finite number of mixture components, we finally propose a nonparametric Bayesian approach which assumes an infinite number of components. We further enhance our model by simultaneously detecting informative features in the process of clustering. Through extensive empirical experiments, we demonstrate the merits of the proposed learning frameworks on diverse high dimensional datasets and challenging real-world applications

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

A Scale Mixture Perspective of Multiplicative Noise in Neural Networks

Corrupting the input and hidden layers of deep neural networks (DNNs) with multiplicative noise, often drawn from the Bernoulli distribution (or 'dropout'), provides regularization that has significantly contributed to deep learning's success. However, understanding how multiplicative corruptions prevent overfitting has been difficult due to the complexity of a DNN's functional form. In this paper, we show that when a Gaussian prior is placed on a DNN's weights, applying multiplicative noise induces a Gaussian scale mixture, which can be reparameterized to circumvent the problematic likelihood function. Analysis can then proceed by using a type-II maximum likelihood procedure to derive a closed-form expression revealing how regularization evolves as a function of the network's weights. Results show that multiplicative noise forces weights to become either sparse or invariant to rescaling. We find our analysis has implications for model compression as it naturally reveals a weight pruning rule that starkly contrasts with the commonly used signal-to-noise ratio (SNR). While the SNR prunes weights with large variances, seeing them as noisy, our approach recognizes their robustness and retains them. We empirically demonstrate our approach has a strong advantage over the SNR heuristic and is competitive to retraining with soft targets produced from a teacher model