Deep neural networks are a powerful tool for feature learning and extraction given their ability to model high-level abstractions in highly complex data. One area worth exploring in feature learning and extraction using deep neural networks is efficient neural connectivity formation for faster feature learning and extraction. Motivated by findings of stochastic synaptic connectivity formation in the brain as well as the brain's uncanny ability to efficiently represent information, we propose the efficient learning and extraction of features via StochasticNets, where sparsely-connected deep neural networks can be formed via stochastic connectivity between neurons. To evaluate the feasibility of such a deep neural network architecture for feature learning and extraction, we train deep convolutional StochasticNets to learn abstract features using the CIFAR-10 dataset, and extract the learned features from images to perform classification on the SVHN and STL-10 datasets. Experimental results show that features learned using deep convolutional StochasticNets, with fewer neural connections than conventional deep convolutional neural networks, can allow for better or comparable classification accuracy than conventional deep neural networks: relative test error decrease of ~4.5% for classification on the STL-10 dataset and ~1% for classification on the SVHN dataset. Furthermore, it was shown that the deep features extracted using deep convolutional StochasticNets can provide comparable classification accuracy even when only 10% of the training data is used for feature learning. Finally, it was also shown that significant gains in feature extraction speed can be achieved in embedded applications using StochasticNets. As such, StochasticNets allow for faster feature learning and extraction performance while facilitate for better or comparable accuracy performances.

Exponential growth in Electronic Healthcare Records (EHR) has resulted in new opportunities and urgent needs for discovery of meaningful data-driven representations and patterns of diseases in Computational Phenotyping research. Deep Learning models have shown superior performance for robust prediction in computational phenotyping tasks, but suffer from the issue of model interpretability which is crucial for clinicians involved in decision-making. In this paper, we introduce a novel knowledge-distillation approach called Interpretable Mimic Learning, to learn interpretable phenotype features for making robust prediction while mimicking the performance of deep learning models. Our framework uses Gradient Boosting Trees to learn interpretable features from deep learning models such as Stacked Denoising Autoencoder and Long Short-Term Memory. Exhaustive experiments on a real-world clinical time-series dataset show that our method obtains similar or better performance than the deep learning models, and it provides interpretable phenotypes for clinical decision making.

Online discussion forums are complex webs of overlapping subcommunities (macrolevel structure, across threads) in which users enact different roles depending on which subcommunity they are participating in within a particular time point (microlevel structure, within threads). This sub-network structure is implicit in massive collections of threads. To uncover this structure, we develop a scalable algorithm based on stochastic variational inference and leverage topic models (LDA) along with mixed membership stochastic block (MMSB) models. We evaluate our model on three large-scale datasets, Cancer-ThreadStarter (22K users and 14.4K threads), Cancer-NameMention(15.1K users and 12.4K threads) and StackOverFlow (1.19 million users and 4.55 million threads). Qualitatively, we demonstrate that our model can provide useful explanations of microlevel and macrolevel user presentation characteristics in different communities using the topics discovered from posts. Quantitatively, we show that our model does better than MMSB and LDA in predicting user reply structure within threads. In addition, we demonstrate via synthetic data experiments that the proposed active sub-network discovery model is stable and recovers the original parameters of the experimental setup with high probability.

This paper proposes a boosting-based solution addressing metric learning problems for high-dimensional data. Distance measures have been used as natural measures of (dis)similarity and served as the foundation of various learning methods. The efficiency of distance-based learning methods heavily depends on the chosen distance metric. With increasing dimensionality and complexity of data, however, traditional metric learning methods suffer from poor scalability and the limitation due to linearity as the true signals are usually embedded within a low-dimensional nonlinear subspace. In this paper, we propose a nonlinear sparse metric learning algorithm via boosting. We restructure a global optimization problem into a forward stage-wise learning of weak learners based on a rank-one decomposition of the weight matrix in the Mahalanobis distance metric. A gradient boosting algorithm is devised to obtain a sparse rank-one update of the weight matrix at each step. Nonlinear features are learned by a hierarchical expansion of interactions incorporated within the boosting algorithm. Meanwhile, an early stopping rule is imposed to control the overall complexity of the learned metric. As a result, our approach guarantees three desirable properties of the final metric: positive semi-definiteness, low rank and element-wise sparsity. Numerical experiments show that our learning model compares favorably with the state-of-the-art methods in the current literature of metric learning.

Topic models are popular for modeling discrete data (e.g., texts, images, videos, links), and provide an efficient way to discover hidden structures/semantics in massive data. One of the core problems in this field is the posterior inference for individual data instances. This problem is particularly important in streaming environments, but is often intractable. In this paper, we investigate the use of the Frank-Wolfe algorithm (FW) for recovering sparse solutions to posterior inference. From detailed elucidation of both theoretical and practical aspects, FW exhibits many interesting properties which are beneficial to topic modeling. We then employ FW to design fast methods, including ML-FW, for learning latent Dirichlet allocation (LDA) at large scales. Extensive experiments show that to reach the same predictiveness level, ML-FW can perform tens to thousand times faster than existing state-of-the-art methods for learning LDA from massive/streaming data.

Blind Source Separation (BSS) has proven to be a powerful tool for the analysis of composite patterns in engineering and science. We introduce Convex Analysis of Mixtures (CAM) for separating non-negative well-grounded sources, which learns the mixing matrix by identifying the lateral edges of the convex data scatter plot. We prove a sufficient and necessary condition for identifying the mixing matrix through edge detection, which also serves as the foundation for CAM to be applied not only to the exact-determined and over-determined cases, but also to the under-determined case. We show the optimality of the edge detection strategy, even for cases where source well-groundedness is not strictly satisfied. The CAM algorithm integrates plug-in noise filtering using sector-based clustering, an efficient geometric convex analysis scheme, and stability-based model order selection. We demonstrate the principle of CAM on simulated data and numerically mixed natural images. The superior performance of CAM against a panel of benchmark BSS techniques is demonstrated on numerically mixed gene expression data. We then apply CAM to dissect dynamic contrast-enhanced magnetic resonance imaging data taken from breast tumors and time-course microarray gene expression data derived from in-vivo muscle regeneration in mice, both producing biologically plausible decomposition results.

A large number of statistical models are "doubly-intractable": the likelihood normalising term, which is a function of the model parameters, is intractable, as well as the marginal likelihood (model evidence). This means that standard inference techniques to sample from the posterior, such as Markov chain Monte Carlo (MCMC), cannot be used. Examples include, but are not confined to, massive Gaussian Markov random fields, autologistic models and Exponential random graph models. A number of approximate schemes based on MCMC techniques, Approximate Bayesian computation (ABC) or analytic approximations to the posterior have been suggested, and these are reviewed here. Exact MCMC schemes, which can be applied to a subset of doubly-intractable distributions, have also been developed and are described in this paper. As yet, no general method exists which can be applied to all classes of models with doubly-intractable posteriors. In addition, taking inspiration from the Physics literature, we study an alternative method based on representing the intractable likelihood as an infinite series. Unbiased estimates of the likelihood can then be obtained by finite time stochastic truncation of the series via Russian Roulette sampling, although the estimates are not necessarily positive. Results from the Quantum Chromodynamics literature are exploited to allow the use of possibly negative estimates in a pseudo-marginal MCMC scheme such that expectations with respect to the posterior distribution are preserved. The methodology is reviewed on well-known examples such as the parameters in Ising models, the posterior for Fisher-Bingham distributions on the $d$-Sphere and a large-scale Gaussian Markov Random Field model describing the Ozone Column data. This leads to a critical assessment of the strengths and weaknesses of the methodology with pointers to ongoing research.

We show that natural classes of regularized learning algorithms with a form of recency bias achieve faster convergence rates to approximate efficiency and to coarse correlated equilibria in multiplayer normal form games. When each player in a game uses an algorithm from our class, their individual regret decays at $O(T^{-3/4})$, while the sum of utilities converges to an approximate optimum at $O(T^{-1})$--an improvement upon the worst case $O(T^{-1/2})$ rates. We show a black-box reduction for any algorithm in the class to achieve $\tilde{O}(T^{-1/2})$ rates against an adversary, while maintaining the faster rates against algorithms in the class. Our results extend those of [Rakhlin and Shridharan 2013] and [Daskalakis et al. 2014], who only analyzed two-player zero-sum games for specific algorithms.

Most users of online services have unique behavioral or usage patterns. These behavioral patterns can be exploited to identify and track users by using only the observed patterns in the behavior. We study the task of identifying users from statistics of their behavioral patterns. Specifically, we focus on the setting in which we are given histograms of users' data collected during two different experiments. We assume that, in the first dataset, the users' identities are anonymized or hidden and that, in the second dataset, their identities are known. We study the task of identifying the users by matching the histograms of their data in the first dataset with the histograms from the second dataset. In recent works, the optimal algorithm for this user identification task is introduced. In this paper, we evaluate the effectiveness of this method on three different types of datasets and in multiple scenarios. Using datasets such as call data records, web browsing histories, and GPS trajectories, we show that a large fraction of users can be easily identified given only histograms of their data; hence these histograms can act as users' fingerprints. We also verify that simultaneous identification of users achieves better performance compared to one-by-one user identification. We show that using the optimal method for identification gives higher identification accuracy than heuristics-based approaches in practical scenarios. The accuracy obtained under this optimal method can thus be used to quantify the maximum level of user identification that is possible in such settings. We show that the key factors affecting the accuracy of the optimal identification algorithm are the duration of the data collection, the number of users in the anonymized dataset, and the resolution of the dataset. We analyze the effectiveness of k-anonymization in resisting user identification attacks on these datasets.

Many model selection algorithms produce a path of fits specifying a sequence of increasingly complex models. Given such a sequence and the data used to produce them, we consider the problem of choosing the least complex model that is not falsified by the data. Extending the selected-model tests of Fithian et al. (2014), we construct p-values for each step in the path which account for the adaptive selection of the model path using the data. In the case of linear regression, we propose two specific tests, the max-t test for forward stepwise regression (generalizing a proposal of Buja and Brown (2014)), and the next-entry test for the lasso. These tests improve on the power of the saturated-model test of Tibshirani et al. (2014), sometimes dramatically. In addition, our framework extends beyond linear regression to a much more general class of parametric and nonparametric model selection problems. To select a model, we can feed our single-step p-values as inputs into sequential stopping rules such as those proposed by G'Sell et al. (2013) and Li and Barber (2015), achieving control of the familywise error rate or false discovery rate (FDR) as desired. The FDR-controlling rules require the null p-values to be independent of each other and of the non-null p-values, a condition not satisfied by the saturated-model p-values of Tibshirani et al. (2014). We derive intuitive and general sufficient conditions for independence, and show that our proposed constructions yield independent p-values.