Minwise hashing is a standard technique in the context of search for efficiently computing set similarities. The recent development of b-bit minwise hashing provides a substantial improvement by storing only the lowest b bits of each hashed value. In this paper, we demonstrate that b-bit minwise hashing can be naturally integrated with linear learning algorithms such as linear SVM and logistic regression, to solve large-scale and high-dimensional statistical learning tasks, especially when the data do not fit in memory. We compare $b$-bit minwise hashing with the Count-Min (CM) and Vowpal Wabbit (VW) algorithms, which have essentially the same variances as random projections. Our theoretical and empirical comparisons illustrate that b-bit minwise hashing is significantly more accurate (at the same storage cost) than VW (and random projections) for binary data.

Stochastic Gradient Descent (SGD) is a popular algorithm that can achieve state-of-the-art performance on a variety of machine learning tasks. Several researchers have recently proposed schemes to parallelize SGD, but all require performance-destroying memory locking and synchronization. This work aims to show using novel theoretical analysis, algorithms, and implementation that SGD can be implemented *without any locking*. We present an update scheme called Hogwild which allows processors access to shared memory with the possibility of overwriting each other's work. We show that when the associated optimization problem is sparse, meaning most gradient updates only modify small parts of the decision variable, then Hogwild achieves a nearly optimal rate of convergence. We demonstrate experimentally that Hogwild outperforms alternative schemes that use locking by an order of magnitude.

Many functional descriptions of spiking neurons assume a cascade structure where inputs are passed through an initial linear filtering stage that produces a low-dimensional signal that drives subsequent nonlinear stages. This paper presents a novel and systematic parameter estimation procedure for such models and applies the method to two neural estimation problems: (i) compressed-sensing based neural mapping from multi-neuron excitation, and (ii) estimation of neural receptive yields in sensory neurons. The proposed estimation algorithm models the neurons via a graphical model and then estimates the parameters in the model using a recently-developed generalized approximate message passing (GAMP) method. The GAMP method is based on Gaussian approximations of loopy belief propagation. In the neural connectivity problem, the GAMP-based method is shown to be computational efficient, provides a more exact modeling of the sparsity, can incorporate nonlinearities in the output and significantly outperforms previous compressed-sensing methods. For the receptive field estimation, the GAMP method can also exploit inherent structured sparsity in the linear weights. The method is validated on estimation of linear nonlinear Poisson (LNP) cascade models for receptive fields of salamander retinal ganglion cells.

We consider the problem of estimating neural spikes from extracellular voltage recordings. Most current methods are based on clustering, which requires substantial human supervision and produces systematic errors by failing to properly handle temporally overlapping spikes. We formulate the problem as one of statistical inference, in which the recorded voltage is a noisy sum of the spike trains of each neuron convolved with its associated spike waveform. Joint maximum-a-posteriori (MAP) estimation of the waveforms and spikes is then a blind deconvolution problem in which the coefficients are sparse. We develop a block-coordinate descent method for approximating the MAP solution. We validate our method on data simulated according to the generative model, as well as on real data for which ground truth is available via simultaneous intracellular recordings. In both cases, our method substantially reduces the number of missed spikes and false positives when compared to a standard clustering algorithm, primarily by recovering temporally overlapping spikes. The method offers a fully automated alternative to clustering methods that is less susceptible to systematic errors.

We introduce the Gamma-Exponential Process (GEP), a prior over a large family ofcontinuous time stochastic processes. A hierarchical version of this prior (HGEP; the Hierarchical GEP) yields a useful model for analyzing complex time series. Models based on HGEPs display many attractive properties: conjugacy, exchangeability and closed-form predictive distribution for the waiting times, and exact Gibbs updates for the time scale parameters. After establishing these properties, weshow how posterior inference can be carried efficiently using Particle MCMC methods [1]. This yields a MCMC algorithm that can resample entire sequences atomicallywhile avoiding the complications of introducing slice and stick auxiliary variables of the beam sampler [2]. We applied our model to the problem of estimating the disease progression in multiple sclerosis [3], and to RNA evolutionary modeling[4]. In both domains, we found that our model outperformed the standard rate matrix estimation approach.

Determining interactions between entities and the overall organization and clustering of nodes in networks is a major challenge when analyzing biological and social network data. Here we extend the Indian Buffet Process (IBP), a nonparametric Bayesian model, to integrate noisy interaction scores with properties of individual entities for inferring interaction networks and clustering nodes within these networks. We present an application of this method to study how microRNAs regulate mRNAs in cells. Analysis of synthetic and real data indicates that the method improves upon prior methods, correctly recovers interactions and clusters, and provides accurate biological predictions.

We consider the minimization of a convex objective function defined on a Hilbert space, which is only available through unbiased estimates of its gradients. This problem includes standard machine learning algorithms such as kernel logistic regression and least-squares regression, and is commonly referred to as a stochastic approximation problem in the operations research community. We provide a non-asymptotic analysis of the convergence of two well-known algorithms, stochastic gradient descent (a.k.a.~Robbins-Monro algorithm) as well as a simple modification where iterates are averaged (a.k.a.~Polyak-Ruppert averaging). Our analysis suggests that a learning rate proportional to the inverse of the number of iterations, while leading to the optimal convergence rate in the strongly convex case, is not robust to the lack of strong convexity or the setting of the proportionality constant. This situation is remedied when using slower decays together with averaging, robustly leading to the optimal rate of convergence. We illustrate our theoretical results with simulations on synthetic and standard datasets.

Non-negative data are commonly encountered in numerous fields, making non-negative least squares regression (NNLS) a frequently used tool. At least relative to its simplicity, it often performs rather well in practice. Serious doubts about its usefulness arise for modern high-dimensional linear models. Even in this setting - unlike first intuition may suggest - we show that for a broad class of designs, NNLS is resistant to overfitting and works excellently for sparse recovery when combined with thresholding, experimentally even outperforming L1-regularization. Since NNLS also circumvents the delicate choice of a regularization parameter, our findings suggest that NNLS may be the method of choice.

Knowledge-based support vector machines (KBSVMs) incorporate advice from domain experts, which can improve generalization significantly. A major limitation that has not been fully addressed occurs when the expert advice is imperfect, which can lead to poorer models. We propose a model that extends KBSVMs and is able to not only learn from data and advice, but also simultaneously improve the advice. The proposed approach is particularly effective for knowledge discovery in domains with few labeled examples. The proposed model contains bilinear constraints, and is solved using two iterative approaches: successive linear programming and a constrained concave-convex approach. Experimental results demonstrate that these algorithms yield useful refinements to expert advice, as well as improve the performance of the learning algorithm overall.

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multi-output Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.