We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that kernel herding decreases the error of expectations of functions in the Hilbert space at a rate O(1/T) which is much faster than the usual O(1/pT) for iid random samples. We illustrate kernel herding by approximating Bayesian predictive distributions.

Learning problems such as logistic regression are typically formulated as pure optimization problems defined on some loss function. We argue that this view ignores the fact that the loss function depends on stochastically generated data which in turn determines an intrinsic scale of precision for statistical estimation. By considering the statistical properties of the update variables used during the optimization (e.g. gradients), we can construct frequentist hypothesis tests to determine the reliability of these updates. We utilize subsets of the data for computing updates, and use the hypothesis tests for determining when the batch-size needs to be increased. This provides computational benefits and avoids overfitting by stopping when the batch-size has become equal to size of the full dataset. Moreover, the proposed algorithms depend on a single interpretable parameter – the probability for an update to be in the wrong direction – which is set to a single value across all algorithms and datasets. In this paper, we illustrate these ideas on three L1 regularized coordinate algorithms: L1 -regularized L2 -loss SVMs, L1 -regularized logistic regression, and the Lasso, but we emphasize that the underlying methods are much more generally applicable.

The paper develops a connection between traditional perceptron algorithms and recently introduced herding algorithms. It is shown that both algorithms can be viewed as an application of the perceptron cycling theorem. This connection strengthens some herding results and suggests new (supervised) herding algorithms that, like CRFs or discriminative RBMs, make predictions by conditioning on the input attributes. We develop and investigate variants of conditional herding, and show that conditional herding leads to practical algorithms that perform better than or on par with related classifiers such as the voted perceptron and the discriminative RBM.

Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, information retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing elements of a sparse data matrix. One of the biggest challenges in this case is filling in a column or row of the matrix with very few observations. In this paper we introduce a Bayesian matrix factorization model that performs regression against side information known about the data in addition to the observations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonparametric mixture model for the prior of the rows and columns of the factored matrices that gives a different regularization for each latent class. Besides providing a richer prior, the posterior distribution of mixture assignments reveals the latent classes. Using Gibbs sampling for inference, we apply our model to the Netflix Prize problem of predicting movie ratings given an incomplete user-movie ratings matrix. Incorporating rating information with gathered metadata information, our Bayesian approach outperforms other matrix factorization techniques even when using fewer dimensions.

Distributed learning is a problem of fundamental interest in machine learning and cognitive science. In this paper, we present asynchronous distributed learning algorithms for two well-known unsupervised learning frameworks: Latent Dirichlet Allocation (LDA) and Hierarchical Dirichlet Processes (HDP). In the proposed approach, the data are distributed across P processors, and processors independently perform Gibbs sampling on their local data and communicate their information in a local asynchronous manner with other processors. We demonstrate that our asynchronous algorithms are able to learn global topic models that are statistically as accurate as those learned by the standard LDA and HDP samplers, but with significant improvements in computation time and memory. We show speedup results on a 730-million-word text corpus using 32 processors, and we provide perplexity results for up to 1500 virtual processors. As a stepping stone in the development of asynchronous HDP, a parallel HDP sampler is also introduced.

A general modeling framework is proposed that unifies nonparametric-Bayesian models, topic-models and Bayesian networks. This class of infinite state Bayes nets (ISBN) can be viewed as directed networks of'hierarchical Dirichlet processes' (HDPs) where the domain of the variables can be structured (e.g.

We investigate the problem of learning a widely-used latent-variable model - the Latent Dirichlet Allocation (LDA) or "topic" model - using distributed computation, whereeach of

A wide variety of Dirichlet-multinomial'topic' models have found interesting applications inrecent years. While Gibbs sampling remains an important method of inference in such models, variational techniques have certain advantages such as easy assessment of convergence, easy optimization without the need to maintain detailed balance, a bound on the marginal likelihood, and sidestepping of issues with topic-identifiability. The most accurate variational technique thus far, namely collapsed variational latent Dirichlet allocation, did not deal with model selection nor did it include inference for hyperparameters. We address both issues by generalizing thetechnique, obtaining the first variational algorithm to deal with the hierarchical Dirichlet process and to deal with hyperparameters of Dirichlet variables.

This class of infinite state Bayes nets (ISBN) can be viewed as directed networks of'hierarchical Dirichlet processes' (HDPs) where the domain of the variables can be structured (e.g.

Latent Dirichlet allocation (LDA) is a Bayesian network that has recently gained much popularity in applications ranging from document modeling to computer vision. Due to the large scale nature of these applications, current inference procedures like variational Bayes and Gibbs sampling have been found lacking. In this paper we propose the collapsed variational Bayesian inference algorithm for LDA, and show that it is computationally efficient, easy to implement and significantly more accurate than standard variational Bayesian inference for LDA.