South America
Optimistic Concurrency Control for Distributed Unsupervised Learning Stefanie Jegelka
Research on distributed machine learning algorithms has focused primarily on one of two extremes--algorithms that obey strict concurrency constraints or algorithms that obey few or no such constraints. We consider an intermediate alternative in which algorithms optimistically assume that conflicts are unlikely and if conflicts do arise a conflict-resolution protocol is invoked. We view this "optimistic concurrency control" paradigm as particularly appropriate for large-scale machine learning algorithms, particularly in the unsupervised setting. We demonstrate our approach in three problem areas: clustering, feature learning and online facility location. We evaluate our methods via large-scale experiments in a cluster computing environment.
PAC-Bayes-Empirical-Bernstein Inequality
We present a PAC-Bayes-Empirical-Bernstein inequality. The inequality is based on a combination of the PAC-Bayesian bounding technique with an Empirical Bernstein bound. We show that when the empirical variance is significantly smaller than the empirical loss the PAC-Bayes-Empirical-Bernstein inequality is significantly tighter than the PAC-Bayes-kl inequality of Seeger (2002) and otherwise it is comparable. Our theoretical analysis is confirmed empirically on a synthetic example and several UCI datasets. The PAC-Bayes-Empirical-Bernstein inequality is an interesting example of an application of the PAC-Bayesian bounding technique to self-bounding functions.
Documents as multiple overlapping windows into a grid of counts
In text analysis documents are often represented as disorganized bags of words; models of such count features are typically based on mixing a small number of topics [1,2]. Recently, it has been observed that for many text corpora documents evolve into one another in a smooth way, with some features dropping and new ones being introduced. The counting grid [3] models this spatial metaphor literally: it is a grid of word distributions learned in such a way that a document's own distribution of features can be modeled as the sum of the histograms found in a window into the grid. The major drawback of this method is that it is essentially a mixture and all the content must be generated by a single contiguous area on the grid. This may be problematic especially for lower dimensional grids. In this paper, we overcome this issue by introducing the Componential Counting Grid which brings the componential nature of topic models to the basic counting grid. We evaluated our approach on document classification and multimodal retrieval obtaining state of the art results on standard benchmarks.
Variance Reduction for Stochastic Gradient Optimization
Stochastic gradient optimization is a class of widely used algorithms for training machine learning models. To optimize an objective, it uses the noisy gradient computed from the random data samples instead of the true gradient computed from the entire dataset. However, when the variance of the noisy gradient is large, the algorithm might spend much time bouncing around, leading to slower convergence and worse performance. In this paper, we develop a general approach of using control variate for variance reduction in stochastic gradient. Data statistics such as low-order moments (pre-computed or estimated online) is used to form the control variate. We demonstrate how to construct the control variate for two practical problems using stochastic gradient optimization. One is convex--the MAP estimation for logistic regression, and the other is non-convex--stochastic variational inference for latent Dirichlet allocation. On both problems, our approach shows faster convergence and better performance than the classical approach.
Direct 0-1 Loss Minimization and Margin Maximization with Boosting
We propose a boosting method, DirectBoost, a greedy coordinate descent algorithm that builds an ensemble classifier of weak classifiers through directly minimizing empirical classification error over labeled training examples; once the training classification error is reduced to a local coordinatewise minimum, Direct-Boost runs a greedy coordinate ascent algorithm that continuously adds weak classifiers to maximize any targeted arbitrarily defined margins until reaching a local coordinatewise maximum of the margins in a certain sense.
Bayesian Estimation of Latently-grouped Parameters in Undirected Graphical Models
In large-scale applications of undirected graphical models, such as social networks and biological networks, similar patterns occur frequently and give rise to similar parameters. In this situation, it is beneficial to group the parameters for more efficient learning. We show that even when the grouping is unknown, we can infer these parameter groups during learning via a Bayesian approach. We impose a Dirichlet process prior on the parameters. Posterior inference usually involves calculating intractable terms, and we propose two approximation algorithms, namely a Metropolis-Hastings algorithm with auxiliary variables and a Gibbs sampling algorithm with "stripped" Beta approximation (Gibbs SBA). Simulations show that both algorithms outperform conventional maximum likelihood estimation (MLE). Gibbs SBA's performance is close to Gibbs sampling with exact likelihood calculation. Models learned with Gibbs SBA also generalize better than the models learned by MLE on real-world Senate voting data.
Streaming Variational Bayes
The framework makes streaming updates to the estimated posterior according to a user-specified approximation batch primitive. We demonstrate the usefulness of our framework, with variational Bayes (VB) as the primitive, by fitting the latent Dirichlet allocation model to two large-scale document collections. We demonstrate the advantages of our algorithm over stochastic variational inference (SVI) by comparing the two after a single pass through a known amount of data--a case where SVI may be applied--and in the streaming setting, where SVI does not apply.
Causal Inference on Time Series using Restricted Structural Equation Models
Causal inference uses observational data to infer the causal structure of the data generating system. We study a class of restricted Structural Equation Models for time series that we call Time Series Models with Independent Noise (TiMINo). These models require independent residual time series, whereas traditional methods like Granger causality exploit the variance of residuals. This work contains two main contributions: (1) Theoretical: By restricting the model class (e.g. to additive noise) we provide general identifiability results. They cover lagged and instantaneous effects that can be nonlinear and unfaithful, and non-instantaneous feedbacks between the time series.