For massive data sets, efficient computation commonly relies on distributed algorithms that store and process subsets of the data on different machines, minimizing communication costs. Our focus is on regression and classification problems involving many features. A variety of distributed algorithms have been proposed in this context, but challenges arise in defining an algorithm with low communication, theoretical guarantees and excellent practical performance in general settings. We propose a MEdian Selection Subset AGgregation Estimator (message) algorithm, which attempts to solve these problems. The algorithm applies feature selection in parallel for each subset using Lasso or another method, calculates the'median' feature inclusion index, estimates coefficients for the selected features in parallel for each subset, and then averages these estimates. The algorithm is simple, involves very minimal communication, scales efficiently in both sample and feature size, and has theoretical guarantees. In particular, we show model selection consistency and coefficient estimation efficiency. Extensive experiments show excellent performance in variable selection, estimation, prediction, and computation time relative to usual competitors.

Kernel machines such as kernel SVM and kernel ridge regression usually construct high quality models; however, their use in real-world applications remains limited due to the high prediction cost.

We analyze the behavior of nearest neighbor classification in metric spaces and provide finite-sample, distribution-dependent rates of convergence under minimal assumptions. These are more general than existing bounds, and enable us, as a by-product, to establish the universal consistency of nearest neighbor in a broader range of data spaces than was previously known. We illustrate our upper and lower bounds by introducing a new smoothness class customized for nearest neighbor classification. We find, for instance, that under the Tsybakov margin condition the convergence rate of nearest neighbor matches recently established lower bounds for nonparametric classification.

We combine the ideas behind trees and Gaussian graphical models to form a new nonparametric family of graphical models. Our approach is to attach nonparanormal "blossoms", with arbitrary graphs, to a collection of nonparametric trees. The tree edges are chosen to connect variables that most violate joint Gaussianity. The non-tree edges are partitioned into disjoint groups, and assigned to tree nodes using a nonparametric partial correlation statistic. A nonparanormal blossom is then "grown" for each group using established methods based on the graphical lasso. The result is a factorization with respect to the union of the tree branches and blossoms, defining a high-dimensional joint density that can be efficiently estimated and evaluated on test points. Theoretical properties and experiments with simulated and real data demonstrate the effectiveness of blossom trees.

Neural Information Processing Systems http://nips.cc/

This paper presents a representation theory for permutation-valued functions, which in their general form can also be called listwise ranking functions. Pointwise ranking functions assign a score to each object independently, without taking into account the other objects under consideration; whereas listwise loss functions evaluate the set of scores assigned to all objects as a whole. In many supervised learning to rank tasks, it might be of interest to use listwise ranking functions instead; in particular, the Bayes Optimal ranking functions might themselves be listwise, especially if the loss function is listwise. A key caveat to using listwise ranking functions has been the lack of an appropriate representation theory for such functions. We show that a natural symmetricity assumption that we call exchangeability allows us to explicitly characterize the set of such exchangeable listwise ranking functions. Our analysis draws from the theories of tensor analysis, functional analysis and De Finetti theorems. We also present experiments using a novel reranking method motivated by our representation theory.

In many important machine learning applications, the source distribution used to estimate a probabilistic classifier differs from the target distribution on which the classifier will be used to make predictions. Due to its asymptotic properties, sample reweighted empirical loss minimization is a commonly employed technique to deal with this difference. However, given finite amounts of labeled source data, this technique suffers from significant estimation errors in settings with large sample selection bias. We develop a framework for learning a robust bias-aware (RBA) probabilistic classifier that adapts to different sample selection biases using a minimax estimation formulation. Our approach requires only accurate estimates of statistics under the source distribution and is otherwise as robust as possible to unknown properties of the conditional label distribution, except when explicit generalization assumptions are incorporated. We demonstrate the behavior and effectiveness of our approach on binary classification tasks.

We present a technique for significantly speeding up Alternating Least Squares (ALS) and Gradient Descent (GD), two widely used algorithms for tensor factorization. By exploiting properties of the Khatri-Rao product, we show how to efficiently address a computationally challenging sub-step of both algorithms. Our algorithm, DFacTo, only requires two sparse matrix-vector products and is easy to parallelize. DFacTo is not only scalable but also on average 4 to 10 times faster than competing algorithms on a variety of datasets. For instance, DFacTo only takes 480 seconds on 4 machines to perform one iteration of the ALS algorithm and 1,143 seconds to perform one iteration of the GD algorithm on a 6.5 million 2.5 million 1.5 million dimensional tensor with 1.2 billion non-zero entries.

Proximal gradient descent (PGD) and stochastic proximal gradient descent (SPGD) are popular methods for solving regularized risk minimization problems in machine learning and statistics. In this paper, we propose and analyze an accelerated variant of these methods in the mini-batch setting. This method incorporates two acceleration techniques: one is Nesterov's acceleration method, and the other is a variance reduction for the stochastic gradient. Accelerated proximal gradient descent (APG) and proximal stochastic variance reduction gradient (Prox-SVRG) are in a trade-off relationship. We show that our method, with the appropriate mini-batch size, achieves lower overall complexity than both APG and Prox-SVRG.

The ever-increasing size of modern data sets combined with the difficulty of obtaining label information has made semi-supervised learning one of the problems of significant practical importance in modern data analysis. We revisit the approach to semi-supervised learning with generative models and develop new models that allow for effective generalisation from small labelled data sets to large unlabelled ones. Generative approaches have thus far been either inflexible, inefficient or non-scalable. We show that deep generative models and approximate Bayesian inference exploiting recent advances in variational methods can be used to provide significant improvements, making generative approaches highly competitive for semi-supervised learning.