While minwise hashing is promising for large-scale learning in massive binary data, the preprocessing cost is prohibitive as it requires applying (e.g.,) $k=500$ permutations on the data. The testing time is also expensive if a new data point (e.g., a new document or a new image) has not been processed. In this paper, we develop a simple \textbf{one permutation hashing} scheme to address this important issue. While it is true that the preprocessing step can be parallelized, it comes at the cost of additional hardware and implementation. Also, reducing $k$ permutations to just one would be much more \textbf{energy-efficient}, which might be an important perspective as minwise hashing is commonly deployed in the search industry. While the theoretical probability analysis is interesting, our experiments on similarity estimation and SVM \& logistic regression also confirm the theoretical results.

The problem of multiple change point estimation is considered for sequences with unknown number of change points. A consistency framework is suggested that is suitable for highly dependent time-series, and an asymptotically consistent algorithm is proposed. In order for the consistency to be established the only assumption required is that the data is generated by stationary ergodic time-series distributions. No modeling, independence or parametric assumptions are made; the data are allowed to be dependent and the dependence can be of arbitrary form. The theoretical results are complemented with experimental evaluations.

Probabilistic latent variable models are one of the cornerstones of machine learning. They offer a convenient and coherent way to specify prior distributions over unobserved structure in data, so that these unknown properties can be inferred via posterior inference. Such models are useful for exploratory analysis and visualization, for building density models of data, and for providing features that can be used for later discriminative tasks. A significant limitation of these models, however, is that draws from the prior are often highly redundant due to i.i.d. assumptions on internal parameters. For example, there is no preference in the prior of a mixture model to make components non-overlapping, or in topic model to ensure that co-ocurring words only appear in a small number of topics. In this work, we revisit these independence assumptions for probabilistic latent variable models, replacing the underlying i.i.d.\ prior with a determinantal point process (DPP). The DPP allows us to specify a preference for diversity in our latent variables using a positive definite kernel function. Using a kernel between probability distributions, we are able to define a DPP on probability measures. We show how to perform MAP inference with DPP priors in latent Dirichlet allocation and in mixture models, leading to better intuition for the latent variable representation and quantitatively improved unsupervised feature extraction, without compromising the generative aspects of the model.

We introduce a class of discrete divergences on sets (equivalently binary vectors) that we call the submodular-Bregman divergences. We consider two kinds, defined either from tight modular upper or tight modular lower bounds of a submodular function. We show that the properties of these divergences are analogous to the (standard continuous) Bregman divergence. We demonstrate how they generalize many useful divergences, including the weighted Hamming distance, squared weighted Hamming, weighted precision, recall, conditional mutual information, and a generalized KL-divergence on sets. We also show that the generalized Bregman divergence on the Lovász extension of a submodular function, which we call the Lovász-Bregman divergence, is a continuous extension of a submodular Bregman divergence. We point out a number of applications, and in particular show that a proximal algorithm defined through the submodular Bregman divergence provides aframework for many mirror-descent style algorithms related to submodular function optimization. We also show that a generalization of the k-means algorithm using the Lovász Bregman divergence is natural in clustering scenarios where ordering is important. A unique property of this algorithm is that computing the mean ordering is extremely efficient unlike other order based distance measures.

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into account both sparsity and low rank properties of the matrices. Oracle inequalities are derived and illustrate the trade-offs in the choice of smoothing parameters when modeling the joint effect of sparsity and low rank property. The estimate is computed efficiently using proximal methods through a generalized forward-backward agorithm.

We propose a new stochastic gradient method for optimizing the sum of
 a finite set of smooth functions, where the sum is strongly convex.
 While standard stochastic gradient methods
 converge at sublinear rates for this problem, the proposed method incorporates a memory of previous gradient values in order to achieve a linear convergence 
rate. In a machine learning context, numerical experiments indicate that the new algorithm can dramatically outperform standard
 algorithms, both in terms of optimizing the training error and reducing the test error quickly.

A new result in convex analysis on the calculation of proximity operators in certain scalednorms is derived. We describe efficient implementations of the proximity calculationfor a useful class of functions; the implementations exploit the piece-wise linear nature of the dual problem. The second part of the paper applies the previous result to acceleration of convex minimization problems, and leads to an elegant quasi-Newton method. The optimization method compares favorably againststate-of-the-art alternatives. The algorithm has extensive applications including signal processing, sparse recovery and machine learning and classification.

In many applications, one has information, e.g., labels that are provided in a semi-supervised manner, about a specific target region of a large data set, and one wants to perform machine learning and data analysis tasks nearby that pre-specified target region. Locally-biased problems of this sort are particularly challenging for popular eigenvector-based machine learning and data analysis tools. At root, the reason is that eigenvectors are inherently global quantities. In this paper, we address this issue by providing a methodology to construct semi-supervised eigenvectors of a graph Laplacian, and we illustrate how these locally-biased eigenvectors can be used to perform locally-biased machine learning. These semi-supervised eigenvectors capture successively-orthogonalized directions of maximum variance, conditioned on being well-correlated with an input seed set of nodes that is assumed to be provided in a semi-supervised manner. We also provide several empirical examples demonstrating how these semi-supervised eigenvectors can be used to perform locally-biased learning.

This paper proposes an efficient online learning algorithm to track the smoothing functions of Additive Models. The key idea is to combine the linear representation of Additive Models with a Recursive Least Squares (RLS) filter. In order to quickly track changes in the model and put more weight on recent data, the RLS filter uses a forgetting factor which exponentially weights down observations by the order of their arrival. The tracking behaviour is further enhanced by using an adaptive forgetting factor which is updated based on the gradient of the a priori errors. Using results from Lyapunov stability theory, upper bounds for the learning rate are analyzed. The proposed algorithm is applied to 5 years of electricity load data provided by the French utility company Electricite de France (EDF). Compared to state-of-the-art methods, it achieves a superior performance in terms of model tracking and prediction accuracy.

Several machine learning methods allow for abstaining from uncertain predictions. While being common for settings like conventional classification, abstention has been studied much less in learning to rank. We address abstention for the label ranking setting, allowing the learner to declare certain pairs of labels as being incomparable and, thus, to predict partial instead of total orders. In our method, such predictions are produced via thresholding the probabilities of pairwise preferences between labels, as induced by a predicted probability distribution on the set of all rankings. We formally analyze this approach for the Mallows and the Plackett-Luce model, showing that it produces proper partial orders as predictions and characterizing the expressiveness of the induced class of partial orders. These theoretical results are complemented by experiments demonstrating the practical usefulness of the approach.