Many practical techniques for probabilistic inference require a sequence of distributions that interpolate between a tractable distribution and an intractable distribution of interest. Usually, the sequences used are simple, e.g., based on geometric averages between distributions. When models are expressed as probabilistic programs, the models themselves are highly structured objects that can be used to derive annealing sequences that are more sensitive to domain structure. We propose an algorithm for transforming probabilistic programs to coarse-to-fine programs which have the same marginal distribution as the original programs, but generate the data at increasing levels of detail, from coarse to fine. We apply this algorithm to an Ising model, its depth-from-disparity variation, and a factorial hidden Markov model. We show preliminary evidence that the use of coarse-to-fine models can make existing generic inference algorithms more efficient.

We learn sensor trees from training data to minimize sensor acquisition costs during test time. Our system adaptively selects sensors at each stage if necessary to make a confident classification. We pose the problem as empirical risk minimization over the choice of trees and node decision rules. We decompose the problem, which is known to be intractable, into combinatorial (tree structures) and continuous parts (node decision rules) and propose to solve them separately. Using training data we greedily solve for the combinatorial tree structures and for the continuous part, which is a non-convex multilinear objective function, we derive convex surrogate loss functions that are piecewise linear. The resulting problem can be cast as a linear program and has the advantage of guaranteed convergence, global optimality, repeatability and computational efficiency. We show that our proposed approach outperforms the state-of-art on a number of benchmark datasets.

In this study, we propose an automatic learning method for variables selection based on Lasso in epidemiology context. One of the aim of this approach is to overcome the pretreatment of experts in medicine and epidemiology on collected data. These pretreatment consist in recoding some variables and to choose some interactions based on expertise. The approach proposed uses all available explanatory variables without treatment and generate automatically all interactions between them. This lead to high dimension. We use Lasso, one of the robust methods of variable selection in high dimension. To avoid over fitting a two levels cross-validation is used. Because the target variable is account variable and the lasso estimators are biased, variables selected by lasso are debiased by a GLM and used to predict the distribution of the main vector of malaria which is Anopheles. Results show that only few climatic and environmental variables are the mains factors associated to the malaria risk exposure.

We consider a generic convex optimization problem associated with regularized empirical risk minimization of linear predictors. The problem structure allows us to reformulate it as a convex-concave saddle point problem. We propose a stochastic primal-dual coordinate (SPDC) method, which alternates between maximizing over a randomly chosen dual variable and minimizing over the primal variable. An extrapolation step on the primal variable is performed to obtain accelerated convergence rate. We also develop a mini-batch version of the SPDC method which facilitates parallel computing, and an extension with weighted sampling probabilities on the dual variables, which has a better complexity than uniform sampling on unnormalized data. Both theoretically and empirically, we show that the SPDC method has comparable or better performance than several state-of-the-art optimization methods.

The Mahalanobis distance is commonly used in multi-object trackers for measurement-to-track association. Starting with the original definition of the Mahalanobis distance we review its use in association. Given that there is no principle in multi-object tracking that sets the Mahalanobis distance apart as a distinguished statistical distance we revisit the global association hypotheses of multiple hypothesis tracking as the most general association setting. Those association hypotheses induce a distance-like quantity for assignment which we refer to as association log-likelihood distance. We compare the ability of the Mahalanobis distance to the association log-likelihood distance to yield correct association relations in Monte-Carlo simulations. It turns out that on average the distance based on association log-likelihood performs better than the Mahalanobis distance, confirming that the maximization of global association hypotheses is a more fundamental approach to association than the minimization of a certain statistical distance measure.

Supervised classification is still one of the hot topics for high dimensional and functional data due to the importance of their applications and the intrinsic difficulty in a general setup. In this context, there is a vast literature on classification methods which include: linear classification,k -nearest neighbors and kernel rules, classification based on partial least squares, reproducing kernels or depth measures. Complete surveys of the literature are the works by Ba ıllo et al. [1], Cuevas [13] and Delaigle and Hall [16]. In the book Contributions in infinite-dimensional statistics and related topics [7], there are also several recent advances in supervised and unsupervised classification. See for instance, Chapters 2, 5, 22 or 48, or directly, Chapter 1 of this issue (Bongiorno et al. [6]). In this context, very recently there have been of great interest to develop aggregation methods. In particular, there is a large list of linear aggregation methods like boosting (Breiman [8], Breiman [9]), random forest (Breiman [10], Biau et al. [3], Biau [5]), among others. All these methods exhibit an important improvement when combining a subset of classifiers to produce a new one. Most of the contributions to the aggregation literature have been proposed for nonparametric regression, a problem closely related to classification rules, which can be obtained just by plugging in the estimate of the regression function into the Bayes rule (see for instance, Yang [19] and Bunea et al. [11]).

Online Passive-Aggressive (PA) learning is a class of online margin-based algorithms suitable for a wide range of real-time prediction tasks, including classification and regression. PA algorithms are formulated in terms of deterministic point-estimation problems governed by a set of user-defined hyperparameters: the approach fails to capture model/prediction uncertainty and makes their performance highly sensitive to hyperparameter configurations. In this paper, we introduce a novel PA learning framework for regression that overcomes the above limitations. We contribute a Bayesian state-space interpretation of PA regression, along with a novel online variational inference scheme, that not only produces probabilistic predictions, but also offers the benefit of automatic hyperparameter tuning. Experiments with various real-world data sets show that our approach performs significantly better than a more standard, linear Gaussian state-space model.

We study in this paper the consequences of using the Mean Absolute Percentage Error (MAPE) as a measure of quality for regression models. We show that finding the best model under the MAPE is equivalent to doing weighted Mean Absolute Error (MAE) regression. We also show that, under some asumptions, universal consistency of Empirical Risk Minimization remains possible using the MAPE.

The paper provides results regarding the computational complexity of hybrid system identification. More precisely, we focus on the estimation of piecewise affine (PWA) maps from input-output data and analyze the complexity of computing a global minimizer of the error. Previous work showed that a global solution could be obtained for continuous PWA maps with a worst-case complexity exponential in the number of data. In this paper, we show how global optimality can be reached for a slightly more general class of possibly discontinuous PWA maps with a complexity only polynomial in the number of data, however with an exponential complexity with respect to the data dimension. This result is obtained via an analysis of the intrinsic classification subproblem of associating the data points to the different modes. In addition, we prove that the problem is NP-hard, and thus that the exponential complexity in the dimension is a natural expectation for any exact algorithm.

In this paper, we focus on the stochastic block model (SBM),a probabilistic tool describing interactions between nodes of a network using latent clusters. The SBM assumes that the networkhas a stationary structure, in which connections of time varying intensity are not taken into account. In other words, interactions between two groups are forced to have the same features during the whole observation time. To overcome this limitation,we propose a partition of the whole time horizon, in which interactions are observed, and develop a non stationary extension of the SBM,allowing to simultaneously cluster the nodes in a network along with fixed time intervals in which the interactions take place. The number of clusters (K for nodes, D for time intervals) as well as the class memberships are finallyobtained through maximizing the complete-data integrated likelihood by means of a greedy search approach. After showing that the model works properly with simulated data, we focus on a real data set. We thus consider the three days ACM Hypertext conference held in Turin,June 29th - July 1st 2009. Proximity interactions between attendees during the first day are modelled and an interestingclustering of the daily hours is finally obtained, with times of social gathering (e.g. coffee breaks) recovered by the approach. Applications to large networks are limited due to the computational complexity of the greedy search which is dominated bythe number $K\_{max}$ and $D\_{max}$ of clusters used in the initialization. Therefore,advanced clustering tools are considered to reduce the number of clusters expected in the data, making the greedy search applicable to large networks.