Dynamic ensemble selection (DES) techniques work by estimating the level of competence of each classifier from a pool of classifiers. Only the most competent ones are selected to classify a given test sample. Hence, the key issue in DES is the criterion used to estimate the level of competence of the classifiers in predicting the label of a given test sample. In order to perform a more robust ensemble selection, we proposed the META-DES framework using meta-learning, where multiple criteria are encoded as meta-features and are passed down to a meta-classifier that is trained to estimate the competence level of a given classifier. In this technical report, we present a step-by-step analysis of each phase of the framework during training and test. We show how each set of meta-features is extracted as well as their impact on the estimation of the competence level of the base classifier. We show that using the dynamic selection of linear classifiers through the META-DES framework, we can solve complex nonlinear classification problems where other combination techniques such as AdaBoost cannot. Introduction Multiple Classifier Systems (MCS) aim to combine classifiers in order to increase the recognition accuracy in pattern recognition systems [1, 2]. MCS are composed of three phases [3]: (1) Generation, (2) Selection, and (3) Integration. In the first phase, a pool of classifiers is generated. In the second phase, a single classifier or a subset having the best classifiers of the pool is(are) selected. We refer to the subset of classifiers as the Ensemble of Classifiers (EoC).

We introduce a minorization-maximization approach to optimizing common measures of discovery significance in high energy physics. The approach alternates between solving a weighted binary classification problem and updating class weights in a simple, closed-form manner. Moreover, an argument based on convex duality shows that an improvement in weighted classification error on any round yields a commensurate improvement in discovery significance. We complement our derivation with experimental results from the 2014 Higgs boson machine learning challenge.

The general perception is that kernel methods are not scalable, and neural nets are the methods of choice for nonlinear learning problems. Or have we simply not tried hard enough for kernel methods? Here we propose an approach that scales up kernel methods using a novel concept called "doubly stochastic functional gradients". Our approach relies on the fact that many kernel methods can be expressed as convex optimization problems, and we solve the problems by making two unbiased stochastic approximations to the functional gradient, one using random training points and another using random functions associated with the kernel, and then descending using this noisy functional gradient. We show that a function produced by this procedure after $t$ iterations converges to the optimal function in the reproducing kernel Hilbert space in rate $O(1/t)$, and achieves a generalization performance of $O(1/\sqrt{t})$. This doubly stochasticity also allows us to avoid keeping the support vectors and to implement the algorithm in a small memory footprint, which is linear in number of iterations and independent of data dimension. Our approach can readily scale kernel methods up to the regimes which are dominated by neural nets. We show that our method can achieve competitive performance to neural nets in datasets such as 8 million handwritten digits from MNIST, 2.3 million energy materials from MolecularSpace, and 1 million photos from ImageNet.

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

As empirically demonstrated by the Word Sense Disambiguation (WSD) tasks of the last SensEval/SemEval exercises, assigning the appropriate meaning to words in context has resisted all attempts to be successfully addressed. Many authors argue that one possible reason could be the use of inappropriate sets of word meanings. In particular, WordNet has been used as a de-facto standard repository of word meanings in most of these tasks. Thus, instead of using the word senses defined in WordNet, some approaches have derived semantic classes representing groups of word senses. However, the meanings represented by WordNet have been only used for WSD at a very fine-grained sense level or at a very coarse-grained semantic class level (also called SuperSenses). We suspect that an appropriate level of abstraction could be on between both levels. The contributions of this paper are manifold. First, we propose a simple method to automatically derive semantic classes at intermediate levels of abstraction covering all nominal and verbal WordNet meanings. Second, we empirically demonstrate that our automatically derived semantic classes outperform classical approaches based on word senses and more coarse-grained sense groupings. Third, we also demonstrate that our supervised WSD system benefits from using these new semantic classes as additional semantic features while reducing the amount of training examples. Finally, we also demonstrate the robustness of our supervised semantic class-based WSD system when tested on out of domain corpus.

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.

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.