Most classification methods are based on the assumption that data conforms to a stationary distribution. The machine learning domain currently suffers from a lack of classification techniques that are able to detect the occurrence of a change in the underlying data distribution. Ignoring possible changes in the underlying concept, also known as concept drift, may degrade the performance of the classification model. Often these changes make the model inconsistent and regular updatings become necessary. Taking the temporal dimension into account during the analysis of Web usage data is a necessity, since the way a site is visited may indeed evolve due to modifications in the structure and content of the site, or even due to changes in the behavior of certain user groups. One solution to this problem, proposed in this article, is to update models using summaries obtained by means of an evolutionary approach based on an intelligent clustering approach. We carry out various clustering strategies that are applied on time sub-periods. To validate our approach we apply two external evaluation criteria which compare different partitions from the same data set. Our experiments show that the proposed approach is efficient to detect the occurrence of changes.

In sparse regression modeling via regularization such as the lasso, it is important to select appropriate values of tuning parameters including regularization parameters. The choice of tuning parameters can be viewed as a model selection and evaluation problem. Mallows' $C_p$ type criteria may be used as a tuning parameter selection tool in lasso-type regularization methods, for which the concept of degrees of freedom plays a key role. In the present paper, we propose an efficient algorithm that computes the degrees of freedom by extending the generalized path seeking algorithm. Our procedure allows us to construct model selection criteria for evaluating models estimated by regularization with a wide variety of convex and non-convex penalties. Monte Carlo simulations demonstrate that our methodology performs well in various situations. A real data example is also given to illustrate our procedure.

Classification is the basis of cognition. Unlike other solutions, this study approaches it from the view of outliers. We present an expanding algorithm to detect outliers in univariate datasets, together with the underlying foundation. The expanding algorithm runs in a holistic way, making it a rather robust solution. Synthetic and real data experiments show its power. Furthermore, an application for multi-class problems leads to the introduction of the oscillator algorithm. The corresponding result implies the potential wide use of the expanding algorithm.

Structured sparse coding and the related structured dictionary learning problems are novel research areas in machine learning. In this paper we present a new application of structured dictionary learning for collaborative filtering based recommender systems. Our extensive numerical experiments demonstrate that the presented technique outperforms its state-of-the-art competitors and has several advantages over approaches that do not put structured constraints on the dictionary elements.

Recently, image categorization has been an active research topic due to the urgent need to retrieve and browse digital images via semantic keywords. This paper formulates image categorization as a multi-label classification problem using recent advances in matrix completion. Under this setting, classification of testing data is posed as a problem of completing unknown label entries on a data matrix that concatenates training and testing features with training labels. We propose two convex algorithms for matrix completion based on a Rank Minimization criterion specifically tailored to visual data, and prove its convergence properties.

Probabilistic logics are receiving a lot of attention today because of their expressive power for knowledge representation and learning. However, this expressivity is detrimental to the tractability of inference, when done at the propositional level. To solve this problem, various lifted inference algorithms have been proposed that reason at the first-order level, about groups of objects as a whole. Despite the existence of various lifted inference approaches, there are currently no completeness results about these algorithms. The key contribution of this paper is that we introduce a formal definition of lifted inference that allows us to reason about the completeness of lifted inference algorithms relative to a particular class of probabilistic models. We then show how to obtain a completeness result using a first-order knowledge compilation approach for theories of formulae containing up to two logical variables.

We consider a global optimization problem of a deterministic function f in a semimetric space,given a finite budget ofnevaluations. The functionf is assumed to be locally smooth (around one of its global maxima) with respect to a semi-metric l. We describe two algorithms based on optimistic exploration that use a hierarchical partitioningof the space at all scales. A first contribution is an algorithm, DOO, that requires the knowledge of l. We report a finite-sample performance bound in terms of a measure of the quantity of near-optimal states. We then define a second algorithm, SOO, which does not require the knowledge of the semimetric lunder which f is smooth, and whose performance is almost as good as DOO optimally-fitted.

In this paper, we give a new generalization error bound of Multiple Kernel Learning (MKL) for a general class of regularizations. Our main target in this paper is dense type regularizations including ℓp-MKL that imposes ℓp-mixed-norm regularization instead of ℓ1-mixed-norm regularization. According to the recent numerical experiments, the sparse regularization does not necessarily show a good performance compared with dense type regularizations. Motivated by this fact, this paper gives a general theoretical tool to derive fast learning rates that is applicable to arbitrary monotone norm-type regularizations in a unifying manner. As a by-product of our general result, we show a fast learning rate of ℓp-MKL that is tightest among existing bounds. We also show that our general learning rate achieves the minimax lower bound. Finally, we show that, when the complexities of candidate reproducing kernel Hilbert spaces are inhomogeneous, dense type regularization shows better learning rate compared with sparse ℓ1 regularization.

Consider a sequence of bits where we are trying to predict the next bit from the previous bits. Assume we are allowed to say `predict 0' or `predict 1', and our payoff is $+1$ if the prediction is correct and $-1$ otherwise. We will say that at each point in time the loss of an algorithm is the number of wrong predictions minus the number of right predictions so far. In this paper we are interested in algorithms that have essentially zero (expected) loss over any string at any point in time and yet have small regret with respect to always predicting $0$ or always predicting $1$. For a sequence of length $T$ our algorithm has regret $14\epsilon T $ and loss $2\sqrt{T}e^{-\epsilon^2 T} $ in expectation for all strings. We show that the tradeoff between loss and regret is optimal up to constant factors. Our techniques extend to the general setting of $N$ experts, where the related problem of trading off regret to the best expert for regret to the 'special' expert has been studied by Even-Dar et al. (COLT'07). We obtain essentially zero loss with respect to the special expert and optimal loss/regret tradeoff, improving upon the results of Even-Dar et al (COLT'07) and settling the main question left open in their paper. The strong loss bounds of the algorithm have some surprising consequences. First, we obtain a parameter free algorithm for the experts problem that has optimal regret bounds with respect to $k$-shifting optima, i.e. bounds with respect to the optimum that is allowed to change arms multiple times. Moreover, for {\em any window of size $n$} the regret of our algorithm to any expert never exceeds $O(\sqrt{n(\log N+\log T)})$, where $N$ is the number of experts and $T$ is the time horizon, while maintaining the essentially zero loss property.

We consider the hypothesis testing problem of detecting a shift between the means of two multivariate normal distributions in the high-dimensional setting, allowing for the data dimension p to exceed the sample size n. Our contribution is a new test statistic for the two-sample test of means that integrates a random projection with the classical Hotelling T squared statistic. Working within a high- dimensional framework that allows (p,n) to tend to infinity, we first derive an asymptotic power function for our test, and then provide sufficient conditions for it to achieve greater power than other state-of-the-art tests. Using ROC curves generated from simulated data, we demonstrate superior performance against competing tests in the parameter regimes anticipated by our theoretical results. Lastly, we illustrate an advantage of our procedure with comparisons on a high-dimensional gene expression dataset involving the discrimination of different types of cancer.