Semi-supervised learning has recently emerged as a new paradigm in the machine learning community. It aims at exploiting simultaneously labeled and unlabeled data for classification. We introduce here a new semi-supervised algorithm. Its originality is that it relies on a discriminative approach to semisupervised learning rather than a generative approach, as it is usually the case. We present ...

In this paper, we consider the logistic regression model with an integrated regressor driven by a general linear process. In particular, we derive the limit distributions of the nonlinear least squares (NLS) estimators and their t-ratios of the parameters in the model. It is shown that the NLS estimators are generally not efficient. Moreover, the t-ratios for the level parameters have limit dis...

Based on the experience of teaching logistic regression to non-mathematicians, a number of areas of possible confusion are identified that may arise particularly when the method is contrasted with multiple linear regression. The fact that the model is multiplicative in odds ratios means that the concept of interaction needs to be clearly defined. Confidence intervals for the estimates of the od...

We extend logistic regression by using t-exponential families which were introduced recently in statistical physics. We examine our algorithm for both binary classfication and multiclass classfication with both L1 and L2 regularizer. The objective function of our algorithm is non-convex, an efficient block coordinate descent optimization scheme is derived for estimating the parameters. Because ...

Bayesian analyses of multivariate binary or categorical outcomes typically rely on probit or mixed effects logistic regression models that do not have a marginal logistic structure for the individual outcomes. In addition, difficulties arise when simple noninformative priors are chosen for the covariance parameters. Motivated by these problems, we propose a new type of multivariate logistic dis...

Learning from data streams is a well researched task both in theory and practice. As remarked by Clarkson, Hazan and Woodru [12], many classi cation problems cannot be very well solved in a streaming setting. For previous model assumptions, there exist simple, yet highly arti cial lower bounds prohibiting space e cient onepass algorithms. At the same time, several classi cation algorithms are o...

In this paper the asymptotic behavior of penalized spline estimators is studied using bivariate splines over triangulations and an energy functional as the penalty. The rate of L2 convergence is derived, which achieves the optimal nonparametric convergence rate established by Stone (1982). The asymptotic normality of the penalized spline estimators is established, which is shown to hold uniform...