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...

Today, there are not many good measures for detecting influential observations in case of fitting a logistic regression model. So, the purpose this article is to extrapolate from pre-existing deletion diagnostics defined points multiple linear regression, i.e. DFFITS, DFBETAS and Cook's Distance scenario binary model then view multinomial as special same. The threshold determining whether an ob...

This article proposes a method for multiclass classification problems using ensembles of multinomial logistic regression models. A multinomial logit model is used as a base classifier in ensembles from random partitions of predictors. The multinomial logit model can be applied to each mutually exclusive subset of the feature space without variable selection. By combining multiple models the pro...

In binary classification problems it is common for the two classes to be imbalanced: one case is very rare compared to the other. In this paper we consider the infinitely imbalanced case where one class has a finite sample size and the other class’s sample size grows without bound. For logistic regression, the infinitely imbalanced case often has a useful solution. Under mild conditions, the in...

In this report, several experiments have been conducted on a spam data set with Logistic Regression based on Gradient Descent approach. First, the overfitting effect is shown with basic settings (vanilla version). Then Stochastic Gradient Descent and 2-Norm Regularization techniques are both implemented with demonstration of the benefits of these two methods in preventing overfitting. Besides, ...