We introduce a new method for building classification models when we have prior knowledge of how the classes can be arranged in a hierarchy, based on how easily they can be distinguished. The new method uses a Bayesian form of the multinomial logit (MNL, a.k.a. “softmax”) model, with a prior that introduces correlations between the parameters for classes that are nearby in the tree. We compare ...

where mj : R → R is a nonparametric smooth function and the error εj is independent of the covariate Xj. As is usual in a robust framework, we will assume that the errors εj are such that εj = σj Uj, where Uj has a symmetric distribution Gj(·) with scale 1, so that we are able to identify the error’s scale, σj. When second moments exist, as it is the case of the classical approach, these condit...

Multinomial subjective opinions are a special type of belief functions, where belief mass can be assigned to singletons of the frame as well as to the whole frame, but not to overlapping subsets of the frame. The multiplicative product of two multinomial opinions applies to the Cartesian product of the two corresponding frames. The challenge when multiplying multinomial opinions is that the raw...

The cumulative displacement-time curve is the most common and direct method used to predict deformation trends of landslides divide stages. A new based on inverse logistic function considering distance weighting (IDW) proposed displacement landslides, quantitative standards dividing stages determining critical sliding time are put forward. applied in some landslide cases according monitoring da...

Many popular linear classifiers, such as logistic regression, boosting, or SVM, are trained by optimizing a margin-based risk function. Traditionally, these risk functions are computed based on a labeled dataset. We develop a novel technique for estimating such risks using only unlabeled data and the marginal label distribution. We prove that the proposed risk estimator is consistent on high-di...

Some language types are more frequent among the world’s languages than others, and the field of linguistic typology attempts to elucidate the reasons for such differences in type frequency. However, there is no consensus in that field about the stochastic processes that shape these frequencies, and there is thus likewise no agreement about the expected probability distribution of typological fr...

We extend the results of [LMT] to the non-symmetric and quasiconvex cases. Namely, we consider finite-dimensional space endowed with gauge of either closed convex body (not necessarily symmetric) or closed symmetric quasi-convex body. We show that if a generic subspace of some fixed proportional dimension of one such space is isomorphic to a generic quotient of some proportional dimension of an...

Logistic regression analysis is used to model categorical dependent variable. It is usually used in social sciences and clinical research. Human thoughts and disease diagnosis in clinical research contain vagueness. This situation leads researchers to combine fuzzy set and statistical theories. Fuzzy logistic regression analysis is one of the outcomes of this combination and it is used in situa...

Recently, many papers have begun to consider so-called non-QRT birational maps of the plane. Compared to the QRT family of maps which preserve each biquadratic curve in a fibration of the plane, non-QRT maps send a biquadratic curve to another biquadratic curve belonging to the same fibration or to a biquadratic curve from a different fibration of the plane. In this communication, we give the g...