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Admissible point transformations between Burgers equations with linear damping and time-dependent coefficients are described and used in order to exhaustively classify Lie symmetries of these equations. Optimal systems of one- and…
Because of its mathematical tractability, the Gaussian mixture model holds a special place in the literature for clustering and classification. For all its benefits, however, the Gaussian mixture model poses problems when the data is skewed…
In this paper, we present a Weibull link (skewed) model for categorical response data arising from binomial as well as multinomial model. We show that, for such types of categorical data, the most commonly used models (logit, probit and…
In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal…
In this paper, we focus on the COM-type negative binomial distribution with three parameters, which belongs to COM-type $(a,b,0)$ class distributions and family of equilibrium distributions of arbitrary birth-death process. Besides, we show…
The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric…
A major factor contributing to the success of modern representation learning is the ease of performing various vector operations. Recently, objects with geometric structures (eg. distributions, complex or hyperbolic vectors, or regions such…
Continuous mixtures of distributions are widely employed in the statistical literature as models for phenomena with highly divergent outcomes; in particular, many familiar heavy-tailed distributions arise naturally as mixtures of…
Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…
The Burr type XII (BXII) distribution has been largely used in different fields due to its great flexibility for fitting data. These applications have typically involved data showing heavy-tailed behaviors. In order to give more flexibility…
Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly…
Food classification serves as the basic step of image-based dietary assessment to predict the types of foods in each input image. However, food image predictions in a real world scenario are usually long-tail distributed among different…
The mainstream theory of hypothesis testing in high-dimensional regression typically assumes the underlying true model is a low-dimensional linear regression model, yet the Box-Cox transformation is a regression technique commonly used to…
The packing of elastic sheets is investigated in a quasi two-dimensional experimental setup: a sheet is pulled through a rigid hole acting as a container, so that its configuration is mostly prescribed by the cross-section of the sheet in…
We give several applications of the thick distributional calculus. We consider homogeneous distributions, point source fields, and higher order derivatives of order $0.$
Semantic segmentation usually suffers from a long-tail data distribution. Due to the imbalanced number of samples across categories, the features of those tail classes may get squeezed into a narrow area in the feature space. Towards a…
Variational inequalities as an effective tool for solving applied problems, including machine learning tasks, have been attracting more and more attention from researchers in recent years. The use of variational inequalities covers a wide…
Survival analysis is a challenging variation of regression modeling because of the presence of censoring, where the outcome measurement is only partially known, due to, for example, loss to follow up. Such problems come up frequently in…
In this article, we combine Bhargava's geometry-of-numbers methods with the dynamical point-counting methods of Eskin--McMullen and Benoist--Oh to develop a new technique for counting integral points on symmetric varieties lying within…
The smooth piecewise-linear models cover a wide range of applications nowadays. Basically, there are two classes of them: models are transitional or hyperbolic according to their behaviour at the phase-transition zones. This study explored…