Related papers: Generalized Score Distribution
A class of discrete probability distributions contains distributions with limited support. A typical example is some variant of a Likert scale, with response mapped to either the $\{1, 2, \ldots, 5\}$ or $\{-3, -2, \ldots, 2, 3\}$ set. An…
Subjective responses from Multimedia Quality Assessment (MQA) experiments are conventionally analysed with methods not suitable for the data type these responses represent. Furthermore, obtaining subjective responses is resource intensive.…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
Estimation of density functions supported on general domains arises when the data is naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching…
Many probabilistic models that have an intractable normalizing constant may be extended to contain covariates. Since the evaluation of the exact likelihood is difficult or even impossible for these models, score matching was proposed to…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
In selective classification (SC), a classifier abstains from making predictions that are likely to be wrong to avoid excessive errors. To deploy imperfect classifiers -- either due to intrinsic statistical noise of data or for robustness…
There are phenomena that cannot be measured without subjective testing. However, subjective testing is a complex issue with many influencing factors. These interplay to yield either precise or incorrect results. Researchers require a tool…
Score-based generative models (SGMs) have emerged as one of the most popular classes of generative models. A substantial body of work now exists on the analysis of SGMs, focusing either on discretization aspects or on their statistical…
Score-based generative modeling (SGM) has grown to be a hugely successful method for learning to generate samples from complex data distributions such as that of images and audio. It is based on evolving an SDE that transforms white noise…
In this paper we develop a very general class of bivariate discrete distributions. The basic idea is very simple. The marginals are obtained by taking the random geometric sum of a baseline distribution function. The proposed class of…
While score-based generative models (SGMs) have achieved remarkable success in enormous image generation tasks, their mathematical foundations are still limited. In this paper, we analyze the approximation and generalization of SGMs in…
We study a new parametric family of distributions on the ordered simplex $\nabla^{d-1} = \{y \in \mathbb{R}^d: y_1 \geq \dots \geq y_d \geq 0, \sum_{k=1}^d y_k = 1\}$, which we call Generalized Rank Dirichlet (GRD) distributions. Their…
We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…
Few shot learning is an important problem in machine learning as large labelled datasets take considerable time and effort to assemble. Most few-shot learning algorithms suffer from one of two limitations- they either require the design of…
Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of…
Analyzing football score data with statistical techniques, we investigate how the highly co-operative nature of the game is reflected in averaged properties such as the distributions of scored goals for the home and away teams. It turns out…
For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…
The datasets of most image quality assessment studies contain ratings on a categorical scale with five levels, from bad (1) to excellent (5). For each stimulus, the number of ratings from 1 to 5 is summarized and given in the form of the…
In many areas of applied statistics and machine learning, generating an arbitrary number of independent and identically distributed (i.i.d.) samples from a given distribution is a key task. When the distribution is known only through…