Related papers: Zero-Class Poisson for Rare-Event Studies
A novel model of systematic errors for the regression of Poisson data is applied to hypothesis testing of nested model components with the introduction of a generalization of the $\Delta C$ statistic that applies in the presence of…
Understanding the statistics of collisions among locally confined gas particles poses a major challenge. In this work we investigate $\mathbb Z^d$-map lattices coupled by collision with simplified local dynamics that offer significant…
Classification based on Zero-shot Learning (ZSL) is the ability of a model to classify inputs into novel classes on which the model has not previously seen any training examples. Providing an auxiliary descriptor in the form of a set of…
We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs are from parametrized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover…
Selective classification is a powerful tool for automated decision-making in high-risk scenarios, allowing classifiers to act only when confident and abstain when uncertainty is high. Given a target accuracy, our goal is to minimize…
Current approaches for collision avoidance and space traffic management face many challenges, mainly due to the continuous increase in the number of objects in orbit and the lack of scalable and automated solutions. To avoid catastrophic…
Detection of out-of-distribution (OOD) samples is crucial for safe real-world deployment of machine learning models. Recent advances in vision language foundation models have made them capable of detecting OOD samples without requiring…
Within the framework of probability models for overdispersed count data, we propose the generalized fractional Poisson distribution (gfPd), which is a natural generalization of the fractional Poisson distribution (fPd), and the standard…
This paper presents a new method to estimate systematic errors in the maximum-likelihood regression of count data. The method is applicable in particular to X-ray spectra in situations where the Poisson log-likelihood, or the Cash…
The minor probability events detection is a crucial problem in Big data. Such events tend to include rarely occurring phenomenons which should be detected and monitored carefully. Given the prior probabilities of separate events and the…
Mediation analysis is an increasingly popular statistical method for explaining causal pathways to inform intervention. While methods have increased, there is still a dearth of robust mediation methods for count outcomes with excess zeroes.…
In modern scientific research, small-scale studies with limited participants are increasingly common. However, interpreting individual outcomes can be challenging, making it standard practice to combine data across studies using random…
The model representing two independent Poisson processes, labelled as "signal" and "background" and both contributing at the same time to the total number of counted events, is considered from a Bayesian point of view. This is a widely used…
Existing integer-valued autoregressive (INAR) models for count random fields suffer from difficulties in characterizing the stationary marginal distribution and in computing conditional probabilities (as required for likelihood inference).…
We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…
Regression for count data is widely performed by models such as Poisson, negative binomial (NB) and zero-inflated regression. A challenge often faced by practitioners is the selection of the right model to take into account dispersion,…
The problem of estimating the ratio of the means of a two-component Poisson mixture model is considered, when each component is subject to zero-inflation, i.e., excess zero counts. The. resulting {\it zero-inflated Poisson mixture (ZIPM)…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…