Quantitatively modeling the spatial distribution and uncertainties of landcover classes is crucial in geographic information science. However, currently suitable methods for modeling multinomial categorical variables for geographical analyses are rare because of the complex spatial interdependence of multinomial classes. In this paper we use a recently presented two-dimensional Markov chain mod...

We propose a novel distribution that generalizes the Multinomial distribution to enable dependencies between dimensions. Our novel distribution is based on the parametric form of the Poisson MRF model [1] but is fundamentally different because of the domain restriction to a fixed-length vector like in a Multinomial where the number of trials is fixed or known. Thus, we propose the Fixed-Length ...

Probabilistic language modelling has been widely used in information retrieval. It estimates document models under the multinomial distribution assumption, and uses query likelihood to rank documents. In this paper, we aim to generalize this distribution assumption by exploring the use of fully-observable Boltzmann Machines (BMs) for document modelling. BM is a stochastic recurrent network and ...

Several Differential Evolution variants with modified search dynamics have been recently proposed, to improve the performance of the method. This work borrows ideas from adaptive filter theory to develop an “online” algorithmic adaptation framework. The proposed framework is based on tracking the parameters of a multinomial distribution to reflect changes in the evolutionary process. As such, w...

Various random combinatorial objects, such as mappings, trees, forests, and subsets of a finite set, are constructed with probability distributions related to the binomial and multinomial expansions due to Abel, Cayley and Hurwitz. Relations between these combinatorial objects, such as Joyal’s bijection between mappings and marked rooted trees, have interesting probabilistic interpretations, an...

This paper provides estimators of discrete choice models, including binary, ordered, and multinomial response (choice) models. The estimators closely resemble ordinary and two stage least squares. The distribution of the model’s latent variable error is unknown and may be related to the regressors, e.g., the model could have errors that are heteroscedastic or correlated with regressors. The est...

The author-topic model is a generative model for documents that extends Latent Dirichilet Allocation to include authorship information, which is proposed by Michal Rosen-Zvi et al. The model connects each author to a multinomial distribution over topics and associated each topic with a words’ multinomial distribution. A document with multiple authors is modeled as a distribution over topics tha...

Many practical modeling problems involve discrete data that are best represented as draws from multinomial or categorical distributions. For example, nucleotides in a DNA sequence, children’s names in a given state and year, and text documents are all commonly modeled with multinomial distributions. In all of these cases, we expect some form of dependency between the draws: the nucleotide at on...