Abstract-The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count-and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural and computational advantages of the NB process. A variety of NB processes, including the betageometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

Significance This paper compares the probabilistic accuracy of short-term forecasts of reported deaths due to COVID-19 during the first year and a half of the pandemic in the United States. Results show high variation in accuracy between and within stand-alone models and more consistent accuracy from an ensemble model that combined forecasts from all eligible models. This demonstrates that an ensemble model provided a reliable and comparatively accurate means of forecasting deaths during the COVID-19 pandemic that exceeded the performance of all of the models that contributed to it. This work strengthens the evidence base for synthesizing multiple models to support public-health action.

We consider analysis of noisy and incomplete hyperspectral imagery, with the objective of removing the noise and inferring the missing data. The noise statistics may be wavelength-dependent, and the fraction of data missing (at random) may be substantial, including potentially entire bands, offering the potential to significantly reduce the quantity of data that need be measured. To achieve this objective, the imagery is divided into contiguous three-dimensional (3D) spatio-spectral blocks, of spatial dimension much less than the image dimension. It is assumed that each such 3D block may be represented as a linear combination of dictionary elements of the same dimension, plus noise, and the dictionary elements are learned in situ based on the observed data (no a priori training). The number of dictionary elements needed for representation of any particular block is typically small relative to the block dimensions, and all the image blocks are processed jointly ("collaboratively") to infer the underlying dictionary. We address dictionary learning from a Bayesian perspective, considering two distinct means of imposing sparse dictionary usage. These models allow inference of the number of dictionary elements needed as well as the underlying wavelength-dependent noise statistics. It is demonstrated that drawing the dictionary elements from a Gaussian process prior, imposing structure on the wavelength dependence of the dictionary elements, yields significant advantages, relative to the more-conventional approach of using an i.i.d. Gaussian prior for the dictionary elements; this advantage is particularly evident in the presence of noise. The framework is demonstrated by processing hyperspectral imagery with a significant number of voxels missing uniformly at random, with imagery at specific wavelengths missing entirely, and in the presence of substantial additive noise.

BackgroundHigh-throughput bio-OMIC technologies are producing high-dimension data from bio-samples at an ever increasing rate, whereas the training sample number in a traditional experiment remains small due to various difficulties. This “large p, small n” paradigm in the area of biomedical “big data” may be at least partly solved by feature selection algorithms, which select only features significantly associated with phenotypes. Feature selection is an NP-hard problem. Due to the exponentially increased time requirement for finding the globally optimal solution, all the existing feature selection algorithms employ heuristic rules to find locally optimal solutions, and their solutions achieve different performances on different datasets.ResultsThis work describes a feature selection algorithm based on a recently published correlation measurement, Maximal Information Coefficient (MIC). The proposed algorithm, McTwo, aims to select features associated with phenotypes, independently of each other, and achieving high classification performance of the nearest neighbor algorithm. Based on the comparative study of 17 datasets, McTwo performs about as well as or better than existing algorithms, with significantly reduced numbers of selected features. The features selected by McTwo also appear to have particular biomedical relevance to the phenotypes from the literature.ConclusionMcTwo selects a feature subset with very good classification performance, as well as a small feature number. So McTwo may represent a complementary feature selection algorithm for the high-dimensional biomedical datasets.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0990-0) contains supplementary material, which is available to authorized users.