A beta-negative binomial (BNB) process is proposed, leading to a beta-gamma-Poisson process, which may be viewed as a "multi-scoop" generalization of the beta-Bernoulli process. The BNB process is augmented into a beta-gamma-gamma-Poisson hierarchical structure, and applied as a nonparametric Bayesian prior for an infi…
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48 results for “Poisson binomial”
Two approaches improve parameter learning in various mixture models.
problem Parameter learning in mixture models.
method Complex-analytic and algebraic-combinatorial methods.
result Improved sample sufficiency for parameter estimation in specific mixture models.
Hierarchical Count Echo State Network Models with Application to Graduate Student Enrollmentsstat.ME
The paper proposes count echo state networks for forecasting graduate student enrollments.
problem Forecasting graduate student enrollments from historical data.
method Developed hierarchical count echo state networks and compared them to Poisson autoregressions and negative binomial models.
result Hierarchical negative binomial based echo state network is the superior model.
Identifiability of Generalized Hypergeometric Distribution (GHD) Directed Acyclic Graphical Modelsstat.ML
We introduce a new class of identifiable DAG models where the conditional distribution of each node given its parents belongs to a family of generalized hypergeometric distributions (GHD). A family of generalized hypergeometric distributions includes a lot of discrete distributions such as the binomial, Beta-binomial, …
The logistic regression model is known to converge to a Poisson point process model if the binary response tends to infinitely imbalanced. In this paper, it is shown that this phenomenon is universal in a wide class of link functions on binomial regression. The proof relies on the extreme value theory. For the logit, p…
The th-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of ; and by the absence of…
New results for modeling voter probabilities in elections.
problem Modeling voter preferences with aggregate data and individual covariates.
method Maximum likelihood estimation for Poisson binomial distribution, approximated with heteroscedastic Gaussian.
result Existence and curvature results for the MLE of the Poisson binomial likelihood.
Holistic GLMs add constraints for better model quality.
problem Improving classical linear regression models.
method Sparsity-inducing, sign-coherence, and linear constraints.
result Holistic GLMs reliably solve GLMs for various responses.
A common approach to analyze a covariate-sample count matrix, an element of which represents how many times a covariate appears in a sample, is to factorize it under the Poisson likelihood. We show its limitation in capturing the tendency for a covariate present in a sample to both repeat itself and excite related ones…
PBM mechanism improves privacy and accuracy in federated learning.
problem Secure and private federated learning with limited privacy budget.
method Poisson Binomial mechanism for discrete differential privacy.
result Achieves same privacy-accuracy trade-offs as Gaussian mechanism.
Neural Negative Binomial Regression for Weekly Seismicity Forecasting: Per-Cell Dispersion Estimation and Tail Risk Assessmentphysics.geo-ph
New model predicts weekly earthquakes with better tail risk assessment.
problem Violation of Poisson assumption in seismic data.
method Neural network for per-cell overdispersion estimation.
result 8.6% reduction in mean pinball deviation, 12.5% lower CRPS in tail events.
Unified NMF models for various noise distributions, improving feature extraction.
problem Inadequate assumptions for NMF under complex data distributions.
method Unified framework using MM-algorithms for traditional and convex NMF under Tweedie and Negative Binomial models.
result Unified multiplicative update rules for all models, including novel updates for convex NMF.
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 f…
We define a family of probability distributions for random count matrices with a potentially unbounded number of rows and columns. The three distributions we consider are derived from the gamma-Poisson, gamma-negative binomial, and beta-negative binomial processes. Because the models lead to closed-form Gibbs sampling …
We present a new modeling technique for solving the problem of ecological inference, in which individual-level associations are inferred from labeled data available only at the aggregate level. We model aggregate count data as arising from the Poisson binomial, the distribution of the sum of independent but not identic…
The paper introduces the concept of a cluster structure to define a joint distribution of the sample size and its exchangeable random partitions. The cluster structure allows the probability distribution of the random partitions of a subset of the sample to be dependent on the sample size, a feature not presented in a …
We present a constructive and self-contained approach to data driven general partition-of-unity copulas that were recently introduced in the literature. In particular, we consider Bernstein-, negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data.
We introduce negative binomial matrix factorization (NBMF), a matrix factorization technique specially designed for analyzing over-dispersed count data. It can be viewed as an extension of Poisson matrix factorization (PF) perturbed by a multiplicative term which models exposure. This term brings a degree of freedom fo…
NegBio-VAE models neural spike counts with negative binomial distribution.
problem Limited biological plausibility of continuous latent variables in VAEs for neural spike modeling.
method Proposes a negative binomial latent-variable model with a dispersion parameter for overdispersed spike count modeling.
result NegBio-VAE outperforms competing models in reconstruction and generation tasks.
In this paper we discuss Bayesian nonconvex penalization for sparse learning problems. We explore a nonparametric formulation for latent shrinkage parameters using subordinators which are one-dimensional Lévy processes. We particularly study a family of continuous compound Poisson subordinators and a family of discrete…
Count data, for example the number of observed cases of a disease in a city, often arise in the fields of healthcare analytics and epidemiology. In this paper, we consider performing regression on multivariate data in which our outcome is a count. Specifically, we derive log-likelihood functions for finite mixtures of …
We introduce a new dynamical system for sequentially observed multivariate count data. This model is based on the gamma--Poisson construction---a natural choice for count data---and relies on a novel Bayesian nonparametric prior that ties and shrinks the model parameters, thus avoiding overfitting. We present an effici…
New copulas based on general partitions-of-unity and their applications to risk management (part II)q-fin.RM
We present a constructive and self-contained approach to data driven infinite partition-of-unity copulas that were recently introduced in the literature. In particular, we consider negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data in arbitrary …
Probability distributions produced by the cross-entropy loss for ordinal classification problems can possess undesired properties. We propose a straightforward technique to constrain discrete ordinal probability distributions to be unimodal via the use of the Poisson and binomial probability distributions. We evaluate …
A new method for modeling insurance claim frequencies using random proportions.
problem Inaccurate fitting of classical distributions to insurance claim frequency data.
method Modeling claim frequencies using random proportions of insurance contracts and applying goodness-of-fit tests.
result A new statistical approach for better modeling insurance claim frequencies.
Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block Models, and Multi-layer Networksmath.ST
Paper optimizes clustering for multi-layer networks and discrete mixtures.
problem Optimizing clustering in multi-layer networks and discrete mixtures.
method Two-stage method: tensor-based initialization and likelihood-based refinement.
result Achieves minimax optimal error rate for multi-layer networks and discrete mixtures.
Study optimizes smart contract adoption under high demand variability using Negative Binomial models.
problem Effective supply chain management under high demand variability.
method Combines dynamic Negative Binomial demand modeling with endogenous smart contract adoption optimization.
result The NB model outperforms other benchmarks in forecasting and optimizing smart contract adoption and order quantity.
Convolutional dictionary learning based auto-encoders for natural exponential-family distributionscs.LG
Convolutional auto-encoders learn natural exponential family distributions.
problem Learning latent variables for non-Gaussian data.
method Inspired by CDL, combines CNN and deep learning for natural exponential family data.
result Improved unsupervised and competitive supervised performance.
New method improves mHealth user engagement using Thompson sampling for count data.
problem Optimizing mHealth interventions for distal outcomes through proximal context.
method Combines count data models with Thompson sampling for contextual bandits.
result Improves user engagement in mHealth trials compared to existing methods.
A gamma process dynamic Poisson factor analysis model is proposed to factorize a dynamic count matrix, whose columns are sequentially observed count vectors. The model builds a novel Markov chain that sends the latent gamma random variables at time as the shape parameters of those at time , which are linked …
Modified EAT method improves Poisson gradient estimation.
problem Challenging differentiation through Poisson-distributed latent variables.
method Exponential Arrival Time (EAT) simulation with modifications and Gumbel-SoftMax relaxation.
result Modified EAT method provides unbiased first moment and reduced second-moment bias.
Proposes a new model to better handle overdispersed count time series.
problem Heterogeneous overdispersed count time series.
method Negative-Binomial Randomized Gamma Markov Process.
result Significantly improves predictive performance and fast convergence of inference algorithm.
Develops Bayesian inference methods for gamma models.
problem Challenges in inference for models with gamma functions.
method Data augmentation scheme using Exponential Reciprocal Gamma distributions.
result Scalable EM and MCMC algorithms developed.
Develops a data augmentation method for models with gamma functions.
problem Models with gamma functions lack natural conjugate priors, complicating inference and prediction.
method Derives Pólya Inverse Gamma distributions and applies them to scalable EM and MCMC algorithms.
result Provides scalable algorithms for inference and prediction in models with gamma functions.
The paper improves Fisher-Pitman tests for Poisson mixtures, detecting autism-related genes.
problem Detecting differentially expressed genes between autism and control subjects.
method Nonparametric Poisson mixtures and Fisher-Pitman permutation tests.
result The tests reveal genes missed by common methods, demonstrating rate optimality.
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
Paper proposes a new estimator for generic discrete distributions.
problem Estimating gradients for stochastic nodes in deep generative models.
method Generalized Gumbel-Softmax estimator using truncation, Gumbel-Softmax trick, and linear transformation.
result Efficacy and practical value demonstrated in synthetic examples and topic models.
Data thinning splits observations into independent parts for convolution-closed distributions.
problem Validation of unsupervised learning results in settings with limited data.
method Data thinning, splitting observations into independent parts following the same distribution.
result Data thinning provides an attractive alternative to cross-validation in settings with limited sample splitting.
Tight Bounds on the Binomial CDF, and the Minimum of i.i.d Binomials, in terms of KL-Divergencemath.PR
The study tightens bounds on binomial probabilities and minimums using KL-divergence.
problem Tightening bounds on binomial probabilities and minimums of i.i.d. Binomials.
method Applied Sanov's theorem to derive upper and lower bounds on binomial tail probabilities and minimums, expressed in terms of KL-divergence.
result High probability upper and lower bounds on the minimum of i.i.d. Binomial random variables, finite sample, asymptotically tight.
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
Efficient Bayesian variable selection for binomial and negative binomial data.
problem Computational challenges in Bayesian variable selection for complex models.
method Tempered Gibbs Sampling and MCMC scheme.
result Demonstrated effectiveness on cancer data with thousands of covariates.
Multi-Purpose Binomial Model: Fitting all Moments to the Underlying Geometric Brownian Motionq-fin.PR
We construct a binomial tree model fitting all moments to the approximated geometric Brownian motion. Our construction generalizes the classical Cox-Ross-Rubinstein, the Jarrow-Rudd, and the Tian binomial tree models. The new binomial model is used to resolve a discontinuity problem in option pricing.
Estimates GLMs robustly against label corruptions.
problem Learning GLMs under adversarial label corruptions.
method Iterative trimmed maximum likelihood estimator.
result Achieves minimax near-optimal risk.
Proposes a novel classifier for probabilistic record linkage.
problem Probabilistic record linkage across databases.
method Graphical model based on mixture of Poisson distributions with latent variables, using gamma priors and supervised labels.
result Classifier works effectively with sparse and streaming data.
Extends CRR model with q-binomial random walks for asset pricing.
problem Asset pricing with time-varying probabilities and trend parameters.
method Introduces a q-binomial extension of the CRR model with non-self-similar binomial trees.
result Convergence to Black-Scholes formula with rate O(N^(-1/2)).
The abstract reviews models for analyzing count data.
problem Challenges in analyzing count data with standard methods.
method Review of generalized linear models and multinomial models.
result Fundamental connections between multinomial and count models.
Paper develops efficient method for probability estimation.
problem Estimating probabilities with high efficiency.
method Adaptive Monte Carlo estimation using truncated inverse binomial sampling.
result Proposed method is orders of magnitude more efficient.
GMWB Riders in a Binomial Framework - Pricing, Hedging, and Diversification of Mortality Riskq-fin.PR
We construct a binomial model for a guaranteed minimum withdrawal benefit (GMWB) rider to a variable annuity (VA) under optimal policyholder behaviour. The binomial model results in explicitly formulated perfect hedging strategies funded using only periodic fee income. We consider the separate perspectives of the insur…