Modeling trading volume curves using hierarchical Poisson processes.
problem Predicting trading volume curves for financial instruments.
method Hierarchical Poisson process model based on hierarchical Dirichlet process with MCMC algorithm.
result Demonstrated scalability on NASDAQ stocks, including Apple.
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…
Framework captures missing data in sparse data sets.
problem Capturing missing data in extremely sparse data sets.
method Coupled compound Poisson factorization with stochastic variational inference.
result Explicitly modeling missing data improves results in clustering, prediction, and matrix factorization.
New Gamma-Poisson model improves topic selection for short text.
problem Topic modelling for short text using Poisson distribution.
method Gamma-Poisson mixture model with collapsed Gibbs sampler.
result Gamma-Poisson model selects more accurate number of topics.
Improved semi-supervised learning for large networks using TV-EM and Neural Simpletrons.
problem Challenges in inference and learning for large-scale generative networks.
method Combining Neural Simpletrons with TV-EM for efficient, scalable learning.
result Significant improvements in learning efficiency and performance on semi-supervised tasks.
Posterior regularization enhances Bayesian hierarchical mixture clustering by improving node separation.
problem High nodal variance in BHMC trees, leading to weak separation between nodes at higher levels.
method Employing Posterior Regularization to impose max-margin constraints on nodes at every level.
result Improves cluster separation in BHMC models, enhancing overall model performance.
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.
This tutorial explains fitting mixture distributions to data.
problem Fitting mixture distributions to data.
method Step-by-step tutorial covering two and multiple distributions, including numerical simulations.
result Detailed explanation of fitting mixture distributions, including examples and applications.
Discriminative classifier for compositional data using hierarchical mixture of Generalized Dirichlet models.
problem Classifying compositional data, especially in spam detection and color space identification.
method Hierarchical mixture of discriminative Generalized Dirichlet classifiers, using variational approximation for parameter learning.
result First time a variational upper-bound for Generalized Dirichlet mixture is proposed in literature.
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.
Non-negative matrix factorization models based on a hierarchical Gamma-Poisson structure capture user and item behavior effectively in extremely sparse data sets, making them the ideal choice for collaborative filtering applications. Hierarchical Poisson factorization (HPF) in particular has proved successful for scala…
New method uses dendrograms for better mixture model selection and clustering.
problem Selecting the correct number of components in finite mixture models.
method Hierarchical clustering tree derived from overfitted latent mixing measures.
result Consistently selects the true number of mixing components and optimal convergence rate for parameter estimation.
Developed shrinkage methods for Poisson regression models with experts to handle multicollinearity.
problem Multicollinearity in Poisson regression models with experts.
method Ridge and Liu-type shrinkage methods.
result Shrinkage methods offer more reliable estimates for coefficients in multicollinearity.
New algorithm separates sparse sources from Poisson measurements.
problem Blind source separation of sparse sources from Poisson measurements.
method pGMCA algorithm for Poisson measurements.
result Recovery of sparse sources from Poisson measurements.
A model for the phenomenological description of tick-by-tick share prices in a stock exchange is introduced. It is based on mixtures of compound Poisson processes. Preliminary results based on Monte Carlo simulation show that this model can reproduce various stylized facts.
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.
New dropout method prevents overfitting in hierarchical models.
problem Overfitting in hierarchical mixture of experts.
method Variant of dropout applied hierarchically, not unitwise.
result Prevents overfitting and improves generalization in hierarchical models.
Flexible models cluster RNA sequencing data.
problem Clustering discrete data from RNA sequencing studies.
method Finite mixtures of multivariate Poisson-log normal factor analyzers with constraints.
result Models give favorable clustering performance on real and simulated data.
Bayesian nonparametric method for hierarchical clustering.
problem Hierarchical non-overlapping clustering of a dataset.
method Combining nCRP and HDP for complex latent mixture features.
result Solid empirical results compared to existing algorithms.
Proposes GPHMEs using Gaussian processes for hierarchical expert models.
problem Hierarchical mixtures of experts with complex gating functions.
method Gaussian process-gated hierarchical mixtures of experts (GPHMEs) with non-linear gating and expert functions.
result Outperforms tree-based HMEs and achieves good performance with reduced complexity.
Model captures context-dependent neural correlations using Poisson mixtures.
problem Capturing context-dependent noise correlations in neural populations.
method Conditional finite mixtures of Poisson distributions, cross-validation for dimensionality, EM algorithm.
result Model successfully captures stimulus-dependent correlations in V1 neuron responses.
DGMM uses deep layers of Gaussian mixtures for flexible data modeling.
problem Efficiently modeling complex data relationships.
method Deep Gaussian Mixture Models (DGMM) with nested mixtures of linear models and factor models.
result DGMM provides a flexible nonlinear model for data description.
Paper develops a consistent estimator for discrete mixture models.
problem Estimating mixing probability density in discrete mixture models.
method Develops an L1 consistent estimator under specific conditions. result Consistent estimation of mixing probability density for every density f. A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
Models predict soccer match outcomes with similar accuracy.
problem Predicting soccer match outcomes (win, draw, loss).
method Compared Bradley-Terry extensions and hierarchical Poisson log-linear model. Parameters estimated using log-likelihood or integrated nested Laplace approximations. Predictive performance assessed using temporal validation.
result Bradley-Terry extensions and hierarchical Poisson log-linear model perform similarly in predicting match outcomes.
We survey agglomerative hierarchical clustering algorithms and discuss efficient implementations that are available in R and other software environments. We look at hierarchical self-organizing maps, and mixture models. We review grid-based clustering, focusing on hierarchical density-based approaches. Finally we descr…
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.
We investigate the class of σ-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor p…
Tree-based variational inference improves PLN model for hierarchical count data.
problem Limited applicability of PLN model in ecosystems due to lack of hierarchical tree structures.
method Introduced PLN-Tree model integrating structured variational inference techniques.
result Enhanced generative improvements and practical interpretability in microbiome modeling.
A hierarchical routing mixture of experts model for complex regression tasks.
problem Complex data distribution in regression tasks.
method Binary tree-structured hierarchical routing mixture of experts (HRME) model with classifiers and simple regression models.
result Effective prediction with simple leaf experts in multimodal data.
DPGDS models sequential count data with deep hierarchical structure and temporal dependencies.
problem Modeling sequentially observed multivariate count data with hierarchical and temporal dependencies.
method Developed deep Poisson-gamma dynamical systems with data augmentation and MCMC inference.
result Demonstrated excellent predictive performance and interpretable latent structure.
This paper presents theory for Normalized Random Measures (NRMs), Normalized Generalized Gammas (NGGs), a particular kind of NRM, and Dependent Hierarchical NRMs which allow networks of dependent NRMs to be analysed. These have been used, for instance, for time-dependent topic modelling. In this paper, we first introdu…
We develop dependent hierarchical normalized random measures and apply them to dynamic topic modeling. The dependency arises via superposition, subsampling and point transition on the underlying Poisson processes of these measures. The measures used include normalised generalised Gamma processes that demonstrate power …
Enhances neural forecasting for hierarchically organized time series data.
problem Probabilistic coherent forecasting of time series data across different levels of aggregation.
method Proposes a coherent multivariate mixture output for neural forecasting architectures, optimizing with a composite likelihood objective.
result 13.2% average accuracy improvements on most datasets compared to state-of-the-art baselines.
Improved HMoE models using Laplace gating function enhance expert specialization and performance.
problem Improving performance of hierarchical mixture of experts models.
method Used Laplace gating function instead of Softmax in hierarchical mixture of experts models.
result Laplace gating function accelerates expert convergence and enhances specialization.
Generative model learns hierarchical structure for better sample diversity.
problem Generating high-quality samples from arbitrary distributions.
method Hierarchical mixtures of generators inspired by hierarchical mixture of experts.
result Hierarchical model generates high-quality and diverse samples.
A new method uses online mixtures of tasks to improve meta-learning efficiency.
problem Difficulty in meta-learning when tasks are dissimilar or change over time.
method Proposes a Dirichlet process mixture of hierarchical Bayesian models for task-dependent hyperparameter selection.
result Better handles latent distribution shift on evolving few-shot learning benchmarks.
This paper computes exact posterior distributions of mixture weights in hierarchical Bayesian models.
problem Uncertainty in class membership or data-generating processes in heterogeneous data.
method Exact marginalization of mixture weights using dynamic programming and FFT for two components, and joint dynamic program for K >= 3 components.
result Exact posterior distributions of mixture weights are finite mixtures of Beta distributions, providing credible intervals and per-observation local false-discovery rates.
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…
Paper proposes VampPrior to improve VAEs.
problem Improving variational auto-encoders (VAEs) with a new prior.
method Integrates a Variational Mixture of Posteriors (VampPrior) into VAEs.
result The hierarchical VampPrior architecture learns better models and avoids latent dimension issues.
This study improves fast non-Bayesian Poisson factorization for implicit-feedback recommendation systems.
problem Improving recommendation quality and speed for implicit-feedback data.
method Regularized Poisson models, frequentist optimization, sparse solutions.
result Frequentist approach yields better top-N recommendations with shorter fitting times.
Bayesian model explains sentence comprehension better than distance-based account.
problem Sentence comprehension latency and dependency distance.
method Bayesian hierarchical mixture process modeling.
result Direct-access model fits Chinese relative clause data better.
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.
New test improves clustering accuracy for Gaussian mixtures.
problem Improving clustering accuracy for Gaussian mixtures.
method Relative fit test for Gaussian Mixture Models.
result New test provides provable error control and higher power.
VLAC clusters data hierarchically, outperforming GMM.
problem Clustering with multiple attributes or hierarchies.
method Disentangled latent representations for hierarchical clustering.
result VLAC outperforms Gaussian Mixture Models in clustering accuracy.
Novel connections between Neyman-Scott processes and Bayesian nonparametric mixture models enable scalable inference.
problem Efficiently modeling and detecting clusters in spatiotemporal data.
method Adapting collapsed Gibbs sampling for Neyman-Scott processes via connections to mixture of finite mixture models.
result Demonstrated scalability and effectiveness on neural spike trains and document streams.
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.
Improved deep hierarchical VAE with diffusion-based VampPrior.
problem Latent variable generative modeling challenges.
method Hierarchical VAE with amortized diffusion-based VampPrior.
result Better performance with fewer parameters and improved stability.