Dirichlet Process(DP) is a Bayesian non-parametric prior for infinite mixture modeling, where the number of mixture components grows with the number of data items. The Hierarchical Dirichlet Process (HDP), is an extension of DP for grouped data, often used for non-parametric topic modeling, where each group is a mixtur…
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48 results for “non-parametric mixtures”
Study provides guarantees for kernel clustering under non-parametric mixtures.
problem Statistical guarantees for kernel-based clustering without strong assumptions.
method Non-parametric mixture models, kernel-based clustering, consistency guarantees.
result Necessary and sufficient separability conditions for consistent clustering recovery.
BN^2MF identifies unknown exposure patterns in environmental mixtures.
problem Identifying unknown exposure patterns in environmental mixtures.
method Bayesian non-parametric non-negative matrix factorization (BN^2MF) with non-negative continuous priors and a non-parametric sparse prior.
result Estimates patterns of chemical exposures without specifying the number of patterns.
We study the problem of learning a mixture model of non-parametric product distributions. The problem of learning a mixture model is that of finding the component distributions along with the mixing weights using observed samples generated from the mixture. The problem is well-studied in the parametric setting, i.e., w…
Study on Dirichlet process mixtures for clustering consistency.
problem Consistency of clustering with Dirichlet process mixtures.
method Analysis of posterior distribution as sample size increases, focusing on consistency for the number of clusters.
result Consistency for the number of clusters can be achieved with a properly adapted concentration parameter in a Bayesian setting.
Bayesian non-parametric model adapts to concept drifts in streaming data.
problem Inference under concept drift phenomenon for non-stationary data streams.
method Variational inference algorithm for Dirichlet process mixture models with exponential forgetting.
result The proposed model outperforms state-of-the-art algorithms in clustering problems.
New algorithms improve spectral clustering for finite mixture models.
problem Issues with EM algorithm in spectral clustering.
method Spectral decomposition and non-parametric bootstrap sampling.
result Improved convergence and avoidance of poor solutions.
A new MFG framework for evolving clusters from Gaussian mixtures.
problem Evolutionary clustering of time-dependent Gaussian mixtures.
method Control-theoretic framework based on Mean Field Games (MFG) with coupled HJB and Fokker-Planck systems.
result MFG dynamics recover classical EM algorithm trajectories with mass conservation.
Mixture distributions arise in many parametric and non-parametric settings -- for example, in Gaussian mixture models and in non-parametric estimation. It is often necessary to compute the entropy of a mixture, but, in most cases, this quantity has no closed-form expression, making some form of approximation necessary.…
SurvMixClust clusters survival data and predicts individual survival curves.
problem Integrating clustering into survival analysis for precision medicine.
method SurvMixClust learns latent representations for clustering and predicts survival functions using a mixture of non-parametric experts.
result SurvMixClust creates balanced clusters with distinct survival curves, outperforming clustering baselines and competing with non-clustering models in predictive accuracy.
Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to non-parametric Bayesian modeling of complex networks: Using an infinite mixture model …
We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary c…
We present a dual-view mixture model to cluster users based on their features and latent behavioral functions. Every component of the mixture model represents a probability density over a feature view for observed user attributes and a behavior view for latent behavioral functions that are indirectly observed through u…
We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this regularization strategy yields low-complexity sparse models where the number of eff…
This article reviews the Author-Topic Model and presents a new non-parametric extension based on the Hierarchical Dirichlet Process. The extension is especially suitable when no prior information about the number of components necessary is available. A blocked Gibbs sampler is described and focus put on staying as clos…
The paper provides stability guarantees for non-parametric maximum likelihood estimation using statistical mechanics.
problem Non-parametric maximum likelihood estimation and Gaussian mixture models.
method Statistical mechanics analysis to establish stability guarantees for NPMLE.
result High probability upper bounds on the Kullback-Leibler divergence between NPMLE estimators and the true density.
New mixture models for clustering and density estimation of unknown distributions.
problem Clustering and density estimation of data with unknown distributions.
method Two fitting methods: EM algorithm and Bayesian non-parametric method using Gibbs sampler.
result Effective clustering and density estimation of data with unknown distributions.
Elliptical processes extend Gaussian models with heavier tails.
problem Regression and classification with non-Gaussian likelihoods or heavy tails.
method Spline normalizing flow for variational inference of elliptical distributions.
result Elliptical processes outperform Gaussian processes in non-Gaussian settings.
Understanding and interpreting how machine learning (ML) models make decisions have been a big challenge. While recent research has proposed various technical approaches to provide some clues as to how an ML model makes individual predictions, they cannot provide users with an ability to inspect a model as a complete e…
Distributed Collapsed Gibbs Sampler for Dirichlet Process Mixture Models in Federated Learningstat.ML
A new method speeds up DPMM inference for federated learning.
problem Slow inference for large datasets in DPMMs.
method Distributed collapsed Gibbs sampler (DisCGS) for DPMMs.
result Significant reduction in execution time (200x faster) for large datasets.
A fast Modal EM algorithm for Gaussian mixtures.
problem Clustering with Gaussian mixtures.
method Modal EM algorithm for Gaussian mixtures.
result High flexibility in various clustering contexts.
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to mixtures of discrete or Gaussian distributions. In this paper, we propose a kernel m…
Paper proposes a VB method for TS-SBP mixture models with reduced computational cost.
problem Efficiently learning tree-structured stick-breaking process mixture models.
method Utilizes Bayes coding algorithm for context tree models to calculate sums over all possible trees.
result Proposes a learning algorithm with less computational cost for TS-SBP mixture of Gaussians.
A single, stationary topic model such as latent Dirichlet allocation is inappropriate for modeling corpora that span long time periods, as the popularity of topics is likely to change over time. A number of models that incorporate time have been proposed, but in general they either exhibit limited forms of temporal var…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the latter suffers from intractable computation and can lead to overfitting. Taking the i…
We consider a model-based approach to perform batch off-policy evaluation in reinforcement learning. Our method takes a mixture-of-experts approach to combine parametric and non-parametric models of the environment such that the final value estimate has the least expected error. We do so by first estimating the local a…
Gaussian Processes (GPs) are powerful non-parametric Bayesian regression models that allow exact posterior inference, but exhibit high computational and memory costs. In order to improve scalability of GPs, approximate posterior inference is frequently employed, where a prominent class of approximation techniques is ba…
Conjoined Dirichlet Processstat.ML
Develops a non-parametric Dirichlet process method for probabilistic biclustering.
problem Challenges in finding biclusters with strong co-occurrence in rows and columns.
method Dual Dirichlet process mixture models for row and column clustering, with cluster number determined by data.
result Improves bicluster extraction in text mining and gene expression analysis.
In this paper, we suggest a framework to make use of mutual information as a regularization criterion to train Auto-Encoders (AEs). In the proposed framework, AEs are regularized by minimization of the mutual information between input and encoding variables of AEs during the training phase. In order to estimate the ent…
New deep Cox mixture model improves survival analysis performance.
problem Challenges in survival analysis due to censoring and healthcare applications.
method Learning mixtures of Cox regressions with deep neural networks for hazard ratios and non-parametric baseline hazard.
result Our approach outperforms classical and modern survival analysis methods, especially in minority demographics.
This paper studies generalization in machine learning with mixture data.
problem Generalization performance and statistical rates in heterogeneous data.
method Characterization of heterogeneity via pairwise total variation distance, analysis of Rademacher and Gaussian complexities.
result The requirement on heterogeneity increases as function classes get more complex.
Near-optimal tests and confidence sequences for non-parametric data.
problem Flexible statistical inference and decision-making with non-parametric data.
method Classic delayed-start normal-mixture sequential probability ratio tests with asymptotic guarantees.
result Asymptotically optimal type-I error and expected rejection time guarantees.
This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture model…
We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class with respect to appropriate reference measures. The case , in which the manifolds are modelled on Fréchet spaces, is included.…
The article presents a new non-parametric approach for forecasting mortality and fertility using Gaussian process regression.
problem Precise forecasting of demographic movements in developed countries.
method Gaussian process regression with natural cubic spline and spectral mixture covariance functions.
result The approach shows significant improvements in forecasting precision and robustness.
Data clustering has received a lot of attention and numerous methods, algorithms and software packages are available. Among these techniques, parametric finite-mixture models play a central role due to their interesting mathematical properties and to the existence of maximum-likelihood estimators based on expectation-m…
Time-subordinated Brownian motion models improve financial market stochastic distribution.
problem Improving stochastic distribution modeling in financial markets.
method Fourier theory and methodology for time-subordinated Brownian motion models, extending real domain to complex plane.
result Characterization and direct study of stochastic time-change from full process.
Proposes a method to partition univariate data into unimodal subsets.
problem Partitioning univariate multimodal data into unimodal subsets.
method Recursive splitting around valley points of the data density using properties of critical points on the convex hull of the ecdf plot.
result Obtains a hierarchical statistical model of the initial dataset as a mixture of UMMs.
The histogram method is a powerful non-parametric approach for estimating the probability density function of a continuous variable. But the construction of a histogram, compared to the parametric approaches, demands a large number of observations to capture the underlying density function. Thus it is not suitable for …
Generative dynamic texture models (GDTMs) are widely used for dynamic texture (DT) segmentation in the video sequences. GDTMs represent DTs as a set of linear dynamical systems (LDSs). A major limitation of these models concerns the automatic selection of a proper number of DTs. Dirichlet process mixture (DPM) models w…
The paper develops a learning theory for neural network-based CHARME models.
problem Developing a learning theory for CHARME models using neural networks.
method Proves the stationarity and ergodicity of CHARME models under weak conditions, then applies neural networks to derive strong consistency and asymptotic normality of estimators.
result Strong consistency and asymptotic normality of NN-based estimators of CHARME model weights and biases under weak conditions.
Novel approach for estimating joint probability densities using tensor decompositions and dictionaries.
problem Estimating joint probability densities of mixed discrete and continuous variables.
method Low-rank tensor decomposition combined with dictionary learning.
result Better classification and lower error rates compared to existing methods.
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
In many real life problems, objects are described by large number of binary features. For instance, documents are characterized by presence or absence of certain keywords; cancer patients are characterized by presence or absence of certain mutations etc. In such cases, grouping together similar objects/profiles based o…
The book explores universal time-series forecasting using mixture predictors.
problem Sequential probability forecasting in a general setting.
method Mixture predictors combining multiple predictors.
result Universality of mixture predictors in a general probabilistic setting.
Chia and Nakano (2009) introduced the concept of M-decomposability of probability densities in one-dimension. In this paper, we generalize M-decomposability to any dimension. We prove that all elliptical unimodal densities are M-undecomposable. We also derive an inequality to show that it is better to represent an M-de…
New method clusters infant vocalizations using topological data.
problem Clustering infant vocalizations for developmental analysis.
method Topologically augmented signal representation with Dirichlet process mixture model.
result 8 clusters of vocalizations identified in the first 12 months of life.
We investigate coresets - succinct, small summaries of large data sets - so that solutions found on the summary are provably competitive with solution found on the full data set. We provide an overview over the state-of-the-art in coreset construction for machine learning. In Section 2, we present both the intuition be…