New DFP model improves tree clustering and density estimation.
problem Modeling tree structures in data.
method Developed a novel Dirichlet fragmentation process (DFP) and hierarchical mixture model.
result DFP mixture model outperforms existing methods in clustering and density estimation.
The paper introduces a new model to correct bias in treatment effect estimates due to sample selection.
problem Bias in treatment effect estimates due to sample selection.
method Type 2 Tobit Bayesian Additive Regression Trees (TOBART-2) with Dirichlet Process Mixture distribution and soft trees.
result Corrects bias in treatment effect estimates by accounting for nonlinearities and model uncertainty.
We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian ensemble trees (BET) and model them as an infinite mixture Dirichlet process. We show that B…
LDTA expands LDA's topic modeling capacity with tree-structured priors.
problem Limited expressiveness of Dirichlet priors in LDA for complex topic relationships.
method Introduces Latent Dirichlet-Tree Allocation (LDTA) with Dirichlet-Tree (DT) priors, and develops universal mean-field variational inference and Expectation Propagation.
result LDTA enables expressive, tree-structured priors over topic proportions, expanding modeling capacity of LDA.
Bayesian nonparametric machine learning improves instrumental variable inference.
problem Estimating causal effects with nonlinear relationships.
method Bayesian Additive Regression Trees (BART) for estimating functions and Dirichlet Process mixtures for error terms.
result Dramatic improvements in inference with nonlinear data, no manual tuning required.
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of particles (representing the objects) diffusing in some continuous space, analogou…
BART uses trees to model complex regression, but this paper extends it to nonparametric error modeling.
problem BART's parametric error assumption can lead to misleading inference and uncertainty quantification.
method The paper uses a Dirichlet process mixture (DPM) to nonparametrically model the error distribution.
result The extended BART can adapt to non-normal errors while preserving its strengths.
This paper tackles blind image denoising with unknown noise models.
problem Real noisy images have complex noise models that are unknown beforehand.
method Proposes a novel Bayesian nonparametric prior called Dependent Dirichlet Process Tree to model the noise and a variational inference algorithm to recover clean patches.
result Achieves better performance compared to previous approaches on synthesis and real noisy images.
We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a new method of nonparametric regression that accommodates continuous and categorical inputs, and responses that can be modeled by a generalized linear model. We prove conditions for the asymptotic unbiasedness of the DP-GLM regression mean fu…
We introduce the Pitman Yor Diffusion Tree (PYDT) for hierarchical clustering, a generalization of the Dirichlet Diffusion Tree (Neal, 2001) which removes the restriction to binary branching structure. The generative process is described and shown to result in an exchangeable distribution over data points. We prove som…
New model reconstructs cell differentiation paths from single-cell RNA data.
problem Reconstructing dynamic biological phenomena from noisy, heterogeneous, and sparse single-cell RNA-seq data.
method Developed a generative model using Dirichlet diffusion tree and Markov chain Monte Carlo sampler.
result Recovered latent trajectories from simulated single-cell transcriptomes.
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.
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, …
This technique learns interpretable models by encoding the training distribution as a Dirichlet Process and using uncertainty scores as an oracle.
problem Creating small, interpretable models that are still accurate.
method Exploits a Dirichlet Process to encode the training distribution, uses Bayesian Optimization for parameters, and projects data to one dimension using an uncertainty oracle.
result Improves accuracy and size trade-off, applicable across different model families.
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.
We develop a nested hierarchical Dirichlet process (nHDP) for hierarchical topic modeling. The nHDP is a generalization of the nested Chinese restaurant process (nCRP) that allows each word to follow its own path to a topic node according to a document-specific distribution on a shared tree. This alleviates the rigid, …
A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is …
A new parallel clustering method improves speed and accuracy for single cell transcriptomic data.
problem Challenges in clustering single cell transcriptomic data, including poor quality, lack of prior knowledge, and slow computation.
method Parallel Split Merge Sampling on Dirichlet Process Mixture Model (Para-DPMM).
result The Para-DPMM model outperforms existing methods in clustering quality and computational speed.
Universal inequalities for Laplacian eigenvalues on discrete groups.
problem Proving inequalities for Laplacian eigenvalues on discrete groups.
method Analyzing Laplacian eigenvalues with Dirichlet boundary conditions on subsets of discrete groups.
result Yang-type universal inequalities for Cayley graphs of amenable groups and the d-regular tree.
The study analyzes when Bayesian averaging over decision trees is reliable.
problem When do Bayesian model averaging weights over decision trees provide reliable information?
method Closed-form solution for Bayesian decision trees with Catalan-exponential priors.
result Established a complete non-asymptotic theory of rational commitment thresholds.
Paper proposes learnable topological features for efficient phylogenetic inference.
problem Finding appropriate topological structures for phylogenetic inference tasks requires significant design effort and domain expertise.
method Combines raw node features with graph neural networks to automatically adapt to different tasks.
result Demonstrates effectiveness and efficiency on simulated and real data phylogenetic inference tasks.
A new method detects outliers using ensembles of Dirichlet process mixtures.
problem Challenges in unsupervised outlier detection using Dirichlet process mixtures.
method Ensembles of Dirichlet process Gaussian mixtures with random subspace and subsampling.
result Empirically outperforms existing approaches in unsupervised outlier detection.
New model identifies microbial subcommunities robustly, accounting for cross-sample heterogeneity.
problem Inference in LDA is sensitive to the number of subcommunities and often creates artificial ones.
method Incorporates logistic-tree normal (LTN) model into LDA to account for cross-sample heterogeneity.
result Restores robustness of inference and identifies meaningful subcommunities.
This paper uses natural language processing to create the first machine-coded democracy index, which I call Automated Democracy Scores (ADS). The ADS are based on 42 million news articles from 6,043 different sources and cover all independent countries in the 1993-2012 period. Unlike the democracy indices we have today…
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.
LDDP models space-time dependencies in DP using Gaussian processes.
problem Lack of dependency information in basic DP models for spatial and temporal data.
method Developed location dependent Dirichlet processes (LDDP) integrating Gaussian processes.
result Demonstrated effectiveness on image segmentation task.
Consistency of DSDP proved with exponential convergence.
problem Consistency analysis for Doubly Stochastic Dirichlet Process.
method Proved components consistency with simulation and real-world experiments.
result Exponential convergence of posterior probability.
Deviance-style normalization for sparse, jointly overdispersed count matrices
problem Jointly overdispersed count matrices
method Dirichlet-multinomial deviance residualization
result Preserves exact sparsity, evaluates in constant time, recovers multinomial residual
A new hybrid MCMC method guides MCMC with tree-based clustering for faster and more efficient inference.
problem Slow convergence of MCMC methods in posterior inference for NRM mixture models.
method Tree-guided MCMC (tgMCMC) that combines MCMC's convergence guarantees with IBHC's efficiency.
result tgMCMC provides faster convergence and better performance compared to MCMC and IBHC alone.
Paper derives a formula for the determinant of Dirichlet-to-Neumann operator on Riemann surfaces.
problem Bounding asymptotics of a conformal invariant under degeneration of Riemann surfaces.
method Meyer-Vietoris formula, gluing, height function on moduli space, properness of height function, Steklov isospectral metrics, Laplacian with Dirichlet/Neumann boundary conditions.
result Properness of height function on moduli space of genus zero hyperbolic surfaces implies compactness theorem for Steklov isospectral metrics.
We propose the supervised hierarchical Dirichlet process (sHDP), a nonparametric generative model for the joint distribution of a group of observations and a response variable directly associated with that whole group. We compare the sHDP with another leading method for regression on grouped data, the supervised latent…
In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from…
We describe a simple and efficient procedure for approximating the Lévy measure of a Gamma(α,1) random variable. We use this approximation to derive a finite sum-representation that converges almost surely to Ferguson's representation of the Dirichlet process based on arrivals of a homogeneous Poisson process.…
Directly proves CRP from stick-breaking process without measure theory.
problem Indirect proof of CRP from stick-breaking process is complex.
method Direct proof using stick-breaking process to CRP, avoiding measure theory.
result Direct proof connects stick-breaking process to CRP.
This paper proves a Faber-Krahn inequality for trees with given matching number.
problem Proving a Faber-Krahn inequality for trees with specific properties.
method Characterization of trees with given matching number.
result The Faber-Krahn inequality holds for trees with given matching number.
We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that is a key component of our model. Features can have either a unique distribution…
Bayesian nonparametric approach for clustering non-exchangeable groups.
problem Clustering grouped data with dependencies among groups.
method Graphical Dirichlet process modeling with Markov property.
result Efficient posterior inference algorithm developed.
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.
Bayesian model learns complex multivariate dependencies.
problem Learning dependency structures across multiple dimensions.
method Flexible Gaussian process priors and Dirichlet process for structure learning.
result Efficient variational inference for model parameters.
Flexible nonparametric model for discrete choice analysis.
problem Modeling heterogeneity in discrete choice data without fixed component limits.
method Dirichlet process mixture model with expectation maximisation algorithm.
result Proposed model outperforms latent class MNL and mixed MNL models in both fit and predictive ability.
Scalable algorithm for extracting topic hierarchies from large text corpora.
problem Efficient inference for hierarchical topic models on large datasets.
method Partially collapsed Gibbs sampling (PCGS) algorithm combined with efficient distributed implementation.
result 111 times more efficient than previous implementation for hLDA.
Proposes CHDP for modeling cooperative hierarchical structures with Dirichlet processes.
problem Lack of flexible topic modeling for cooperative hierarchical structures.
method Introduces Cooperative Hierarchical Dirichlet Processes (CHDP) with superposition and maximization measures.
result Demonstrates improved modeling of cooperative hierarchical structures with CHDP.
Proposes MLDP for modeling multilinear data.
problem Handling data with interactions from multiple factors.
method Combines Dirichlet processes with multilinear factor analysis.
result Achieved state-of-the-art performance on real-world data.
We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating cluster parameters. The second approach marginalizes out several cluster parameters …
This paper proposes a Hilbert space embedding for Dirichlet Process mixture models via a stick-breaking construction of Sethuraman. Although Bayesian nonparametrics offers a powerful approach to construct a prior that avoids the need to specify the model size/complexity explicitly, an exact inference is often intractab…
The Dirichlet random walk on manifolds has a positive escape rate if the cover is non-amenable.
problem Analyzing the stochastic behavior of Dirichlet random walks on manifolds.
method Defining a recursive process on Galoisian covers and proving a theorem about the escape rate.
result The escape rate is positive if and only if the cover is non-amenable.
Dynamic topic model detects abnormal behavior in video sequences.
problem Detecting abnormal behavior in sequential video data.
method Dynamic Hierarchical Dirichlet Process with online inference algorithms.
result The dynamic model improves abnormal behavior detection performance.
Bayesian methods model diverse groups with censored data.
problem Pooling and analyzing small heterogeneous groups of time-to-event data.
method Three Bayesian nonparametric methods: Dirichlet process, hierarchical Dirichlet process, and nested Dirichlet process.
result Model accuracy comparison on simulated and real-world datasets.