TPBS models improve robustness to overfitting with localized Dirichlet energy regularization.
problem Global Dirichlet energy-based regularization fails for TPBS models due to perfect interpolation.
method Propose local Dirichlet energy regularization and two inference estimators.
result TPBS models outperform neural networks in overfitting regimes and maintain competitive performance otherwise.
Enhances topic models to better handle polysemous words.
problem Lack of polysemy handling in Gaussian latent Dirichlet allocation.
method Introduces a hierarchical structure to capture polysemy in Gaussian latent Dirichlet allocation.
result Significantly improves polysemy detection and provides more parsimonious topic representations.
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.
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.
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.
Proposes Dirichlet Simplex Nest for probabilistic modeling of various data types.
problem Modeling and inference for diverse data types.
method Probabilistic models based on Dirichlet distribution and Voronoi tessellation, with fast and accurate inference algorithms exploiting convex geometry and simplicial structure.
result Inference algorithms achieve consistency and strong error bounds across various settings and data distributions.
Bayesian models that mix multiple Dirichlet prior parameters, called Multi-Dirichlet priors (MD) in this paper, are gaining popularity. Inferring mixing weights and parameters of mixed prior distributions seems tricky, as sums over Dirichlet parameters complicate the joint distribution of model parameters. This paper s…
New portfolios outperform traditional methods by using factor weights.
problem Improving portfolio allocation in markets driven by factors.
method Factor-weighted Dirichlet portfolios outperform uniform Dirichlet portfolios.
result Factor-weighted portfolios outperform uniformly sampled portfolios in market returns.
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…
A new GAN model LDAGAN uses Latent Dirichlet Allocation to model multimodal images.
problem Ignoring the structure and multimodal characteristics of vision data in GANs.
method Introduced a Dirichlet prior for multimodal image generation leading to LDAGAN. LDAGAN defines generative modes for each sample and uses a VEM algorithm for adversarial training.
result Experimental results show LDAGAN outperforms other GANs on real-world datasets.
Dirichlet pruning compresses neural networks by removing unimportant units.
problem Compressing large neural network models without sacrificing performance.
method Assigns Dirichlet distribution over network layers' units and uses variational inference to estimate parameters.
result Achieves state-of-the-art compression performance on larger architectures like VGG and ResNet.
Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian proc…
Investigates a conjugate prior for Dirichlet distribution.
problem No specific problem stated; focuses on mathematical investigation.
method Investigates a conjugate class for the Dirichlet distribution within the exponential family.
result Identifies a conjugate prior for the Dirichlet distribution.
The paper studies graphs minimizing Dirichlet energy with analytic boundaries, confirming a conjecture about singularities.
problem Understanding the singularities of area-minimizing currents with real analytic boundaries.
method Analyzing multi-valued graphs with real analytic interfaces that minimize Dirichlet energy.
result Dirichlet energy-minimizers with analytic boundary singularities are discrete in 2 dimensions, confirming a conjecture by B. White.
Efficiently approximates uncertainty in classification models using Dirichlet distributions.
problem Inefficient computation of uncertainty estimates in Bayesian deep learning.
method Revised Laplace Bridge method to construct a Dirichlet approximation of softmax output distributions.
result The Dirichlet approximation leads to more efficient computation and better uncertainty estimates.
Study introduces a variational approach for efficient KL divergence estimation in Dirichlet mixture models.
problem Efficient estimation of KL divergence in Dirichlet mixture models.
method Variational approach for a closed-form solution.
result Superior efficiency and accuracy compared to Monte Carlo methods.
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.
Derive Dirichlet scalar curvature energy functional variation formula
problem Dirichlet scalar curvature energy functional
method First variation formula
result Introduce Dirichlet-Einstein metrics
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.
Proposes Dirichlet Variational Autoencoder (DirVAE) for better latent representation.
problem Improving latent representation in autoencoders.
method Uses Dirichlet prior and stochastic gradient method with inverse Gamma approximation to address collapsing issues.
result DirVAE outperforms baselines in log-likelihood and classification accuracy.
DBU models struggle with robust uncertainty estimates under adversarial attacks.
problem Robustness of DBU models in adversarial settings.
method Investigated robustness of DBU models under adversarial attacks; proposed median smoothing approach.
result DBU models are not robust in indicating correctly and wrongly classified samples, detecting adversarial examples, and distinguishing ID and OOD data.
Walley's Imprecise Dirichlet Model (IDM) for categorical i.i.d. data extends the classical Dirichlet model to a set of priors. It overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the imprecise=robust sets or i…
Tree structures are ubiquitous in data across many domains, and many datasets are naturally modelled by unobserved tree structures. In this paper, first we review the theory of random fragmentation processes [Bertoin, 2006], and a number of existing methods for modelling trees, including the popular nested Chinese rest…
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…
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.
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 …
Solves a specific Dirichlet problem on Hermitian manifolds.
problem Solving Dirichlet problem for Monge-Ampère type equations on Hermitian manifolds.
method Solves the Dirichlet problem for Monge-Ampère type equations for (n−1)-plurisubharmonic functions on Hermitian manifolds. result Solves a specific Dirichlet problem on Hermitian manifolds.
Trapezoids uniquely identified by their Dirichlet Laplace spectrum.
problem Identifying trapezoids based on their spectral properties.
method Analyzing the Dirichlet Laplace spectrum of non-obtuse trapezoids.
result Non-obtuse trapezoids are uniquely determined by their Dirichlet Laplace spectrum.
DiAL uses Bayesian Dirichlet random fields for active learning with sparse labels.
problem Active learning with limited labeled data.
method Bayesian Dirichlet random field for feature-conditional class probabilities, calibrating with graph Laplacian.
result Competitive performance in low-label rate graph learning tasks.
Study non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.
problem Non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.
method Description of range in terms of Dirichlet-to-Neumann tensor, construction of hypersurface invariants.
result Unique conformally invariant Dirichlet-to-Neumann hypersurface invariants for Poincaré-Einstein fillings.
Study classifies ruled surfaces critical to Dirichlet energy.
problem Identifying ruled surfaces critical to Dirichlet energy.
method Explicit parametrization of ruled surfaces.
result Classification of ruled surfaces as critical points of Dirichlet energy.
jLDADMM offers Java tools for topic modeling on texts.
problem Topic modeling on texts, especially short texts.
method Collaborated Gibbs sampling for LDA and DMM models.
result Alternative topic modeling solutions for normal or short texts.
We present a mixed multinomial logit (MNL) model, which leverages the truncated stick-breaking process representation of the Dirichlet process as a flexible nonparametric mixing distribution. The proposed model is a Dirichlet process mixture model and accommodates discrete representations of heterogeneity, like a laten…
Nonparametric mixture models based on the Dirichlet process are an elegant alternative to finite models when the number of underlying components is unknown, but inference in such models can be slow. Existing attempts to parallelize inference in such models have relied on introducing approximations, which can lead to in…
Enhances uncertainty estimation in neural networks using Dirichlet-based MC Dropout.
problem Deterministic predictions without uncertainty estimates in neural networks.
method Integrates Dirichlet-based framework within Monte Carlo Dropout.
result Improves quality of uncertainty estimates in deep learning models.
Solves a specific Dirichlet problem for Lagrangian mean curvature equations.
problem Solving the Dirichlet problem for Lagrangian mean curvature equations.
method Solves the Dirichlet problem for Lagrangian mean curvature equations on uniformly convex domains.
result Solves the Dirichlet problem for Lagrangian mean curvature equations.
The paper studies higher order Dirichlet-to-Neumann maps on graphs and their eigenvalues.
problem Analyzing eigenvalues of higher order Dirichlet-to-Neumann maps on graphs.
method Introducing and studying higher order Dirichlet-to-Neumann maps on graphs, deriving estimates on eigenvalues.
result Raulot-Savo-type estimates on the eigenvalues of the DtN maps.
Solves a specific Dirichlet problem on Riemannian manifolds.
problem Dirichlet problem for degenerate fully nonlinear elliptic equations on Riemannian manifolds.
method Derives existence of C1,1-solutions under appropriate assumptions. result Existence of C1,1-solutions. Study compares eigenvalues on spherically symmetric manifolds to Euclidean balls.
problem Comparing eigenvalues on spherically symmetric manifolds to Euclidean balls.
method Examines Dirichlet Laplace eigenvalues on balls of spherically symmetric manifolds and Euclidean space.
result Eigenvalues on spherically symmetric manifolds are smaller for small radii, but larger for hyperbolic spaces.
We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in these rotationally symm…
Driven by the multi-level structure of human intracranial electroencephalogram (iEEG) recordings of epileptic seizures, we introduce a new variant of a hierarchical Dirichlet Process---the multi-level clustering hierarchical Dirichlet Process (MLC-HDP)---that simultaneously clusters datasets on multiple levels. Our sei…
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.
Study on geometry of Dirichlet distributions using Fisher-Rao metric.
problem Understanding the geometry of Dirichlet distributions.
method Analysis of Fisher-Rao metric on Dirichlet distribution parameter space.
result Geodesic completeness and negative sectional curvature of the space.
Flexible evidential deep learning improves uncertainty quantification in machine learning.
problem Overconfident predictions in machine learning models can lead to serious consequences.
method Proposes flexible evidential deep learning (F-EDL) to model uncertainty over class probabilities using a flexible Dirichlet distribution.
result Empirically demonstrates state-of-the-art uncertainty quantification performance across diverse scenarios.
Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.
problem Understanding machine learning methods for data with varying intrinsic dimensions.
method Γ-convergence of graph Dirichlet energies and spectral convergence of graph Laplacians on intersecting manifolds of varying dimensions.
result Normalized Dirichlet energy converges to a tensorized Dirichlet energy that adapts to all dimensions simultaneously.
DPMM-CFL clusters clients for federated learning without fixed K, improving performance.
problem Improving federated learning performance under non-IID client heterogeneity.
method DPMM-CFL uses a Dirichlet Process Mixture Model to infer both cluster number and client assignments.
result DPMM-CFL optimizes per-cluster federated objectives and jointly infers cluster number and assignments.
Paper presents a reparameterized DP-DLGMM for clustering.
problem Non-parametric DP priors in DLGMM are hard to couple with variational inference.
method Closed-form updates for DP-DLGMM's variational posterior.
result Model generates realistic samples and performs competitively in semi-supervised settings.
The paper finds universal inequalities for eigenvalues on hyperbolic spaces.
problem Eigenvalues of the Dirichlet Laplacian on conformally flat Riemannian manifolds.
method Establishes universal inequalities for eigenvalues of the Dirichlet Laplacian on hyperbolic spaces.
result Establishes universal inequalities for eigenvalues of the Dirichlet Laplacian on hyperbolic spaces.