arXiv research

Proposes a nonparametric tensor factorization for sparse data.

Proposes a new model for clustering passenger trips considering hierarchical and multi-dimensional data.

Proposes a new model for clustering passenger trajectories with graphs.

Study non-linear Dirichlet-to-Neumann map for Poincaré-Einstein fillings.

Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.

Gradient estimate for harmonic functions with boundary condition proved.

TPBS models improve robustness to overfitting with localized Dirichlet energy regularization.

Graph Laplacians adapt to different manifold dimensions, while Dirichlet energies converge to a tensorized Dirichlet energy.

Proves well-posedness for Einstein equations with specific boundary data.

Abstract: Expresses zeta-determinant of Dirichlet-to-Neumann operator on forms.

New tensorization theorem for Sobolev spaces on product spaces.

A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed light on the relationship between the scattering construction of Graham-Zworski…

A new method detects outliers using ensembles of Dirichlet process mixtures.

Study on Dirichlet process mixtures for clustering consistency.

We introduce a dynamic generative model, Bayesian allocation model (BAM), which establishes explicit connections between nonnegative tensor factorization (NTF), graphical models of discrete probability distributions and their Bayesian extensions, and the topic models such as the latent Dirichlet allocation. BAM is base…

Computes indices of mixed order Dirac-type operators and related tensor fields.

Develops tensor calculus for submanifolds of arbitrary codimension.

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…

We consider moment matching techniques for estimation in Latent Dirichlet Allocation (LDA). By drawing explicit links between LDA and discrete versions of independent component analysis (ICA), we first derive a new set of cumulant-based tensors, with an improved sample complexity. Moreover, we reuse standard ICA techni…

The paper proves gradient estimates for nonlinear parabolic equations on smooth metric measure spaces.

We describe a simple and efficient procedure for approximating the Lévy measure of a $\text{Gamma}(α,1)$ 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.…

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 technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-clu…

Bayesian nonparametric approach for clustering non-exchangeable groups.

Community detection is the task of detecting hidden communities from observed interactions. Guaranteed community detection has so far been mostly limited to models with non-overlapping communities such as the stochastic block model. In this paper, we remove this restriction, and provide guaranteed community detection f…

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…

Solves curvature problems on manifolds with negative curvature.

Proposes MLDP for modeling multilinear 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.

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…

The Chinese restaurant process (CRP) and the stick-breaking process are the two most commonly used representations of the Dirichlet process. However, the usual proof of the connection between them is indirect, relying on abstract properties of the Dirichlet process that are difficult for nonexperts to verify. This shor…

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…

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which exploits a certain tensor structure in their low-order observable moments (typically…

Paper presents a reparameterized DP-DLGMM for clustering.

Unified framework for DRO and DTA using Bayesian nonparametrics.

Improved Gaussian process experts model for complex data.

Bayesian neural networks improve with summary information and Dirichlet process.

This paper introduces a deep learning ensemble forecasting model using Dirichlet process.

DPMM-CFL clusters clients for federated learning without fixed K, improving performance.

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference methods for the DP often provide a gold standard in terms asymptotic accuracy, they ca…

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…

This paper proposes a novel dynamic Hierarchical Dirichlet Process topic model that considers the dependence between successive observations. Conventional posterior inference algorithms for this kind of models require processing of the whole data through several passes. It is computationally intractable for massive or …

We present a non-parametric Bayesian latent variable model capable of learning dependency structures across dimensions in a multivariate setting. Our approach is based on flexible Gaussian process priors for the generative mappings and interchangeable Dirichlet process priors to learn the structure. The introduction of…

Method learns Dirichlet-to-Neumann maps on graphs using Gaussian processes.

The paper shows how gradient flow on over-parametrized tensor decomposition behaves like deflation.