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…
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48 results for “Dirichlet diffusion tree”
Pitman-Yor Diffusion Treesstat.ML
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…
Reconstructing probabilistic trees of cellular differentiation from single-cell RNA-seq dataq-bio.QM
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.
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.
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.
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…
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.
Diffusion Boosted Treesstat.ML
DBT combines diffusion models and boosting for supervised learning.
problem Supervised learning problems.
method Diffusion Boosting paradigm and Diffusion Boosted Trees (DBT).
result DBT outperforms deep neural network-based diffusion models and is effective on real-world classification tasks.
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…
An efficient algorithm for aligning diffusion trees to networks with information asymmetry.
problem Aligning diffusion trees to networks with information asymmetry.
method Tree correlation tests for extracting alignment information.
result Explicit lower bounds on the probability of correct matches for each vertex on the diffusion tree.
DTS improves inference-time alignment of diffusion models with less compute.
problem Inference-time alignment of diffusion models suffers from inaccurate value estimation and inefficient reuse of past computations.
method Diffusion Tree Sampling (DTS) uses a tree-based approach to propagate terminal rewards and iteratively refine value estimates.
result DTS produces asymptotically exact samples and matches the FID of best-performing baselines with up to 10x less compute.
New findings on diffusion rates in wind-tree model with rational parameters.
problem Understanding diffusion rates in the wind-tree model with rational parameters.
method Analyzing real numbers in [0,1) as diffusion rates and providing a criterion for Lyapunov spectrum.
result Exhibit an infinite family of wind-tree billiards with the interior of the Lyapunov spectrum being the full square (0,1)^2.
This paper analyzes MCMC algorithms on large graphs using Dirichlet forms.
problem Analyzing the behavior of MCMC algorithms in high-dimensional problems.
method Utilizes Mosco convergence of Dirichlet forms to study RWM algorithm on large graphs.
result Demonstrates the advantages of Dirichlet form approach over standard diffusion methods.
We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli '16. After constructing diffusions, we investigate conservativeness and the wea…
We study the problem of identifying the source of a diffusion spreading over a regular tree. When the degree of each node is at least three, we show that it is possible to construct confidence sets for the diffusion source with size independent of the number of infected nodes. Our estimators are motivated by analogous …
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.
TreeDSB solves mOT problems on tree-structured costs for Wasserstein barycenters.
problem Optimal transport with multiple marginals and tree-structured quadratic costs.
method Tree-based Diffusion Schrödinger Bridge (TreeDSB) for continuous and dynamic solutions.
result TreeDSB efficiently computes Wasserstein barycenters in high dimensions.
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.
Causal Inference with the Instrumental Variable Approach and Bayesian Nonparametric Machine Learningstat.ML
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.
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.
Treeffuser predicts tabular data distributions using gradient-boosted trees.
problem Probabilistic prediction with flexible, non-parametric models.
method Gradient-boosted trees for score estimation in conditional diffusion model.
result Treeffuser outperforms existing methods in probabilistic prediction tasks.
Study quantum diffusion on spectral triples and spinor bundles.
problem Characterize quantum diffusion on almost commutative spectral triples.
method Spin geometry, C *-Dirichlet forms, quantum stochastic flows.
result Existence of covariant quantum stochastic flows on spinor bundles.
Paper develops a new method for game options in local volatility models.
problem Optimal stopping in one-dimensional diffusion with general coefficients.
method Skorokhod embedding to construct recombining tree approximations.
result Construct nearly optimal stopping times with convergence rates.
Constructs rank-based continuous semimartingales for financial markets.
problem Model financial markets using rank-based diffusions.
method Uses Dirichlet forms and Feller property to construct semimartingales.
result Establishes nonexistence of triple collisions and simplified rank process dynamics.
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.
Improves diffusion model performance and efficiency through classical search.
problem Tackles inference-time control in diffusion models.
method Proposes a framework combining local and global search for efficient navigation.
result Significant gains in performance and efficiency across various domains.
The paper examines how curvature-dimension conditions transform under time change for diffusions.
problem Transforming curvature-dimension conditions for diffusions under time change.
method Derives precise transformation formulas for synthetic lower Ricci bounds and curvature-dimension conditions.
result Precise formulas for curvature-dimension conditions under time change for diffusions and metric measure spaces.
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
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.
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…
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.
A new tree-Wasserstein distance for high-dimensional data with latent feature hierarchy.
problem Finding meaningful distances between high-dimensional data samples with latent feature hierarchy.
method Proposes a new tree-Wasserstein distance (TWD) for high-dimensional data with a latent feature hierarchy, using diffusion geometry and tree decoding.
result The proposed TWD effectively recovers the latent feature hierarchy and is efficient and scalable.
A Malliavin-Gamma calculus approach to Score Based Diffusion Generative models for random fieldsmath.PR
Abstract: Generalizes SGMs to infinite-dimensional Hilbertian setting.
problem Difficulties in extending SGMs to infinite-dimensional settings.
method Uses Gamma and Malliavin Calculus, Dirichlet forms, Wiener chaoses, and time-reversal formula.
result Generalized SGMs to Hilbertian setting with finite-dimensional entropic convergence bounds.
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 …
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…
Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametr…
We propose a dynamic mean field model for `systemic risk' in large financial systems, which we derive from a system of interacting diffusions on the positive half-line with an absorbing boundary at the origin. These diffusions represent the distances-to-default of financial institutions and absorption at zero correspon…
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.
Study on hedging risky assets with jumps and costs.
problem Hedging in jump-diffusion models with transaction costs.
method Conditional least square hedging strategy, explicit form for European call options.
result Explicit form of hedging strategy for European call options under transaction costs.
Introduces Star-Shaped DDPMs for non-Gaussian distributions.
problem Difficulties in defining DDPMs for non-Gaussian distributions.
method Star-shaped diffusion process, duality with specific Markovian diffusions, efficient algorithms.
result SS-DDPMs can model distributions like Beta, von Mises-Fisher, Dirichlet, Wishart.
We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as the Heston model, the CEV model and the SABR model, which are widely used as ass…
We study the effect of parameters uncertainties on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, thanks to Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to hedging procedures in order to compute the sensitivities of SDE trajectories with respect…
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, …
Bayesian Additive Regression Trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through the posterior. However, BART assumes IID nor…
Asset Pricing under uncertaintyq-fin.PR
We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute the sensitivity of SDE trajectories with respect to parameter …
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
Many data are naturally modeled by an unobserved hierarchical structure. In this paper we propose a flexible nonparametric prior over unknown data hierarchies. The approach uses nested stick-breaking processes to allow for trees of unbounded width and depth, where data can live at any node and are infinitely exchangeab…
Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorith…