New framework models uncertainty in classification debates.
problem Weak interpretability of existing uncertainty quantification methods.
method Courtroom analogy and Mixture of Dirichlet Experts (MoDEX) model.
result MoDEX achieves state-of-the-art uncertainty quantification performance.
We consider the problem of aggregating models learned from sequestered, possibly heterogeneous datasets. Exploiting tools from Bayesian nonparametrics, we develop a general meta-modeling framework that learns shared global latent structures by identifying correspondences among local model parameterizations. Our propose…
Nonparametric Thompson Sampling achieves optimal regret for risk-averse bandits with sub-Gaussian rewards.
problem Optimizing risk-averse bandit problems with sub-Gaussian rewards.
method Anchor-free nonparametric Thompson Sampling algorithm ρext−NPTSSG. result Achieves regret matching the instance-dependent lower bound to leading order in logn. FedBE aggregates local models into a robust global model via Bayesian inference.
problem Challenges in aggregating non-i.i.d. local models into a global model in federated learning.
method FedBE uses Bayesian inference to sample and combine higher-quality global models from local models.
result FedBE leads to more robust aggregation of local models into a global model, especially when data is non-i.i.d.
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…
PTBCC improves accuracy in multi-class annotation aggregation by learning from prototype confusion matrices.
problem Inaccurate and insufficient confusion matrices for annotators in multi-class classification tasks.
method PTBCC (ProtoType learning-driven Bayesian Classifier Combination) uses prototype confusion matrices to capture annotator expertise.
result PTBCC achieves up to 15% accuracy improvement and 3% higher average accuracy compared to existing methods.
Topic models are frequently used in machine learning owing to their high interpretability and modular structure. However, extending a topic model to include a supervisory signal, to incorporate pre-trained word embedding vectors and to include a nonlinear output function is not an easy task because one has to resort to…
We consider the problem of analyzing the heterogeneity of clustering distributions for multiple groups of observed data, each of which is indexed by a covariate value, and inferring global clusters arising from observations aggregated over the covariate domain. We propose a novel Bayesian nonparametric method reposing …
Study uses RL to optimize global equity portfolios, finds mixed results.
problem Optimizing dynamic portfolio weights across diverse global markets.
method Deep reinforcement learning with Soft Actor-Critic, incorporating various constraints and reward formulations.
result RL strategies achieve competitive performance, but no strategy consistently outperforms Buy and Hold.
Derive Dirichlet scalar curvature energy functional variation formula
problem Dirichlet scalar curvature energy functional
method First variation formula
result Introduce Dirichlet-Einstein metrics
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.
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.
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.
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.
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.
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.
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.
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.
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.
Topic models are widely used to discover the latent representation of a set of documents. The two canonical models are latent Dirichlet allocation, and Gaussian latent Dirichlet allocation, where the former uses multinomial distributions over words, and the latter uses multivariate Gaussian distributions over pre-train…
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.
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.
Geodesic balls with non-negative Ricci curvature have a sharp lower bound on their first Dirichlet eigenvalue.
problem Finding a sharp lower bound for the first Dirichlet eigenvalue of geodesic balls.
method Quantitative explicit inequality linking the width of geodesic balls to the spectral gap.
result A quantitative inequality relating the width of geodesic balls to the spectral gap between the first Dirichlet eigenvalue and its lower bound.
Paper solves Dirichlet problem for p-convex hypersurfaces with curvature constraints.
problem Solving the Dirichlet problem for p-convex hypersurfaces with prescribed curvature. method Proved existence of a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition, obtained an interior curvature estimate.
result Existence of a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition.
Hedge funds have long been viewed as a veritable "black box" of investing since outsiders may never view the exact composition of portfolio holdings. Therefore, the ability to estimate an informative set of asset weights is highly desirable for analysis. We present a compositional state space model for estimation of an…
Study gauge freedoms in elastic wave equations and Dirichlet-to-Neumann map.
problem Recover stiffness tensor and density from Dirichlet-to-Neumann map.
method Analyze invariance under coordinate transformations and gauge freedoms.
result Present gauge freedoms in the Dirichlet-to-Neumann map for Riemannian elastic wave equation.
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.
Estimates eigenvalues of poly-Laplace operator on lattice subgraphs.
problem Estimating eigenvalues of poly-Laplace operator on subgraphs of lattice graphs.
method Introduced discrete poly-Laplace operator, derived upper and lower bounds for eigenvalues.
result Poly-Laplace eigenvalues are at least squares of lower-order poly-Laplace eigenvalues.
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.
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.
Solves Dirichlet problem for harmonic maps to give geodesic insights.
problem Asymptotic Dirichlet problem for harmonic maps.
method Holographic characterization using conformal geodesics.
result Characterizes conformal geodesics on the boundary.
We derive and approximate the conjugate prior of Dirichlet and beta distributions.
problem Intractability of conjugate prior for Dirichlet and beta distributions.
method Derive conjugate prior, define closed-form approximation, and provide algorithm.
result Closed-form approximation enables fully tractable Bayesian treatment.
Solves Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
problem Dirichlet problem for prescribed scalar curvature in Anti-de Sitter space
method Fully non-linear elliptic equation
result Solves if datas are strictly convex
Establishes log-concavity estimates for convex domains' first Dirichlet eigenfunctions.
problem Quantifying the Hessian of log-concave eigenfunctions on convex domains.
method Analyzes log-concavity properties of the first Dirichlet eigenfunction on convex domains.
result Obtains quantitative estimates for the Hessian of logu. Universal inequalities found for Laplacian eigenvalues on convex domains.
problem Finding bounds for Laplacian eigenvalues on convex domains.
method Established two universal inequalities.
result Found new bounds for Laplacian eigenvalues.
The problem of searching for experts in a given academic field is hugely important in both industry and academia. We study exactly this issue with respect to a database of authors and their publications. The idea is to use Latent Semantic Indexing (LSI) and Latent Dirichlet Allocation (LDA) to perform topic modelling i…
In this paper we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem a…
Study uniquely determines Riemannian metric derivatives from boundary data.
problem Determining Riemannian metric derivatives from boundary data.
method Computing the full symbol of the elastic Dirichlet-to-Neumann map.
result The elastic Dirichlet-to-Neumann map uniquely determines all partial derivatives of the Riemannian metric on the boundary.
Solves Dirichlet problem for generalized Hitchin's equation on cyclic Higgs bundles.
problem Existence and uniqueness of solutions to the Dirichlet problem.
method Formulated using subharmonic functions; generalizes Hitchin's equation for diagonal harmonic metrics on cyclic Higgs bundles.
result Existence and uniqueness of solutions to the Dirichlet problem.
Paper solves Dirichlet problem at infinity for Riemannian cones.
problem Solvability of Dirichlet problem at infinity in Riemannian cones.
method Separation of variables and comparison arguments for ODE's.
result Sufficient condition for solvability related to Milnor's classification.
Solves Dirichlet problem for Lagrangian phase equation with critical and supercritical phase.
problem Solving Dirichlet problem for Lagrangian phase equation with critical and supercritical phase.
method Uses interior C2 estimate. result Result is sharp, showing existence of singular solutions in subcritical phase.
The paper compares eigenvalues of Dirichlet, Neumann, and Laplacian on graphs.
problem Eigenvalue comparisons on graphs.
method Analytical comparisons and discussions of eigenvalues and their applications.
result Extensions of eigenvalue estimates for Dirichlet and Neumann eigenvalues.
Study solves complex Hessian equation on Hermitian manifolds.
problem Solving Hessian equations on Hermitian manifolds with mixed structure.
method Derive a priori estimates and solve Dirichlet problem under conditions.
result Solvability of the Dirichlet problem for mixed Hessian equations.
Researchers calculate spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.
problem Calculating spectral invariants from Dirichlet-to-Neumann map for Witten-Laplacian with potential.
method Established an effective procedure to calculate all coefficients of the spectral asymptotic formula of the Dirichlet-to-Neumann map.
result Explicitly provided the first four coefficients of the spectral asymptotic formula.
We provide infinitely many solutions of a Dirichlet problem on balls.
Paper proves new inequalities for hyperbolic space Laplacian eigenvalues.
problem Universal inequalities for eigenvalues of the Dirichlet Laplacian.
method Proves new inequalities for eigenvalues on hyperbolic space.
result Verifies Cheng's conjecture up to a small loss.