arXiv research

Bayesian test assesses conditional independence between variables.

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.

Bayesian method improves few-shot classification accuracy.

New model identifies microbial subcommunities robustly, accounting for cross-sample heterogeneity.

New families of non-tiling domains satisfy Pólya's conjecture.

Falsehood of Pólya's conjecture for spheres shown.

We use the theory of normal variance-mean mixtures to derive a data augmentation scheme for models that include gamma functions. Our methodology applies to many situations in statistics and machine learning, including Multinomial-Dirichlet distributions, Negative binomial regression, Poisson-Gamma hierarchical models, …

Proves Pólya's conjecture for thin products and Riemannian manifolds.

The paper characterizes Pólya's conjecture for spheres and hemispheres, deriving inequalities and bounds.

Study fine Pólya-Szegő inequalities in metric spaces with applications.

The paper extends inequalities to closed Riemannian manifolds.

A new method for detecting anomalies in large, high-dimensional data streams using probabilistic forest models.

Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.

Pólya's theorem extended to meromorphic functions on Riemann surfaces.

Hyper-parameters play a major role in the learning and inference process of latent Dirichlet allocation (LDA). In order to begin the LDA latent variables learning process, these hyper-parameters values need to be pre-determined. We propose an extension for LDA that we call 'Latent Dirichlet allocation Gibbs Newton' (LD…

An affine rearrangement inequality is established which strengthens and implies the recently obtained affine Pólya--Szegö symmetrization principle for functions on $\mathbb{R}^n$. Several applications of this new inequality are derived. In particular, a sharp affine logarithmic Sobolev inequality is established which i…

In this paper, we prove some analogues of Payne-Polya-Weinberger, Hile-Protter and Yang's inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice $\Z^n.$ This partially answers a question posed by Chung and Oden.

Efficient inference for nonparametric Hawkes processes using Pólya-Gamma augmentation.

Study establishes Pólya-Szegő inequalities on submanifolds with small total mean curvature.

The study analyzes when Bayesian averaging over decision trees is reliable.

We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negat…

Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling them. While there are many methods for modeling nonlinear dynamical systems, exist…

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…

In this paper, we study lower bounds for higher eigenvalues of the Dirichlet eigenvalue problem of the Laplacian on a bounded domain $Ω$ in $\mathbb{R}^n$. It is well known that the $k$-th Dirichlet eigenvalue $λ_k$ obeys the Weyl asymptotic formula, that is, \[ λ_k\sim\frac{4π^2}{(ω_n\mathrm{vol}Ω)^\frac{2}{n}}k^\frac…

We reconsider a nonparametric density model based on Gaussian processes. By augmenting the model with latent Pólya--Gamma random variables and a latent marked Poisson process we obtain a new likelihood which is conjugate to the model's Gaussian process prior. The augmented posterior allows for efficient inference by Gi…

LDTA expands LDA's topic modeling capacity with tree-structured priors.

For a given bounded domain $Ω\subset {\Bbb R}^n$ with $C^1$-smooth boundary, we prove the Pólya conjecture for the Neumann eigenvalues. In other words, we prove that \begin{eqnarray*} μ_{k+1}\le \frac{(2π)^2k^{2/n}}{(ω_n \cdot \mbox{vol}\, (Ω))^{2/n}} \quad \;\; \mbox{for all} \;\; k=0,1,2,3,\cdots,\end{eqnarray*} wher…

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

We propose a scalable stochastic variational approach to GP classification building on Polya-Gamma data augmentation and inducing points. Unlike former approaches, we obtain closed-form updates based on natural gradients that lead to efficient optimization. We evaluate the algorithm on real-world datasets containing up…

We address the problem of regret minimization in logistic contextual bandits, where a learner decides among sequential actions or arms given their respective contexts to maximize binary rewards. Using a fast inference procedure with Polya-Gamma distributed augmentation variables, we propose an improved version of Thomp…

Upper bound found for Steklov eigenvalues counting function.

GP-BART improves BART's predictive performance by incorporating Gaussian process priors.

Functional BART adds shape priors to Bayesian tree regression for better curve fitting.

Proposes a new model for better speech segmentation.

The study proves Lieb-Thirring inequalities on hyperbolic manifolds.

Proposes a method to improve hierarchical clustering using set-level structural priors.

Bayesian tree ensemble model for estimating treatment effects in high-dimensional survival data.

Positive-definite kernel functions are fundamental elements of kernel methods and Gaussian processes. A well-known construction of such functions comes from Bochner's characterization, which connects a positive-definite function with a probability distribution. Another construction, which appears to have attracted less…

Study proves inequalities for eigenvalues of fourth-order elliptic operators on Riemannian manifolds.

Bayesian Beta regression for proportions in high dimensions with theoretical guarantees.

Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large …

We present sparse tree-based and list-based density estimation methods for binary/categorical data. Our density estimation models are higher dimensional analogies to variable bin width histograms. In each leaf of the tree (or list), the density is constant, similar to the flat density within the bin of a histogram. His…

In dynamic topic modeling, the proportional contribution of a topic to a document depends on the temporal dynamics of that topic's overall prevalence in the corpus. We extend the Dynamic Topic Model of Blei and Lafferty (2006) by explicitly modeling document level topic proportions with covariates and dynamic structure…

We present an approximate Bayesian inference approach for estimating the intensity of an inhomogeneous Poisson process, where the intensity function is modelled using a Gaussian process (GP) prior via a sigmoid link function. Augmenting the model using a latent marked Poisson process and Pólya--Gamma random variables w…

Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…

We propose a meta path planning algorithm named \emph{Neural Exploration-Exploitation Trees~(NEXT)} for learning from prior experience for solving new path planning problems in high dimensional continuous state and action spaces. Compared to more classical sampling-based methods like RRT, our approach achieves much bet…

Bayesian learning for forests and trees improves graph detection and structure learning.