The paper improves Bayesian precision matrix estimation for high-dimensional sparse data.
problem Estimating sparse precision matrices in high-dimensional settings.
method Tempered posterior with fully specified horseshoe prior.
result Concentration results and theoretical oracle inequality for posterior.
Bayesian method for estimating functional graphical models from neuroimaging data.
problem Estimating dependence structures from functional data in neuroscience.
method Fully Bayesian regularization scheme, including direct Bayesian analog of functional graphical lasso and graphical horseshoe.
result Insight into brain compensation after traumatic brain injury.
Develops a new multivariate regression model for complex outcomes.
problem Flexible, heterogeneous, and residual-dependent multivariate regression problems.
method MultiVCBART framework with Graphical Horseshoe priors.
result Empirically outperforms existing models on sparse, high-dimensional datasets.
Proposes a new method to control FDR using frequentist-assisted horseshoe for high-dimensional testing.
problem Designing tests with frequentist false discovery rate control using horseshoe prior.
method Frequentist-assisted horseshoe procedure for high-dimensional normal means testing.
result Consistently achieves robust finite-sample FDR control in various sparse cases.
Bayesian method improves sparse CCA for multi-view data.
problem Integrative statistical analysis of multi-view high-dimensional data.
method Bayesian infinite factor model with graphical horseshoe prior or diagonal structure to encourage sparsity.
result The proposed Bayesian ScSCCA approach achieves robust estimation of sparse CCA.
We propose a new Bayesian model for flexible nonlinear regression and classification using tree ensembles. The model is based on the RuleFit approach in Friedman and Popescu (2008) where rules from decision trees and linear terms are used in a L1-regularized regression. We modify RuleFit by replacing the L1-regularizat…
T-LoHo model detects structured sparsity and smoothness on graph data.
problem Detecting structured sparsity and smoothness in graph-structured data.
method Tree-based Low-rank Horseshoe (T-LoHo) prior for multivariate parameters.
result Improves anomaly detection on road networks compared to other methods.
The paper proposes a semi-parametric Bayesian network model using Gaussian Processes and Horseshoe priors.
problem Learning semi-parametric relationships in Expert Bayesian Networks with minimal nonlinear components.
method Uses Gaussian Processes and Horseshoe priors to model relationships, prioritizes modifying expert graphs, and generates diverse graphs.
result Models outperform state-of-the-art semi-parametric Bayesian Network models in synthetic and real-world datasets.
Since the advent of the horseshoe priors for regularization, global-local shrinkage methods have proved to be a fertile ground for the development of Bayesian methodology in machine learning, specifically for high-dimensional regression and classification problems. They have achieved remarkable success in computation, …
Proposes EM for sparse horseshoe estimation.
problem Sparse estimation of sparse parameter vectors using the horseshoe prior.
method Expectation-Maximisation (EM) procedure for MAP estimates.
result Our approach performs comparable or superior to state-of-the-art methods.
Bayesian tree ensemble model for estimating treatment effects in high-dimensional survival data.
problem Estimating heterogeneous treatment effects in censored survival data with many covariates.
method Developed a Bayesian tree ensemble model with a horseshoe prior for adaptive shrinkage.
result Accurately estimates treatment effects in high-dimensional covariate spaces and non-linear functions.
Horseshoe priors improve small area estimation by borrowing strength globally but locally.
problem Improving precision of small area estimators through global-local borrowing of strength.
method Developed a tail-robust horseshoe model for Fay-Herriot small area estimation, using heteroscedastic Tweedie identity and regular variation theory.
result The horseshoe model outperforms structured Gaussian smoothing on strongly spatial data, identifying exceptional areas that smoothing suppresses.
HS-MoE selects sparse experts using adaptive priors and data-adaptive gating.
problem Sparse expert selection in mixture-of-experts architectures.
method Combines horseshoe prior with input-dependent gating for data-adaptive sparsity.
result Data-adaptive sparsity in expert usage.
Bayesian Tobit model tackles high-dimensional censored data with Horseshoe prior.
problem High-dimensional censored data with unknown bounds.
method Horseshoe prior for shrinkage, data augmentation for Gibbs sampling.
result Established posterior consistency and concentration rates for Bayesian Tobit models.
Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in a previous paper, which claims that forcing organizes al…
HS-BQR extends horseshoe prior for Bayesian quantile regression.
problem Estimating quantiles in high-dimensional data with bias and error.
method Horseshoe prior for Bayesian quantile regression with a fast sampling algorithm.
result HS-BQR outperforms other shrinkage priors in coefficient bias and forecast error.
Bayesian pliable lasso with horseshoe prior models interactions in GLMs with missing data.
problem Modeling interactions in sparse regression problems with missing responses.
method Bayesian pliable lasso with hierarchical horseshoe prior for sparsity and uncertainty quantification.
result Advantages over existing methods in recovering complex interaction patterns under incomplete data.
Let T be the nilpotent group of 4 x 4 real upper triangular matrices. In this note we show that the Euler equations of certain left-invariant riemannian metrics on T have a horseshoe. We also show, with the aid of a numerical computation of a Melnikov-type integral, that the Euler equations of the sub-riemannian Carnot…
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. Recent work has proposed the use of a horseshoe prior over node pre-activations of a …
In this paper, the use of the Generalized Beta Mixture (GBM) and Horseshoe distributions as priors in the Bayesian Compressive Sensing framework is proposed. The distributions are considered in a two-layer hierarchical model, making the corresponding inference problem amenable to Expectation Maximization (EM). We prese…
Bayesian Beta regression for proportions in high dimensions with theoretical guarantees.
problem Modeling bounded continuous responses in high-dimensional settings with theoretical guarantees.
method Proposes a Bayesian approach using a tempered posterior with Horseshoe prior for shrinkage and variable selection.
result Demonstrates improved estimation accuracy and model interpretability in high-dimensional scenarios.
Bayesian Neural Networks (BNNs) have recently received increasing attention for their ability to provide well-calibrated posterior uncertainties. However, model selection---even choosing the number of nodes---remains an open question. In this work, we apply a horseshoe prior over node pre-activations of a Bayesian neur…
The paper defines and analyzes homotopic rotation sets for surfaces of higher genus.
problem Defining and analyzing homotopic rotation sets for surfaces of higher genus.
method Developed a definition and proved several results using the theory of Le Calvez and Tal.
result Found that the homotopic rotation set can imply the existence of infinitely many periodic orbits under certain conditions.
Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing multidimensional IRT methods, one requires a factorization of the test items. For this t…
Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The ℓ0 penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of all models. A recent area of considerable interest is to develop efficient algor…
Deep-HGP uses Bayesian nonparametric approach for complex data regression.
problem Complex data regression with compositional structures.
method Deep Gaussian processes with a squared-exponential kernel, data-driven lengthscale parameters.
result Posterior distribution optimally recovers unknown true regression curve in terms of quadratic loss.
Proposes a method to identify elements in a skewness matrix for multivariate skew-elliptical distributions.
problem Label switching issue in Bayesian estimation of skewness matrix.
method Imposes a positive lower-triangular constraint and uses Bayesian sparse estimation with horseshoe prior.
result Successfully estimates the true structure of skewness dependency.
Paper proposes new Bayesian neural network models for efficient learning.
problem Efficient learning and model compression in deep neural networks.
method Proposes Spike-and-Slab Group Lasso (SS-GL) and Spike-and-Slab Group Horseshoe (SS-GHS) priors for structured sparsity in Bayesian neural networks.
result Establishes competitive performance in prediction accuracy, model compression, and inference latency compared to baseline models.
Proposes a tail-adaptive shrinkage method for robust sparse estimation.
problem Robust Bayesian methods for high-dimensional regression under diverse sparse regimes.
method Global-local-tail (GLT) Gaussian mixture distribution with tail-adaptive shrinkage.
result GLT posterior contracts at minimax optimal rate for sparse normal mean models.
The study proves the existence of many geodesics on complex manifolds.
problem Existence of closed geodesics on manifolds with non-trivial first Betti number.
method Combining Mañé's theorem with a new theorem about minimal geodesics and transverse homoclinic points.
result Proves the existence of infinitely many closed geodesics of arbitrary large length on manifolds with non-trivial first Betti number.
Li-York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the 2-dimensional disk. In this case a periodic orbit is specified by a braid type and on the se…
Graphical lasso may fail to fit models when data points are insufficient.
problem When does graphical lasso fail to select and fit a graphical model?
method Computational experiments with graphical lasso.
result Graphical lasso may fail when the number of data points is less than the maximum likelihood threshold.
Study on rigidity of translating hypersurfaces not in graphical direction.
problem Rigidity of translating hypersurfaces not in graphical direction.
method Proved rigidity results for complete graphical translating hypersurfaces under specific conditions.
result Entire graphical translating surfaces are flat under certain conditions.
This is a short description of graphic lambda calculus, with special emphasis on a duality suggested by the two different appearances of knot diagrams, in lambda calculus and emergent algebra sectors of the graphic lambda calculus respectively. This duality leads to the introduction of the dual of the graphic beta move…
Bayesian inference corrected for bias in high-dimensional models.
problem Bayesian inference for high-dimensional regression models often produces biased credible sets.
method Debiasing approach based on Bernstein-von Mises theorem.
result Frequentist validity of debiased Bayesian posterior.
We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.
Consider a mean curvature flow of hypersurfaces in Euclidean space, that is initially graphical inside a cylinder. There exists a period of time during which the flow is graphical inside the cylinder of half the radius. Here we prove a lower bound on this period depending on the Lipschitz-constant of the initial graphi…
Undirected graphical models, or Markov networks, are a popular class of statistical models, used in a wide variety of applications. Popular instances of this class include Gaussian graphical models and Ising models. In many settings, however, it might not be clear which subclass of graphical models to use, particularly…
Paper introduces a nonparametric functional graphical model for random functions.
problem Estimating probabilistic conditional independence in functional graphical models.
method Functional sufficient dimension reduction to relax Gaussian or copula Gaussian assumptions.
result Enhances estimation accuracy and retains probabilistic conditional independence.
Graphical models improve portfolio optimization for financial time series.
problem Optimizing portfolios with time-varying covariance patterns.
method Various graphical models (PCA-KMeans, autoencoders, dynamic clustering, structural learning) to capture covariance matrix patterns.
result Graphical models outperform baseline methods in generating steady returns with low risk.
The paper introduces invariants to describe period-doubling routes to chaos in dynamical systems.
problem Understanding the dynamics of period-doubling routes to chaos in complex systems.
method Introducing three topological invariants to describe the topology of period-doubling routes to chaos.
result Ascribed symbolic dynamics to perturbations of the Shilnikov homoclinic scenario and dynamics of the Henon map.
Paper estimates non-causal graphical models using covariance extension and transportation distance.
problem Estimating non-causal graphical models with smoothing relations.
method Proposes a covariance extension problem and uses transportation distance to minimize error with white noise.
result Solution is a double-sided autoregressive non-causal graphical model.
In this paper, we prove a generalization of Rado's Theorem, a fundamental result of minimal surface theory, which says that minimal surfaces over a convex domain with graphical boundaries must be disks which are themselves graphical. We will show that, for a minimal surface of any genus, whose boundary is "almost graph…
Probabilistic graphical models combine the graph theory and probability theory to give a multivariate statistical modeling. They provide a unified description of uncertainty using probability and complexity using the graphical model. Especially, graphical models provide the following several useful properties: - Graphi…
rags2ridges simplifies graphical modeling of high-dimensional data.
problem Graphical modeling of high-dimensional precision matrices.
method Modular framework for extraction, visualization, and analysis of Gaussian graphical models.
result Provides a one-stop-shop for graphical modeling of high-dimensional precision matrices.
We consider the task of estimating a Gaussian graphical model in the high-dimensional setting. The graphical lasso, which involves maximizing the Gaussian log likelihood subject to an l1 penalty, is a well-studied approach for this task. We begin by introducing a surprising connection between the graphical lasso and hi…
Efficient algorithms solve joint graphical lasso problems.
problem Learning graphical models from sparse data.
method Proximal gradient procedures with ADMM backtracking option.
result Proposed algorithms achieve high accuracy and precision.