New Bayesian method for sparse signal recovery using normal product priors.
problem Sparse signal recovery in compressive sensing.
method Developed a two-stage normal product-based hierarchical model using variational Bayesian inference.
result Demonstrated effectiveness through simulations compared to state-of-the-art algorithms.
Study high-dimensional Bayesian linear regression using variational inference.
problem High-dimensional Bayesian linear regression with product priors.
method Non-linear large deviations theory and variational inference.
result Unique optimizer in variational problem governs posterior distribution under separation condition.
We prove a central limit theorem for the components of the eigenvectors corresponding to the d largest eigenvalues of the normalized Laplacian matrix of a finite dimensional random dot product graph. As a corollary, we show that for stochastic blockmodel graphs, the rows of the spectral embedding of the normalized La…
Thompson sampling used for linear bandits with normal-gamma priors.
problem Optimizing decisions in uncertain environments with linear dependencies and unknown parameters.
method Bayesian Thompson sampling with multivariate normal-gamma priors.
result Derivation of a Bayesian regret bound for the approach.
Proposes method for eliciting non-parametric joint priors using normalizing flows.
problem Learning complex non-parametric joint priors for model parameters.
method Expert elicitation combined with normalizing flows for generative modeling.
result Framework supports elicitation of both parametric and non-parametric priors.
Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.
problem Wiegold problem about groups of normal rank > 1
method Topological argument and intricate construction of left-orders
result Free products of nontrivial left-orderable groups have normal rank > 1
Traditionally, multi-layer neural networks use dot product between the output vector of previous layer and the incoming weight vector as the input to activation function. The result of dot product is unbounded, thus increases the risk of large variance. Large variance of neuron makes the model sensitive to the change o…
Paper unifies and simplifies proof of free product conditions.
problem Conditions for normal closure in free product.
method Geometric approaches to normal closure in ambient groups.
result Unified and simplified proof of Dahmani-Guirardel-Osin theorem.
Algorithm learns shared demand structure across dynamic pricing experiments.
problem Learning shared demand parameters across multiple dynamic pricing experiments.
method Meta dynamic pricing algorithm that learns prior online while solving Thompson sampling experiments.
result Algorithm achieves sublinear meta regret in experiment-rich environments.
Adaptive regularization improves neural network performance on small datasets.
problem Improving neural network performance on limited data.
method Adaptive regularization using a matrix-variate normal prior with a Kronecker product structure.
result The method leads to networks with smaller stable ranks and spectral norms, suggesting better generalization.
The paper updates Bayesian CMA-ES with normal Wishart and proves lower expected covariance.
problem Improving the Bayesian CMA-ES algorithm with normal Wishart prior.
method Revisits Bayesian CMA-ES, proves lower expected covariance in normal Wishart, and presents a generalized model.
result Proves that the expected covariance is lower in the normal Wishart prior model due to convexity of the inverse.
Bayesian approach improves CMA-ES algorithm for faster convergence.
problem Improving the CMA-ES algorithm for faster convergence.
method Deriving optimal updates for CMA-ES parameters using conjugate priors.
result New versions of CMA-ES converge faster with normal-Wishart or normal-Inverse Wishart priors.
The paper proposes a new method for updating neural network parameters using gradient conjugate priors.
problem Learning probability distributions of observed data using neural networks.
method Gradient conjugate prior (GCP) update for neural networks, connecting to log-likelihood maximization.
result The method differs from classical Bayesian updates, leading to different limiting behavior of prior parameters.
A method for eliciting expert beliefs using preferential questions and normalizing flows.
problem Eliciting high-dimensional probability distributions from noisy judgments.
method Normalizing flows based on preferential questions with a novel functional prior.
result The method allows for the inference of arbitrarily flexible densities from preferential judgments.
Harmonic unit normal sections studied for Grassmannians induced by cross products.
problem Energy of maps assigning unit vectors to subspaces of Grassmannians.
method Analyzing cross products to induce harmonic sections into sphere bundles.
result All unit normal sections of Grassmannians associated with cross products are harmonic.
Virtual singular braids embed in a group with normal form.
problem Embedding virtual singular braids into algebraic structures.
method Presented a semi-direct product structure and provided a normal form.
result Virtual singular braid group VSGn is a semi-direct product of VSPGn and Sn. Regression Prior Networks improve ensemble performance on regression tasks.
problem Improving ensemble performance on regression tasks.
method Extending Prior Networks and Ensemble Distribution Distillation (EnD2) to regression tasks using the Normal-Wishart distribution. result Regression Prior Networks yield performance competitive with ensemble approaches on regression tasks.
A method for converting NIW parameters for better estimation.
problem Estimating parameters of multivariate normal distribution.
method Convergent procedure for converting mean parameters to natural parameters in NIW family.
result Maximum likelihood estimation of natural parameters from observed statistics.
Develops methods for constructing parameter priors in DAG models.
problem Constructing parameter priors for model choice among DAG models.
method Introduces assumptions and methods for parameter priors construction and marginal likelihood computation.
result The only parameter prior for complete Gaussian DAG models that satisfies assumptions is the normal-Wishart distribution.
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. W…
We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an …
NF-ULA combines Langevin Monte Carlo with normalizing flows for imaging inverse problems.
problem Solving inverse problems in imaging with uncertainty quantification.
method Langevin Monte Carlo with normalizing flow prior.
result NF-ULA outperforms competing methods for severely ill-posed inverse problems.
The study restricts normal subgroups of Kähler groups, proving specific cases and general restrictions.
problem Characterizing normal subgroups of Kähler groups.
method Analyzing embeddings and conjugation actions of surface groups and one-ended hyperbolic groups.
result Restrictions on normal subgroups of Kähler groups, including virtual direct products and surface group properties.
We propose a generalized double Pareto prior for Bayesian shrinkage estimation and inferences in linear models. The prior can be obtained via a scale mixture of Laplace or normal distributions, forming a bridge between the Laplace and Normal-Jeffreys' priors. While it has a spike at zero like the Laplace density, it al…
Bayesian Tensor Network combines prior and data likelihood for efficient prediction and parameter estimation.
problem Overfitting and poor performance in Tensor Network models.
method Introduce prior distribution, use Laplace approximation for posterior predictive distribution, and propose stable initialization for parameter estimation.
result Reduces overfitting and improves performance of Tensor Network models.
We define cuspidal curvature κc (resp. normalized cuspidal curvature μc) along cuspidal edges (resp. at swallowtail singularity) in Riemannian 3-manifolds, and show that it gives a coefficient of the divergent term of the mean curvature function. Moreover, we show that the product κΠ called the product curva…
In this paper, we give some necessary and sufficient conditions for a normal subgroup of an amalgamated product of groups to be finitely generated. We apply these conditions together with Stallings' fibering theorem to prove that an irreducible multilink in a homology 3-sphere fibers if and only if each of its multilin…
We consider higher dimensional generalisations of normal almost contact structures, the so called f.pk-structures where parallelism spans a Lie algebra g (f.pk-g-structures). Two types of these structures are discussed. In the first case, we construct an almost complex structure on a product manifold mirroring K-struct…
A new method learns latent space normalizing flow for approximate inference in generator models.
problem Approximate inference in generator models with complex posterior distributions.
method Jointly learns latent space normalizing flow and generator model using MCMC-based maximum likelihood.
result The short-run Langevin flow approximates the posterior and aligns with the normalizing flow prior.
The LORACs prior improves latent representation interpretability in VAEs.
problem Learning interpretable latent representations in VAEs.
method Flexible Bayesian nonparametric hierarchical clustering prior based on TMC for VAEs.
result Improved interpretability and practical performance of latent space.
A new approach to disentangled representations using structured latent priors.
problem Learning disentangled representations in unsupervised learning.
method Proposed a structured latent prior to encourage disentanglement and mitigate trade-offs.
result The structured latent prior significantly mitigates the trade-off between reconstruction loss and disentanglement.
Derives TAP approximation for Bayesian linear regression.
problem Log-normalizing constant of posterior distribution in high-dimensional linear regression.
method Variational representation and Thouless-Anderson-Palmer approximation.
result Proves TAP approximation for spherical prior in proportional asymptotic regime.
New method estimates covariance in multi-view data with better accuracy and uncertainty.
problem Estimating covariance in multi-view data with shared and view-specific latent factors.
method Spectral decompositions and conditional conjugate priors for factor loadings and residual variances.
result Proves favorable asymptotic properties and excellent performance in simulations and real data.
The paper constructs hypersurfaces in symmetric space products.
problem Creating curvature-adapted hypersurfaces in symmetric space products.
method Constructing hypersurfaces using the product of symmetric spaces.
result Obtained many examples of curvature-adapted hypersurfaces.
New method for hyperparameter tuning in sparse matrix factorization.
problem Hyperparameter tuning in sparse matrix factorization.
method Numerical method based on evaluating the zero point of normalization factor in sparse matrix prior.
result Our method outperforms existing algorithms in ground-truth sparse matrix reconstruction.
Framework for pricing data products in data-poor markets.
problem Challenges in pricing advanced data products due to lack of transaction data.
method Prior-predictive Monte Carlo framework for generating probabilistic price bands.
result Stable probabilistic price bands for data products in data-poor markets.
NMF with specific constraints is equivalent to LDA.
problem Dimensionality reduction of non-negative data.
method NMF with ℓ1 normalization constraints and Dirichlet prior. result NMF with these constraints is equivalent to LDA.
Develops a new framework for estimating joint probability distributions.
problem Estimating joint probability distributions from large sample sizes.
method Tensor product reproducing kernel Hilbert spaces (RKHS) with normalized and positive model.
result Fast computation and applicability to prediction and classification problems.
The study defines and constructs hypersurfaces in a product of two space forms.
problem Characterizing hypersurfaces in a product of two space forms.
method Explicit construction using parallel families of hypersurfaces and isoparametric hypersurfaces.
result Classification of hypersurfaces with constant mean curvature and constant product angle function.
In (exploratory) factor analysis, the loading matrix is identified only up to orthogonal rotation. For identifiability, one thus often takes the loading matrix to be lower triangular with positive diagonal entries. In Bayesian inference, a standard practice is then to specify a prior under which the loadings are indepe…
Study on the geometric Dyson Brownian motion of non-square matrix products.
problem Understanding the spectrum of a product of non-square random matrices.
method Proportional depth-width limit followed by mean-field limit, solving Burgers equation.
result Free log-normal law is obtained in the identity-start case.
Proposes NUV priors for half-space and box constraints.
problem Adding constraints to linear Gaussian models without computational cost.
method Introduces NUV representations for half-space and box constraints.
result Adds constraints to linear Gaussian models without affecting computational tractability.
Geometrically describes surfaces with parallel mean curvature in warped product spaces.
problem Understanding surfaces with parallel mean curvature in warped product spaces.
method Obtained a geometric description using the normal connection.
result Extended a result by Alencar-do Carmo-Tribuzy on surfaces with parallel mean curvature.
The paper extends RDPG model to handle weighted graphs, enabling better analysis of network data.
problem Modeling networks with weighted edges to capture heterogeneous weight distributions.
method Proposes a nonparametric W-RDPG model with latent positions and moment-generating functions.
result Establishes statistical guarantees for estimating nodal latent positions and sampling graphs.
Proves a special type of submanifolds in a curved space.
problem Characterizing submanifolds with specific properties in a curved space.
method Uses the properties of flat normal bundle and parallel mean curvature to prove the submanifolds are warped products.
result Einstein submanifolds with flat normal bundle and parallel mean curvature are warped product of isometric immersions.
Study homeomorphism groups of ordinals, proving strong distortion and normal generators.
problem Understanding algebraic and geometric properties of homeomorphism groups of ordinals.
method Analyzing successor ordinals with connections to permutation groups and manifolds.
result Proves strong distortion and normal generators for homeomorphism groups of ordinals.
Paper calculates volatility distribution for cumulative production.
problem Volatility distribution for cumulative production.
method Generalizes study of volatility with arbitrary distribution function.
result Exact probability distribution function for volatility.
We establish an integral test describing the exact cut-off between recurrence and transience for normally reflected Brownian motion in certain unbounded domains in a class of warped product manifolds. Besides extending a previous result by R. Pinsky, who treated the case in which the ambient space is flat, our result r…