New bounds improve minimax estimation of banded precision matrices.
problem Estimating banded precision matrices with optimal rates.
method Inverting wider blocks of empirical covariance matrices to estimate subblocks of precision matrices.
result Minimax rate matches for banded covariance matrices, improving previous bounds.
The paper makes inference methods available for Gaussian models with banded precision.
problem Efficient inference for Gaussian models with banded precision.
method Develops linear algebra operators for banded matrices within automatic differentiation frameworks.
result The operators enable efficient variational inference and gradient-based sampling for Gaussian models with banded precision.
Paper proves a noncompact version of Gromov's band-width estimate.
problem Proving a precise upper bound for noncompact Riemannian bands.
method Developed a quantitative partitioned manifold index theory.
result Proved a version of Gromov's band-width estimate for noncompact Riemannian bands.
Study extracts brain networks in multiple time-resolutions using deep learning.
problem Analyzing connectivity patterns among brain regions for cognitive tasks.
method Wavelet decomposition, short time windows, Stacked De-noising Auto-Encoder (SDAE), hierarchical clustering.
result Each cluster represents a cognitive task with high performance metrics.
We introduce a new sparse estimator of the covariance matrix for high-dimensional models in which the variables have a known ordering. Our estimator, which is the solution to a convex optimization problem, is equivalently expressed as an estimator which tapers the sample covariance matrix by a Toeplitz, sparsely-banded…
Researchers explore non-coherent banding in site-specific recombination.
problem Understanding non-coherent banding in site-specific recombination.
method Survey of recent developments in non-coherent banding on knots.
result Recent advances in non-coherent banding model for site-specific recombination.
Study on nodal components of random band-limited functions on surfaces, finding a universal law.
problem Distribution of tangencies of nodal components to a vector field on surfaces.
method Analysis of random band-limited functions on smooth compact Riemannian surfaces with vector fields.
result The distribution of tangencies to a vector field on nodal components of random band-limited functions on surfaces follows a universal deterministic law.
A framework estimates multiple precision matrices with shared structures.
problem Estimating multiple precision matrices with shared structures.
method Penalized likelihood framework with iterative algorithm alternating between convex and clustering problems.
result The method outperforms competitors and performs similarly to methods using prior information.
Paper tackles adversarial attacks on A3C path finding, proposing Gradient Band-based Adversarial Training.
problem Adversarial attacks on A3C path finding.
method Gradient Band-based Adversarial Training with CDG method.
result Gradient Band-based Adversarial Training achieves high attack immunity.
Extends spectral torus band inequalities for compact manifolds with scalar curvature bounds.
problem Proving upper bounds for the width of compact manifolds with boundary.
method Utilizes spacetime harmonic functions, μ-bubbles, and spinorial Callias operators.
result Generalizes Schoen-Yau black hole existence theorem to higher dimensions.
Diagonal transformations preserve independence structures in non-Gaussian distributions.
problem Preserving independence structures in non-Gaussian distributions.
method Diagonal nonlinear transformations of multivariate normal variables.
result Independence structures are preserved in non-Gaussian distributions under diagonal transformations.
Studies in recent years have demonstrated that neural organization and structure impact an individual's ability to perform a given task. Specifically, individuals with greater neural efficiency have been shown to outperform those with less organized functional structure. In this work, we compare the predictive ability …
We introduce a matrix representation of a chord on a tangle which leads us to representing tangle chord diagrams as stacks of matrices that we call books. We show that band sum moves, Reidemeister moves as well as orientation changes are implemented on \widetilde{Z}_f - a framed link invariant constructed from the Kont…
We give a diffeomorphism classification of pinched negatively curved manifolds with amenable fundamental groups, namely, they are precisely the Möbius band, and the products of a line with the total spaces of flat vector bundles over closed infranilmanifolds.
Establish optimal Lipschitz lower bounds for functions on manifolds with negative curvature, revealing interplay between width, boundary area, and topology.
problem Width estimates and rigidity of manifolds with negative curvature
method Gromov's μ-bubble method
result Sharp lower bound for boundary area in hyperbolic bands
Proposes a neural network for efficient deep hedging strategies.
problem Hard training of optimal hedging strategies due to action dependence.
method Introduces no-transaction band network, a neural architecture.
result Demonstrates faster and more precise hedging strategies.
We introduce a covariance matrix estimator that both takes into account the heteroskedasticity of financial returns (by using an exponentially weighted moving average) and reduces the effective dimensionality of the estimation (and hence measurement noise) via techniques borrowed from random matrix theory. We calculate…
Method estimates M-matrices in graphical models with improved accuracy.
problem Estimating M-matrices as precision matrices in Gaussian graphical models.
method Adaptive multiple-stage estimation method solving weighted ℓ1-regularized problems.
result Method outperforms state-of-the-art methods in precision matrix estimation and graph edge identification.
We introduce a general framework for estimation of inverse covariance, or precision, matrices from heterogeneous populations. The proposed framework uses a Laplacian shrinkage penalty to encourage similarity among estimates from disparate, but related, subpopulations, while allowing for differences among matrices. We p…
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.
Develops ADMM for estimating precision matrices from noisy, missing data.
problem Estimating precision matrices from noisy and missing data.
method Alternating Direction Method of Multipliers (ADMM) for non-positive semidefinite inputs.
result Empirically compares ADMM with existing methods and characterizes tradeoffs.
Study on estimating covariance and precision matrices along specific subspaces.
problem Estimating covariance and precision matrices along prescribed subspaces or directions.
method Analysis of finite sample covariance, focusing on components corresponding to desired subspaces or directions.
result Estimation accuracy depends almost exclusively on components corresponding to desired subspaces or directions.
Conjugate gradient methods improve efficiency for high-dimensional GLMMs.
problem Efficiency bottleneck in computing high-dimensional GLMM precision matrices.
method Combining spectral analysis and random graph theory with conjugate gradient methods.
result CG-based methods achieve linear scaling in cost with model parameters and observations.
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
Noise-cleaning fMRI brain activity matrices for better precision estimation.
problem Denoise precision matrices of fMRI time series to estimate true matrices.
method Comparison of various noise-cleaning algorithms on synthetic and real fMRI data.
result Optimal Rotationally Invariant Estimator outperforms others in fMRI data.
High-dimensional inference for sparse spectral precision matrices
problem Inference on the spectral precision matrix at a fixed frequency
method Full likelihood-based inference using neighboring discrete Fourier transforms
result Simultaneous control of regularization, finite-sample truncation, and smoothing biases
Knots connected via a trivial band sum to connected sum.
problem Conditions for band-connected sum to equal connected sum.
method Analyzing knots and bands to determine conditions for equality.
result A band is trivial if and only if a band-connected sum equals a connected sum.
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with longer memory than those considered in the current literature. We show that severa…
Trans-Glasso uses transfer learning to estimate precision matrices from related studies.
problem Challenges in precision matrix estimation with limited target samples.
method Two-step transfer learning: multi-task learning followed by differential network estimation.
result Trans-Glasso achieves minimax optimality under certain conditions and outperforms baseline methods in simulations and real-world applications.
Simplified optimization for structured matrices in deep learning.
problem Computational challenges in Riemannian submanifold optimization for structured symmetric positive-definite matrices.
method Proposed a generalized Riemannian normal coordinates that dynamically orthonormalizes the metric and converts the problem into an unconstrained Euclidean space problem.
result Simplified existing approaches for structured covariances and developed matrix-inverse-free 2nd-order optimizers for deep learning with low precision.
Satellite knots can be trivialized by a single band move.
problem Satellite knots and their trivialization.
method Infinite family of satellite knots and a single band move.
result No disjoint band unknotting exists for satellite knots.
Paper proves conditions for estimating precision matrices with Laplacian constraints.
problem Estimating high-dimensional precision matrices with Laplacian constraints.
method Minimizing Stein's loss with conditions on graph connectivity and Laplacian constraints.
result High-dimensional consistency achieved with Laplacian constraints, independent of graph structure.
Deep learning optimizes wireless band switching without measurement gaps.
problem Wireless networks waste data during band switching due to measurement gaps.
method Online-learning based classifier models exploiting spatial and spectral correlation.
result 30% improvement in mean effective rates compared to industry standard.
Paper tackles BA in dual-band systems using ML.
problem Choosing the best frequency band for communication in dual-band systems.
method Formulated as binary classification problem, proposed supervised ML solutions.
result Analytical and Viterbi Algorithm-based solutions for directional BA.
Study shows upper limit for torical band width with spectral curvature bounds.
problem Understanding the band width of torical bands with spectral curvature constraints.
method Used the warped \( μ\)-bubble method with spectral curvature bounds.
result Upper bound for the band width of torical bands is established.
The goal of this study is to explain and examine the statistical underpinnings of the Bollinger Band methodology. We start off by elucidating the rolling regression time series model and deriving its explicit relationship to Bollinger Bands. Next we illustrate the use of Bollinger Bands in pairs trading and prove the e…
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.
New method for privacy amplification without sampling for matrix factorization.
problem Privacy amplification for differentially private model training with matrix factorization.
method Sampling-free bounds based on Rényi divergence and conditional composition.
result Stronger privacy guarantees for small ε, applicable to various matrices.
New rational band moves simplify knot classification.
problem Classifying knots using rational moves.
method Introduced oriented rational band moves and proved their effectiveness.
result Knots that can be unlinkified by rational moves are rationally slice.
Machine learning improves high-dimensional matrix estimation.
problem Efficient estimation of high-dimensional matrices.
method Integrates machine learning with classical optimization algorithms for high-dimensional matrix estimation.
result The reparameterized LADMM achieves faster convergence and higher accuracy.
A new algorithm improves GLasso for sparse precision matrix estimation.
problem Efficiently estimating sparse precision matrices in high-dimensional data.
method A new reparametrization and iterative block coordinate descent algorithm.
result Improved performance comparable to DP-GLasso with a simpler optimization target.
Band surgery affects knot signatures by 0 or 8.
problem Understanding how band surgery impacts knot signatures.
method Using Heegaard Floer d-invariants and L-space properties.
result The absolute value of signature difference is 0 or 8 for quasi-alternating knots related by band surgery.
We give a short proof that if a non-trivial band sum of two knots results in a tight fibered knot, then the band sum is a connected sum. In particular, this means that any prime knot obtained by a non-trivial band sum is not tight fibered. Since a positive L-space knot is tight fibered, a non-trivial band sum never yie…
Proposes a method to classify with matrix-valued predictors using penalized likelihood.
problem Classification with matrix-valued predictors.
method Penalized likelihood method with Kronecker product decomposition for precision matrix estimation.
result Outperforms competitors in classification accuracy, even when assumptions are violated.
Classifies S1-invariant free boundary minimal annuli and Möbius bands in Bn.
problem Classifying S1-invariant free boundary minimal annuli and Möbius bands in Bn. method Analysis of the spectrum of the Dirichlet-to-Neumann map for S1-invariant metrics. result Existence and classification of S1-invariant free boundary minimal annuli and Möbius bands in Bn. Optimal clustering framework selects bands for hyperspectral images.
problem Efficiently choosing representative bands in hyperspectral images.
method Proposes an optimal clustering framework (OCF) and rank on clusters strategy (RCS) for band selection.
result Significantly outperforms other methods on various data sets.
The paper creates nonparametric confidence bands for band-limited functions.
problem Estimating confidence bands for band-limited functions with finite samples and unknown noise.
method Uses Paley-Wiener reproducing kernel Hilbert spaces and gradient-perturbation methods.
result Non-asymptotic guarantees for confidence regions without assuming a parametric model.
A new neural network separates singing voices more effectively.
problem Separating singing voices from mixed signals with high accuracy.
method MBR-FCN that processes different frequency bands with varying resolutions and filters.
result The MBR-FCN achieves better performance with fewer parameters.