New method uses HDP-HMM and multitaper spectral estimation for automated sleep state classification.
problem Manual sleep scoring is subjective, time-consuming, and doesn't capture neural dynamics.
method Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM) with multitaper spectral estimation.
result Automated algorithm recovers sleep dynamics and identifies subject-specific microstates.
Deep learning classifies sleep stages from EEG signals, aiding professionals.
problem Manual scoring of sleep stages from EEG signals is tedious and requires trained professionals.
method Multitaper spectral analysis and deep convolutional neural networks for automatic classification.
result System accurately classifies sleep stages in new patients, favorably compared to state-of-the-art.
Binary and multiclass epilepsy detection methods using EEG features.
problem Epilepsy diagnosis from EEG data.
method Feature extraction from power spectrum, spectrogram, and bispectrogram; eight machine learning algorithms used.
result Random forest and backpropagation algorithms achieved highest accuracy for binary and multiclass classification.
We begin with a review of the notion of a braid group. We then discuss some known solutions to decision problems in braid groups. We then move on to proving new results in braid group algorithmics. We offer a quick solution to the generalized word problem in braid groups, in the special case of cyclic subgroups. We ill…
Paper estimates spectral risk measures for insurance data with truncated and censored data.
problem Estimating spectral risk measures for insurance data with left truncation and right censoring.
method Proposes a non-parametric estimator using product limit estimator and establishes asymptotic normality.
result Proposed estimator outperforms existing methods for small k and small sample sizes.
Estimates spectral projections restricted to uniformly embedded submanifolds.
problem Estimating spectral projections on submanifolds of manifolds with nonpositive curvature.
method Estimates the L2(M)oLq(Σ) norm of spectral projection operators. result Sharp spectral projection estimates for small spectral windows.
Sketching reduces data size for accurate spectral estimation.
problem Estimating spectral density from large simulation datasets.
method Sketching for dimensionality reduction and data compression.
result Sketching provides 90% accurate spectral density estimate with 10% data.
Paper develops a method for estimating spectral density matrices in high-dimensional time series.
problem Estimating spectral density matrices in high-dimensional time series.
method Thresholded versions of averaged periodograms for regularized estimation.
result Consistent estimation of spectral density matrices possible under high-dimensional regime.
Sharp spectral gap estimates on manifolds with integral curvature bounds.
problem Proving spectral gap estimates on manifolds with integral curvature bounds.
method Generalizing previous results to include integral curvature bounds.
result Confirms a conjecture about spectral gap estimates on manifolds with integral curvature bounds.
New estimates show spectral gap stability in RCD spaces, close to Beta distribution.
problem Stability of spectral gap bounds in metric-measure spaces.
method Combines L1-functional inequality and Stein's method. result Sharp quantitative estimate for spectral gap stability.
Deep learning speeds spectral density estimation for large 2D/3D grids.
problem Computational challenges in estimating spectral densities for large grids.
method Deep learning neural network for spectral density estimation.
result Deep learning estimator is a universal approximator and faster than existing methods.
The paper explores rigidity theorems for spectral curvature bounds in 3-manifolds.
problem Classical rigidity results in scalar curvature geometry are extended to the spectral setting.
method Warped μ-bubble method is systematically employed to classify stable weighted minimal hypersurfaces and establish band width estimates. result Classification theorems and band width estimates for spectral Ricci and scalar curvatures are proven.
This note is devoted to optimal spectral estimates for Schrödinger operators on compact connected Riemannian manifolds without boundary. These estimates are based on the use of appropriate interpolation inequalities and on some recent rigidity results for nonlinear elliptic equations on those manifolds.
Estimates spectral risk measures from i.i.d. samples.
problem Estimating spectral risk measures from limited data.
method Numerical integration method for SRM estimation.
result Estimate concentrates exponentially for bounded support distributions.
Estimates spectral gap for sub-Laplacian on compact manifolds.
problem Bounding the spectral gap of sub-Laplacian on compact manifolds.
method Lichnerowicz estimate adaptation for sub-Laplacian on compact manifolds.
result A bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian.
Study spectral estimators for multi-index models to recover low-dimensional signal subspaces.
problem Recovering low-dimensional signal subspaces in multi-index models.
method Spectral estimators for multi-index models.
result Precise asymptotic characterization of spectral methods' performance, revealing a phase transition for weak recovery.
The study proves Strichartz and spectral projection theorems on specific types of curved surfaces.
problem Proving Strichartz and spectral projection theorems on curved surfaces.
method Using large negative curvature neighborhoods, the study proves theorems on asymptotically conic and Euclidean ends surfaces.
result The study proves theorems without loss of interval on specific types of curved surfaces.
Spectral methods improve parameter estimation in structured GLMs.
problem Parameter estimation in high-dimensional generalized linear models with structured data.
method Spectral methods using the principal eigenvector of a data-dependent matrix, with preprocessing for optimal performance.
result Precise asymptotic performance characterization and optimal preprocessing identified.
Bayesian framework integrates spectral deconvolution with expert reasoning for robust peak estimation.
problem Challenges in extracting meaningful peaks from noisy or complex spectra.
method Bayesian spectral deconvolution coupled with a physical-property regression layer.
result Recovery of weak peaks in poly(lactic acid) IR spectra related to degradation rates.
The paper extends spectral estimates to hyperbolic surfaces with hyperbolic ends.
problem Proving a necessary condition for observability of the heat semigroup on manifolds.
method Propagation of smallness estimates of Carleman and Logunov-Malinnikova type.
result Established spectral estimates for surfaces with hyperbolic ends, proving the thickness condition is necessary.
Bayesian model improves spectral estimation from partial, noisy data.
problem Challenges in spectral estimation with partial and noisy observations.
method Joint probabilistic model with Gaussian process prior and Bayes' rule for exact inference.
result Proposed model provides functional-form representation of power spectral density.
New linear spectral estimators improve phase retrieval accuracy.
problem Recovering vectors from magnitude measurements.
method Linear Spectral Estimators (LSPEs) for phase retrieval.
result LSPEs provide accurate initialization vectors and sharp error bounds.
Improved spectral projection estimates on manifolds of non-positive curvature.
problem Estimating spectral projections on manifolds with non-positive curvature.
method New spectral projection estimates, including sharp ones for tori, using pointwise estimates and microlocal L2oLqc Kakeya-Nikodym estimates. result Stronger and more precise spectral projection estimates, including new sharp estimates for tori.
Spectral risk measures are attractive risk measures as they allow the user to obtain risk measures that reflect their subjective risk-aversion. This paper examines spectral risk measures based on an exponential utility function, and finds that these risk measures have nice intuitive properties. It also discusses how th…
A new algorithm estimates spectral gap of Markov chains efficiently.
problem Estimating the spectral gap of a Markov chain efficiently.
method UCPI (Upper Confidence Power Iteration) algorithm
result Estimates spectral gap in O(n) time and O((lnn)2) memory. A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and der…
Sharp spectral gap estimates for higher-order operators on hyperbolic spaces.
problem Estimating spectral gaps for higher-order operators on Cartan-Hadamard manifolds.
method Symmetrization-free proofs based on general functional inequalities.
result Solves a sharp asymptotic problem from Cheng and Yang and answers a question from Kristály.
Paper proposes AMP with spectral initialization for robust signal estimation.
problem Signal estimation from generalized linear model measurements with correlated initialization.
method Approximate message passing (AMP) with spectral initialization.
result Characterization of AMP with spectral initialization in high-dimensional limit.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Spectral ranking methods are improved against semi-random graph sampling.
problem Improving spectral ranking methods in semi-random graph sampling.
method Investigating entry-wise error of spectral algorithms against a semi-random adversary.
result Asymptotic performance can be recovered by reweighting observed edges.
Self-distillation optimally improves model performance in spiked covariance models.
problem Improving model performance in spiked covariance models.
method Developed spectral shrinkage estimators and analyzed self-distillation.
result Self-distillation achieves optimal performance among spectral shrinkage estimators for spiked covariance matrices.
SCOPE estimator improves covariance and precision matrix estimation.
problem Estimating covariance and precision matrices accurately.
method Distributionally robust optimization with convex spectral divergence.
result SCOPE estimator reduces spectral bias and improves condition number.
Develops spectral estimators for network structure with nodal covariates.
problem Identifying observed and unobserved factors affecting network structure.
method Spectral estimators for unobserved blocks and covariates in stochastic blockmodels.
result Asymptotic normality of estimators and superior performance compared to existing methods.
Spectral feature learning improves IV regression for causal effect estimation.
problem Estimating causal effects in the presence of hidden confounders.
method Two-stage least squares estimator based on spectral features.
result Performance of the method depends on strong spectral alignment and slow eigenvalue decay.
Study geometric properties and spectral estimates on warped products.
problem Investigate Ricci curvature and spectral estimates in warped products.
method Establish integral inequalities and sufficient conditions for geometric properties.
result Sufficient conditions for intersection of warped products with totally geodesic hypersurfaces.
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
Estimates spectral gap for Brownian motion on sticky-reflecting domains.
problem Estimating spectral gap for Brownian motion on sticky-reflecting domains.
method Interpolation method and novel applications of Reilly formula.
result Lower bounds for spectral gap derived for general domains.
Spectral clustering for directed graphs using likelihood estimation.
problem Clustering directed graphs with edge directions.
method Maximum likelihood estimation on stochastic block models.
result Significant performance gains over existing methods.
Optimal spectral estimators and AMP combine for efficient weak recovery in orthogonally invariant GLMs.
problem Parameter estimation from generalized linear models with complex correlation structures.
method Spectral initialization and approximate message passing (AMP) algorithm.
result Established rigorous performance guarantees for spectral initialization and AMP.
Kernel estimator improves spectral risk measure estimation.
problem Estimating spectral risk measures accurately.
method Kernel-based estimation of L-statistics for SRMs.
result Kernel estimator is strongly consistent and asymptotically normal.
The paper proves optimal estimates and inequalities for spectral functions on certain manifolds.
problem Optimal estimates and inequalities for spectral functions on weakly 1-complete manifolds.
method Establishes optimal fundamental estimates and weak Morse inequalities for lower energy forms.
result Optimal fundamental estimates and weak Morse inequalities are proven for lower energy forms on weakly 1-complete manifolds.
Study connects spectral clustering to maximum margin and level set estimation.
problem Connecting spectral clustering to maximum margin and level set estimation.
method Obtained bounds on eigenvectors of graph Laplacian matrices in terms of cluster separation and connectivity. Showed sensitivity mitigation by removing outliers and estimating level sets.
result Spectral clustering converges to maximum margin clustering as scaling parameter approaches zero.
Study shows stability of Schrödinger operator spectral data on a manifold.
problem Determining a manifold and potential function from spectral data.
method Approximation of spectral data on a subset to determine manifold and potential.
result Quantitative stability estimate for Schrödinger operator inverse problem.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
Sharp spectral estimates for negatively curved foliations.
problem Estimating the bottom of the spectrum of Riemannian foliations.
method Analyzing the normal exponential map and using it to derive spectral estimates.
result Sharp estimates for the bottom of the spectrum of Riemannian foliations.
Bayesian parametric matrix models provide uncertainty quantification for spectral learning.
problem Uncertainty quantification in spectral learning for safety-critical applications.
method Bayesian parametric matrix models (B-PMMs) that extend PMMs to provide uncertainty estimates.
result B-PMMs achieve exceptional uncertainty calibration (ECE < 0.05) while maintaining favorable scaling.
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
problem Estimating parameters in Gaussian location model with regularization.
method Ridge-regularized log-density-ratio estimation, variational and spectral approaches.
result Regularized variational estimator has lower risk with many observations, spectral estimator with fewer observations.
This work uses neural density estimation to analyze laser-induced breakdown spectroscopy data, enabling accurate predictions and uncertainty quantification.
problem Inference of probability densities in high-dimensional spectral data is often intractable.
method Normalizing flows on structured spectral latent spaces for density estimation and uncertainty quantification.
result The approach enables generation of realistic spectral samples and accurate prediction of state vectors with well-calibrated uncertainties.