Improves learning of spectral mixture kernels with approximate Bayesian inference.
problem Difficult optimization of large number of SM kernel parameters.
method Approximate Bayesian inference using variational distribution of spectral points and random Fourier features.
result Accelerates convergence and leads to better optimal parameters.
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.
New method combines spectral and sparse methods for Gaussian processes.
problem Efficiently fitting Gaussian processes to large datasets.
method Orthogonally decoupled variational Fourier features.
result Competitive performance on synthetic and real-world data.
Study on spectral stability of an embedded annulus under curve shortening and Ricci flows.
problem Spectral stability of Dirichlet eigenvalues on an evolving annulus.
method Variational formulas, Rellich-type identities, and harmonic capacity methods.
result Established quantitative bounds comparing the spectrum of the evolving annulus with a flat cylinder.
This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to edges based on the distance between the points they connect. We investigate the…
This work combines sparse approximation and spectral representations for Gaussian processes.
problem Efficiently approximating Gaussian processes with high-dimensional data.
method Integrates variational approach with spectral representations for sparse Gaussian processes.
result Derives spectral features with almost-independent covariances for Matern kernels.
The C-spectral sequence was introduced by Vinogradov in the late Seventies as a fundamental tool for the study of algebro-geometric properties of jet spaces and differential equations. A spectral sequence arise from the contact filtration of the modules of forms on jet spaces of a fibring (or on a differential equation…
Improved model for non-smooth signals with complex spectra.
problem Current models struggle with non-smooth signals and complex spectral structures.
method CGPCM and RGPCM models with causality and Bayesian nonparametric interpretations, improved variational inference.
result Proposed models show better performance on synthetic and real-world data.
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.
Spectral clustering is a fast and popular algorithm for finding clusters in networks. Recently, Chaudhuri et al. (2012) and Amini et al.(2012) proposed inspired variations on the algorithm that artificially inflate the node degrees for improved statistical performance. The current paper extends the previous statistical…
Harmonic gauge simplifies geometric analysis of Riemannian metrics.
problem Analyzing the Hilbert-Einstein functional and its stability.
method Developed a harmonic gauge to eliminate divergence terms and induce elliptic structure.
result Positivity of curvature operator implies spectral stability of the functional.
fBNNs use stochastic processes for variational inference in neural networks.
problem Difficulties in specifying priors and posteriors in high-dimensional weight spaces.
method Maximize Evidence Lower Bound (ELBO) on stochastic processes, using spectral Stein gradient estimator.
result fBNNs provide reliable uncertainty estimates and extrapolate well with structured priors.
New spectral clustering method improves community detection in sparse networks.
problem Community detection in sparse networks using spectral clustering.
method Data-driven regularization and novel spectral truncation for adjacency matrix.
result Consistency results for community detection in general SBM and beyond.
Paper generalizes spectral flow formulas for compact Lie group actions.
problem Generalizing spectral flow formulas for compact Lie group actions.
method Equivariant version of Dai-Zhang higher spectral flow, embedding formula, adiabatic limit formula for Atiyah-Patodi-Singer eta invariants.
result Generalization of eta forms to equivariant Bismut-Cheeger eta forms.
Flexible SC framework converts voices from non-aligned corpora.
problem Limited practical applications of SC due to lack of parallel corpora.
method Variational auto-encoder framework for non-parallel corpora.
result Framework enables spectral conversion without parallel corpora or alignments.
Spectral Inference Networks learn eigenfunctions from data using optimization.
problem Learning eigenfunctions of linear operators from data.
method Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators and use stochastic optimization.
result Spectral Inference Networks accurately recover eigenfunctions and discover interpretable representations from video data.
New concept of sparse regular variation for better understanding of extreme events.
problem Characterizing the dependence structure of extreme events in multivariate settings.
method Introducing sparse regular variation based on Euclidean projection onto the simplex.
result Sparse regular variation and regular variation are equivalent under mild assumptions.
Proofs for spectral and geometric properties of hyperbolic surfaces.
problem Spectral and geometric properties of hyperbolic surfaces.
method Streamlined proofs for isospectral and quasi-Fuchsian groups.
result Generically, isospectral hyperbolic surfaces are isometric.
Novel CSK kernel improves GP model generalization for non-stationary patterns.
problem Improving generalization of Gaussian process models for non-stationary data.
method Introduced convolutional spectral kernel (CSK) derived from convolution of imaginary radial basis functions, using Fourier transform for interpretation.
result CSK improves GP model generalization on spatiotemporal datasets.
In this paper we study equivariant constrained Willmore tori in the 3-sphere. These tori admit a 1-parameter group of Möbius symmetries and are critical points of the Willmore energy under conformal variations. We show that the associated spectral curve of an equivariant torus is given by a double covering of $\mathbb …
Estimates Markov chain mixing time from a single trajectory.
problem Estimating mixing time of Markov chains from a single trajectory.
method Contraction with respect to total variation, inspired by Wolfer's contraction coefficient.
result Improved confidence intervals and instance-dependent rates for estimating Markov chains.
Spectral sequence connects link homology to branched covers, revealing differences and new theories.
problem Difficult computation of Ozsváth-Szabó spectral sequence.
method Built a simpler isomorphic spectral sequence with a filtered complex of minimal complexity.
result Discovered a new variation of Szabó's theory for links in a thickened annulus.
Study the spectral flow of Dirac operators on spinor bundles.
problem Understanding the asymptotic behavior of spectral flow for Dirac operators.
method Variation of eta invariant and local index theory technique.
result Established a uniform estimate of the eta invariant for large parameter values.
NeuralFLoC unifies registration and clustering of functional data, overcoming phase variation challenges.
problem Challenges in clustering functional data due to phase variation and temporal misalignment.
method NeuralFLoC uses Neural ODE-driven diffeomorphic flows and spectral clustering for joint registration and clustering.
result NeuralFLoC effectively disentangles phase and amplitude variation, achieving state-of-the-art performance.
SRF improves kernel approximation and GP regression performance.
problem Efficient kernel approximation and Bayesian kernel learning in large-scale regression problems.
method Stein variational gradient descent to generate high-quality random features and approximate spectral measure posteriors.
result SRF outperforms traditional approaches in kernel approximation and GP regression.
Neural non-stationary spectral kernels improve performance on benchmark datasets.
problem Learning and discovering complex patterns in data.
method Generalized spectral mixture kernels with input-dependent functions modeled as Gaussian processes and hyperparameter functions as neural networks.
result Neural non-stationary spectral kernels achieve the best performance on benchmark datasets.
Proposes a variational framework for fair clustering.
problem Ensuring fairness in clustering algorithms.
method Integrates fairness term with clustering objectives, using variational approach.
result Derives tight upper bound for optimization, enabling scalable solution.
Study shows how the spectra of negatively curved surfaces vary under certain conditions.
problem Understanding how the Laplace spectra of compact surfaces vary under specific conditions.
method Used time real analyticity of Ricci flow to extend a result from \cite{B} and provide a quantitative estimate of spectral variation.
result Laplace spectra of negatively curved compact surfaces with same genus, area, and curvature bounds vary in a controlled way.
Network Lasso clusters sparse graph clusters efficiently.
problem Local graph clustering of sparse and chain-like clusters.
method Network Lasso minimizes total variation of cluster indicator signals.
result Network Lasso handles sparse clusters difficult for spectral clustering.
This paper applies an AR(1)-GARCH (1, 1) process to detail the conditional distributions of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses the conditional distribution for these contracts to estimate spectral risk measures, which are coherent risk measures …
Researchers prove spectral rigidity of Liouville tori under specific conditions.
problem Spectral rigidity of Liouville tori under generic conformal classes.
method Noncancellation of wave trace and analysis of second order variational formula for energy.
result Laplace isospectral deformations of Liouville metrics on torus are trivial.
Study variation spaces for neural networks, linking them to approximation theory.
problem Understanding the variation spaces of shallow neural networks.
method Examined variation spaces defined by convex hulls and integral representations for a dictionary of functions.
result Found that Barron space, spectral Barron space, and Radon BV space are variation spaces for certain neural networks.
Summary of a talk given at the International Seminar "Analysis of spectral invariants and related operator theory", Tokyo University of Science, Unga Campus, 5-6 Oct. 2009
Proves spectral gap bounds for Teichmüller geodesics on flat surfaces.
problem Quantify spectral gaps for Teichmüller geodesics.
method Bounding spectral gaps in terms of geometric quantities on flat surfaces.
result Quantitative non-uniform hyperbolicity of Teichmüller geodesic flow.
This paper analyzes AJIVE for estimating shared subspace across multiple datasets, revealing its strengths and limitations.
problem Estimating shared subspace across multiple datasets with varying degrees of misalignment.
method Angle-based Joint and Individual Variation Explained (AJIVE) method, a two-stage spectral approach.
result AJIVE's performance in high signal-to-noise ratio (SNR) regimes and its non-diminishing error in low-SNR settings.
A 3-stage method enhances hyperspectral image classification accuracy.
problem Classifying detailed classes in hyperspectral images with limited labeled data.
method Uses Nested Sliding Window and PCA for spatial consistency, SVM for spectral estimation, and TV model for spatial smoothing.
result Our method outperforms state-of-the-art algorithms, especially in scenarios with small training sets.
Interpretable neural network for plant traits and species identification.
problem Plant phenotyping and identification.
method Neural network trained on UPWINS spectral library, with visualization of weights for trait-based spectral features.
result 90% accuracy in species identification with interpretable neural network.
New theorem improves spectral gap for sampling from mixture distributions.
problem Sampling from multimodal distributions with simulated tempering.
method Introduced a decomposition theorem for the restricted spectral gap of simulated tempering.
result Lower bound on the restricted spectral gap for mixture distributions.
Understanding the adaptation process of plants to drought stress is essential in improving management practices, breeding strategies as well as engineering viable crops for a sustainable agriculture in the coming decades. Hyper-spectral imaging provides a particularly promising approach to gain such understanding since…
We encode the variation structure of a quasihomogeneous polynomial with an isolated singularity as introduced by Nemethi in a set of spectral flows of the signature operator on the Milnor bundle by varying global elliptic boundary conditions in a specific way using the quasihomogeneous circle action on the Brieskorn la…
ISVAE enhances interpretability in time series clustering using a novel filter bank.
problem Improving interpretability in time series clustering models.
method Integrates a Filter Bank (FB) into a Variational Autoencoder (VAE) to enhance interpretability and clusterability.
result ISVAE produces a more interpretable and separable encoding with enhanced clusterability.
Spectral methods improve supervised topic modeling efficiency and accuracy.
problem Learning parameters of supervised topic models with spectral methods.
method Two-stage spectral method and single-phase spectral algorithm.
result Spectral algorithms recover both topic distribution and regression weights with provable guarantees.
Domains in infinite jets present the simplest class of diffieties with boundary. In this note some basic elements of geometry of these domains are introduced and an analogue of the C-spectral sequence in this context is studied. This, in particular, allows cohomological interpretation and analysis of initial data, boun…
Calculates spectral flow bounds for reducible solutions to Vafa-Witten equations.
problem Bounding spectral flow between diverging reducible solutions.
method Localization and excision techniques to calculate spectral flow.
result Bounds on spectral flow are given for reducible solutions.
Bayesian method estimates line frequencies with uncertainty.
problem Bayesian estimation of continuous frequencies.
method Variational Bayesian inference with von Mises mixtures.
result Significantly improved performance over point estimates.
Paper improves GP models for big data with a Bayesian approach.
problem Scaling up sparse Gaussian process models for big data.
method Bayesian treatment of spectral frequencies, joint modeling, local data boosting, variational parameterization trick, stochastic optimization.
result sVBSSGP outperforms state-of-the-art models on real-world datasets.
The paper calculates spectral determinants for two complex surfaces.
problem Calculating spectral determinants for complex surfaces.
method Closed explicit formulas, multiplicative relations, Belyi maps, and constant-curvature spheres.
result Spectral determinants of the Bolza surface and Klein quartic are calculated.
A proof of the Willmore conjecture is presented. With the help of the global Weierstrass representation the variational problem of the Willmore functional is transformed into a constrained variational problem on the moduli space of all spectral curves corresponding to periodic solutions of the Davey-Stewartson equation…