Paper proposes a forecasting model combining autoregressive models with spectral attention.
problem Time series forecasting across various domains.
method Combines deep autoregressive models with Spectral Attention (SA) module.
result SAAM consistently demonstrates improved forecasting accuracy compared to state-of-the-art approaches.
Spectral deconfounding improves machine learning models by reducing hidden confounding effects.
problem Machine learning models can be misled by hidden confounders, leading to unreliable predictions.
method Develops a nonlinear spectral deconfounding framework for gradient boosting that modifies boosting dynamics to slow down in confounding-aligned directions.
result Spectrally deconfounded boosting improves estimation of the target function under hidden confounding and is more scalable.
Random hyperbolic surfaces have nearly optimal spectral gaps.
problem Proving the nearly optimal spectral gap conjecture for random Belyi surfaces.
method Using the Brooks-Makover model, the authors show a spectral gap greater than 1/4 - c/log(n).
result A random hyperbolic surface in the Brooks-Makover model has a spectral gap greater than 1/4 - c/log(n).
New method extrapolates spectral densities from smaller models to larger ones.
problem Limited practical computations for large machine learning models.
method Algebraic spectral curve theory for free decompression.
result Framework enables extrapolation of spectral densities with multiple or multi-modal bulks.
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.
Nonparametric models are versatile, albeit computationally expensive, tool for modeling mixture models. In this paper, we introduce spectral methods for the two most popular nonparametric models: the Indian Buffet Process (IBP) and the Hierarchical Dirichlet Process (HDP). We show that using spectral methods for the in…
Optimal spectral method found for inhomogeneous spiked Wigner model.
problem Structured noise in learning scenarios.
method Random matrix theory and spectral analysis.
result Optimal threshold for phase transition in block-structured Wigner model.
A Python package solves source duplication in single channel LVMs using spectral regularisation.
problem Source duplication in LVMs hampers their practical use in single channel applications.
method Spectral regularisation term added to address source duplication issue.
result Spectral regularisation framework enables easier investigation and utilisation of LVMs.
Supervised topic models simultaneously model the latent topic structure of large collections of documents and a response variable associated with each document. Existing inference methods are based on variational approximation or Monte Carlo sampling, which often suffers from the local minimum defect. Spectral methods …
Dual regularized graph Laplacian improves spectral clustering for community detection.
problem Detecting clusters in networks with improved spectral clustering methods.
method Proposes dual regularized graph Laplacian for three spectral clustering approaches.
result Theoretical analysis shows DRSC and DRSLIM yield stable consistent community detection.
Spectral regularization simplifies sequence models by focusing on grammatical simplicity.
problem Sequence modeling challenges in learning tasks.
method Introduces spectral regularization based on Hankel matrices and trace norm, addressing bi-infinite matrices with an unbiased estimator.
result Demonstrates spectral regularization's potential benefits on Tomita grammars.
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.
Spectral clustering identifies clusters of multivariate extremes.
problem Analyzing the dependence structure of multivariate extremes.
method Spectral clustering based on a random k-nearest neighbor graph. result Spectral clustering can consistently identify clusters of multivariate extremes under certain conditions.
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.
Spectral clustering achieves strong consistency in the stochastic block model under certain conditions.
problem Achieving strong consistency in spectral clustering for the stochastic block model.
method Entrywise analysis of the Fielder eigenvector of graph Laplacians.
result Spectral clustering achieves exact recovery of hidden communities under matching information-theoretic limits.
New spectral clustering method for multi-layer networks improves accuracy.
problem Detecting community structure in multi-layer networks.
method Integrative spectral clustering based on adaptive layer aggregation.
result Our methods minimize mis-clustering error and outperform existing methods.
New spectral clustering method using LASSO regularization for robust graph partitioning.
problem Lack of theoretical guarantees for spectral clustering on general graph models.
method 1-spectral clustering on a new random model with LASSO regularization.
result Effective and robust to small noise perturbations, validated by simulations and real data.
Introduces Spectral Graph Network combining spatial and spectral message passing.
problem Relational reasoning in graph structured data.
method Applies message passing to both spatial and spectral domains of a graph.
result Promotes efficient training with fewer iterations and robustness to edge dropout.
Introduces Spectral Attention for better long-range time series forecasting.
problem Challenges in capturing long-range dependencies in time series forecasting.
method Spectral Attention mechanism that preserves temporal correlations and long-range dependencies.
result Achieves state-of-the-art results on 11 real-world time series datasets.
We analyze the performance of spectral clustering for community extraction in stochastic block models. We show that, under mild conditions, spectral clustering applied to the adjacency matrix of the network can consistently recover hidden communities even when the order of the maximum expected degree is as small as $\l…
We analyze DMs using spectral methods to design effective noise schedules.
problem Lack of theoretical foundation for synthesis process decisions in DMs.
method Introduced a frequency response perspective based on Gaussianity assumption.
result Proposed a spectral transfer function to understand DM inference process.
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.
Spectral flow connects manifold geometry to rigidity criteria.
problem Tackling rigidity of simply-connected closed manifolds.
method Spectral deformation flow and invariant-based approach.
result Spherical profile is the unique manifold-compatible asymptotic realization.
Graph signal processing detects hallucinations in large language models.
problem Detecting factual reasoning from hallucinations in large language models.
method Modeling transformer layers as dynamic graphs, using spectral analysis to define diagnostics.
result Spectral signatures can distinguish different types of hallucinations and achieve high accuracy.
Spectral clustering is robust to helpful model changes but not to random changes.
problem Robustness of spectral clustering in the presence of semirandom adversaries.
method Analysis of spectral clustering algorithms under semirandom adversaries.
result Spectral clustering with unnormalized Laplacian is strongly consistent under semirandom adversaries.
In the past decades, spectral clustering (SC) has become one of the most effective clustering algorithms. However, most previous studies focus on spectral clustering tasks with a fixed task set, which cannot incorporate with a new spectral clustering task without accessing to previously learned tasks. In this paper, we…
We consider spectral clustering algorithms for community detection under a general bipartite stochastic block model (SBM). A modern spectral clustering algorithm consists of three steps: (1) regularization of an appropriate adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a k-means type algorithm…
The paper bridges spectral and spatial graph convolutions, improving model capacity and transferability.
problem Improving graph neural networks by bridging spectral and spatial design.
method Theoretical demonstration and general framework for spectral analysis, new spectral convolutions, and depthwise separable convolutions.
result General framework allows spectral analysis of ConvGNNs, showing their performance and limits, and proposing new spectral convolutions.
New kernel models multi-output Gaussian processes accurately.
problem Challenges in modelling cross-covariances for multiple-output Gaussian processes.
method Replaced Gaussian components with block components of finite bandwidth in spectral mixture kernel.
result First multi-output generalization of spectral mixture kernel that can approximate any stationary multi-output kernel to arbitrary precision.
Spectral clustering has been one of the widely used methods for community detection in networks. However, large-scale networks bring computational challenges to the eigenvalue decomposition therein. In this paper, we study the spectral clustering using randomized sketching algorithms from a statistical perspective, whe…
New argument suggests torsion cannot be part of gravity models.
problem The presence of torsion in gravity models is debated.
method Used spectral geometry and pseudo-differential calculus.
result No well-defined functional for torsion in spectral formulation.
Spectral sparsification improves Gaussian graphical models under MTP2 constraints.
problem Learning accurate, sparse graphs from data under MTP2 constraints.
method Spectral graph sparsification applied to Gaussian graphical models.
result Spectral-MTP2 preserves MTP2 and approximates the original model well.
Enhanced spectral clustering for geometric graphs improves clustering accuracy.
problem Ineffective standard spectral clustering for geometric graphs.
method Higher-order spectral clustering using higher-order eigenvectors.
result Established weak and strong consistency for Soft Geometric Block Model.
New methods avoid spectral pollution in transfer operators for accurate analysis.
problem Spectral pollution in finite-dimensional approximations of transfer operators.
method Algorithms for computing spectral properties of transfer operators without spectral pollution.
result Accurate spectral estimation across various applications, including protein folding models.
Spectral clustering with edge counting detects communities in sparse models.
problem Detecting communities in sparse latent space models.
method Spectral clustering followed by edge counting.
result Algorithm achieves consistency and optimality for a broad class of models.
Graph classification improved using spectral features and wavelet filters.
problem Categorizing graphs based on their structure and node attributes.
method Derived spectral features from graph signal processing, designed two Gaussian process models: one simple and one sophisticated.
result Simple and sophisticated Gaussian process models yield competitive performance, including well-calibrated uncertainty estimates.
Quantum computers can enhance spectral methods in machine learning.
problem Spectral methods are fundamental but challenging for classical models.
method Utilizing quantum Fourier Transform for spectral manipulations.
result Quantum computing can offer more efficient spectral design.
New spectral clustering method for graphs with uneven node degrees.
problem Challenges in community detection for graphs with heterogeneous degree distributions.
method Spectral clustering on spherical coordinates with degree correction.
result Improved performance in representing computer networks.
New algorithms improve spectral clustering for finite mixture models.
problem Issues with EM algorithm in spectral clustering.
method Spectral decomposition and non-parametric bootstrap sampling.
result Improved convergence and avoidance of poor solutions.
Novel model captures high-dimensional copulas with spectral dynamics and regularization.
problem Modeling time-varying, asymmetric, tail-dependent copulas in high dimensions.
method Score-driven dynamics for eigenvalues, non-linear shrinkage for biases, parsimonious and scalable.
result Model outperforms recent alternatives in capturing co-movements and diversification potential.
Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-bas…
Model structures on multicomplexes help study complex geometry.
problem Understanding homotopy types of complex manifolds.
method Model category structures on N-multicomplexes with weak equivalences induced by quasi-isomorphisms. result Establishes a basis for studying almost and generalized complex manifolds.
The paper constructs noncompact hyperbolic surfaces with uniform spectral gaps using random graph models.
problem Building noncompact hyperbolic surfaces with uniform spectral gaps.
method Introduced a random graph model Fχ,n to construct expanding families of graphs, then applied these families to create hyperbolic surfaces. result Explicitly constructed an expanding family of graphs in the critical regime, leading to a sequence of complete, noncompact hyperbolic surfaces with uniformly positive spectral gaps.
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.
Developed a diffusion model on spherical data, addressing geometric and stochastic challenges.
problem Diffusion models on spherical data face unique geometric and stochastic issues.
method Extended spectral diffusion to spherical harmonics, introducing modified stochastic differential equations.
result Introduced a geometry-dependent inductive bias in spectral diffusion models.
Essential principal components simplify spectral analysis with minimal training data.
problem Accurate spectral quantification from complex mixtures.
method Identifying essential principal components and using molar extinction coefficients.
result Near one-to-one projection from principal components to mixture constituents.
Proposes a Gaussian process for graph signals using adaptive spectral kernels.
problem Predicting signals on graph nodes with various structures.
method Spectral kernel learning approach that incorporates a polynomial function in the graph spectral domain.
result The model accurately recovers ground truth spectral filters and outperforms in real-world graph data.
Paper proposes a new method for sparse spectral clustering on Stiefel manifold.
problem Sparse spectral clustering on Stiefel manifold with nonsmooth and nonconvex objective.
method Proposes a manifold proximal linear method (ManPL) to solve the original SSC formulation.
result Demonstrates the advantage of ManPL over existing methods on single-cell RNA sequencing data.