Optimizes two-sample tests for non-Euclidean domains using spectral regularization.
problem Optimizing two-sample tests for non-Euclidean domains.
method Spectral regularization of MMD test to achieve minimax optimality.
result Proposes a spectral regularization method that improves test optimality.
Improved MMD test for non-Euclidean data with spectral regularization.
problem Inefficient and impractical MMD goodness-of-fit tests for non-Euclidean data.
method Spectral regularization of MMD test, extending results to general cases.
result Minimax optimal test for non-Euclidean data with appropriate regularization.
We study a class of backtests for forecast distributions in which the test statistic depends on a spectral transformation that weights exceedance events by a function of the modeled probability level. The weighting scheme is specified by a kernel measure which makes explicit the user's priorities for model performance.…
New framework detects directional influence in multivariate time series.
problem Detecting directional influence in multivariate time series.
method Order-constrained spectral non-invariance.
result Unique diagnostic functional for directional influence.
Spectral algorithms improve under covariate shift with novel weighted techniques.
problem Improving spectral algorithms' performance under covariate shift.
method Analysis of spectral algorithms in non-parametric regression over RKHS, proposing a weighted spectral algorithm with clipped weights.
result Normalized weighted spectral algorithm achieves optimal capacity-independent convergence rates, and clipped weights can approach optimal capacity-dependent rates.
New method tests conditional independence using spectral representations.
problem Untestable conditional independence in many settings.
method Spectral representations of partial covariance operators, bi-level contrastive learning.
result Asymptotic validity and power guarantees for CI testing.
We consider the change-point detection problem of deciding, based on noisy measurements, whether an unknown signal over a given graph is constant or is instead piecewise constant over two connected induced subgraphs of relatively low cut size. We analyze the corresponding generalized likelihood ratio (GLR) statistics a…
A new kernel test reduces noise in MMD by focusing on leading eigen-directions.
problem Noise in trailing directional components degrades power of standard kernel two-sample tests.
method Truncate MMD spectral decomposition, retaining only leading eigen-directions.
result Our method achieves superior power and robustness, especially in high-dimensional and unbalanced settings.
Geodesic rays and chordal distances link algebraic and geometric properties of positive metrics.
problem Understanding the geometry of the space of positive metrics at infinity.
method Using Monge-Ampère equations and test configurations, algebraic descriptions of geodesic rays and chordal distances are derived.
result The Mabuchi chordal distance between geodesic rays associated with ample test configurations equals the spectral distance between their filtrations.
One of the challenges in the study of generative adversarial networks is the instability of its training. In this paper, we propose a novel weight normalization technique called spectral normalization to stabilize the training of the discriminator. Our new normalization technique is computationally light and easy to in…
We apply the integral formula of volumes to the family of graded linear series constructed from any test configuration. This solves the conjecture raised by Witt--Nyström so that the sequence of spectral measures for the induced C∗-action on the central fiber converges to the canonical Duistermatt--Heckman …
We consider the weak detection problem in a rank-one spiked Wigner data matrix where the signal-to-noise ratio is small so that reliable detection is impossible. We propose a hypothesis test on the presence of the signal by utilizing the linear spectral statistics of the data matrix. The test is data-driven and does no…
S-GAI initializes MLPs using spectral geometry from data, improving performance.
problem Lack of guidance on initial weights encoding data geometry.
method S-GAI uses SVD to estimate spectral class geometry, initializing MLPs from training data.
result S-GAI-initialized MLPs start from a more informative hidden state and achieve comparable accuracy.
Simple technique turns any adversarial attack into a universal one using few test examples.
problem Creating universal adversarial attacks with minimal data.
method Universalization technique using few adversarial test examples and spectral properties.
result Simple universalization technique achieves comparable fooling rates to state-of-the-art methods.
Efficient tests achieve best error rates in high-dimensional hypothesis testing.
problem Achieving optimal error rates in computationally efficient hypothesis testing.
method Linear spectral statistics and low-degree likelihood ratio analysis.
result An efficient test achieves the best possible error rates among all computationally efficient tests.
Tests if vertices in graphs have the same latent positions.
problem Testing equality of latent positions in random graphs.
method Empirical Mahalanobis distances from spectral embeddings.
result Test statistics follow chi-square distributions under null and local alternatives.
Graph embedding method captures both local and global network structure.
problem Representing and analyzing complex graph networks.
method Spectral embedding based on a generalized graph Laplacian.
result Significant improvement in data analysis tasks.
The paper improves spectral ranking methods for diverse comparison graphs.
problem Estimating preference scores from multiway comparisons with heterogeneous sizes.
method Develops a two-step spectral method for estimating preference scores and their uncertainties.
result The two-step spectral method achieves the same asymptotic efficiency as the Maximum Likelihood Estimator (MLE).
Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data
problem Improving prediction intervals for non-exchangeable time-indexed datasets
method Spectral adaptive conformal prediction
result Improves on fixed spectral weighting while monitoring uncertainty changes
Study tackles distribution shift in combinatorial settings using matrix completion techniques.
problem Tackling distribution shift in combinatorial settings with rigorous statistical guarantees.
method Develops novel algorithms and theoretical results for extrapolating to test distributions not covered in training.
result Achieves bilinear combinatorial extrapolation under gradual spectral decay in high-dimensional data.
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.
New method shows spectral clustering is consistent with theoretical guarantees.
problem Lack of theoretical support for anchor-based spectral clustering.
method Defined and analyzed a specific anchor-based algorithm.
result Theoretical consistency of the method in asymptotic settings.
Galerkin method outperforms graph-based methods in spectral decompositions.
problem Improving spectral decomposition methods in machine learning.
method Restricting study to a small set of test functions using the Galerkin method.
result Statistical and computational superiority of Galerkin method over graph-based approaches.
Paper develops a minimax optimal test for goodness-of-fit using kernel Stein discrepancy.
problem Developing a robust goodness-of-fit test for general domains.
method Kernel Stein Discrepancy (KSD) with spectral regularization and adaptive testing.
result Proposed regularized test achieves minimax optimality up to a logarithmic factor.
A new method simulates a lazy version of a Markov chain for empirical inference.
problem Estimating and testing unknown Markov chains with limited data.
method Simulates an α-lazy version of an unknown Markov chain, making it ergodic.
result The pseudo spectral gap can be applied to non-ergodic Markov chains.
In this work a robust clustering algorithm for stationary time series is proposed. The algorithm is based on the use of estimated spectral densities, which are considered as functional data, as the basic characteristic of stationary time series for clustering purposes. A robust algorithm for functional data is then app…
Deep neural networks can generalize by reducing high-frequency noise over time, not always following a monotonic learning bias.
problem Understanding the learning dynamics and generalization of over-parameterized DNNs.
method Experimental analysis of deep double descent, focusing on the spectral bias of DNNs.
result The high-frequency components of DNNs diminish over training, leading to a second descent in test error.
Deep networks learn clean structure before memorizing corrupted labels, leaving a spectral signature in gradient centered scatter.
problem Deep networks' transition from learning clean structure to memorizing corrupted labels under label noise.
method Analysis of the centered scatter of per-example last-layer gradients to identify Fisher Rank Inflation.
result Fisher Rank Inflation is a spectral signature of memorization under label noise, with effective rank expanding during memorization.
Improved SSD for faster and more accurate goodness-of-fit tests and model learning.
problem Optimal slicing directions for SSD are computationally expensive and sub-optimal.
method Relaxed optimal slicing requirement, active sub-space construction, spectral decomposition.
result 14-80x speed-up in goodness-of-fit tests compared to gradient-based alternatives.
IGT learns graph representations without supervision.
problem Building deep unsupervised graph representations.
method Generic complex-valued spectral graph architecture from Fourier transform generalization, greedy concave objective for discriminative and invariant features.
result IGT learns both discriminative and invariant features from graph topology.
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
The study reveals the spectral structure of attention layers and its implications for generalization.
problem Understanding the spectral structure and generalization of trained attention layers.
method Empirical risk minimization in a single-head tied-attention layer, using random matrix theory, spin-glass theory, and approximate message passing.
result Exact high-dimensional characterization of training and test error, interpolation and recovery thresholds, and spectrum of the key and query matrices.
For random graphs distributed according to stochastic blockmodels, a special case of latent position graphs, adjacency spectral embedding followed by appropriate vertex classification is asymptotically Bayes optimal; but this approach requires knowledge of and critically depends on the model dimension. In this paper, w…
The scale and complexity of modern data sets and the limitations associated with testing large numbers of hypotheses underline the need for feature selection methods. Spectral techniques rank features according to their degree of consistency with an underlying metric structure, but their current graph-based formulation…
CAST improves spectral clustering for multi-scale data by integrating reachability similarity.
problem Applying spectral clustering to multi-scale data where clusters vary in size and density.
method CAST integrates reachability similarity with distance-based similarity to derive a coefficient matrix, then applies trace Lasso regularization.
result CAST provides excellent performance and robustness across various multi-scale data test cases.
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to possess various desirable properties along with a characteristic exploratory fl…
Developed a framework for designing filters in spectral GCNNs with improved performance.
problem Designing effective filters for spectral GCNNs with regularization properties.
method Exploring regularization properties of graph Laplacian and proposing a generalized framework for filter design.
result New filters derived from the framework outperform state-of-the-art techniques in semi-supervised node classification.
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
SML improves pancreatic mass diagnosis accuracy using CT images.
problem Improving accuracy in pancreatic mass screening using CT imaging.
method Spectral machine learning method trained on 30,000 images, choosing fundamental images based on eigenvectors and removing irrelevant pixels.
result Achieved 94.6% test accuracy in diagnosing 113 patients.
Bayesian method estimates Kronecker graphical models from autoregressive processes.
problem Estimating Kronecker graphical models from autoregressive Gaussian processes.
method Bayesian approach to estimate Kronecker graphical models.
result Effectiveness demonstrated through numerical experiments and real-world data application.
We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is…
In this paper, we propose a new measure to gauge the complexity of image classification problems. Given an annotated image dataset, our method computes a complexity measure called the cumulative spectral gradient (CSG) which strongly correlates with the test accuracy of convolutional neural networks (CNN). The CSG meas…
Randomized spectral co-clustering speeds up large-scale directed networks.
problem Co-clustering directed networks efficiently for large-scale data.
method Randomized spectral co-clustering algorithms using random-projection and random-sampling techniques.
result Theoretical and numerical validation of approximation and misclustering error rates.
EGO-MDA identifies optimal spectral-bands for process discrimination.
problem Optimal spectral-bands for process discrimination.
method EGO-MDA, an unsupervised method using EGO and Mixture Discriminant Analysis.
result EGO-MDA achieves at least 70% improvement in median deviance.
In this chapter we review the main literature related to kernel spectral clustering (KSC), an approach to clustering cast within a kernel-based optimization setting. KSC represents a least-squares support vector machine based formulation of spectral clustering described by a weighted kernel PCA objective. Just as in th…
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem is to identify promising (explicit) features leading to a satisfactory out-of-sam…
The random dot product graph (RDPG) is an independent-edge random graph that is analytically tractable and, simultaneously, either encompasses or can successfully approximate a wide range of random graphs, from relatively simple stochastic block models to complex latent position graphs. In this survey paper, we describ…
DynMSA detects market clusters for better portfolio allocation.
problem Identifying stable market clusters for effective portfolio management.
method Combining Random Matrix Theory with modularity optimization and spectral clustering.
result DynMSA outperforms baseline models in intra- and inter-cluster correlation differences.