arXiv research

Study uses spectral risk for learning with heavy-tailed data.

Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation …

Study spectral properties of graph Laplacian for manifold data.

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.

Inference for the stochastic blockmodel is currently of burgeoning interest in the statistical community, as well as in various application domains as diverse as social networks, citation networks, brain connectivity networks (connectomics), etc. Recent theoretical developments have shown that spectral embedding of gra…

The aim of this work is to build financial crisis indicators based on spectral properties of the dynamics of market data. After choosing an optimal size for a rolling window, the historical market data in this window is seen every trading day as a random matrix from which a covariance and a correlation matrix are obtai…

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular he…

In this dissertation we propose alternative analysis of distributed stochastic gradient descent (SGD) algorithms that rely on spectral properties of the data covariance. As a consequence we can relate questions pertaining to speedups and convergence rates for distributed SGD to the data distribution instead of the regu…

The paper studies Hodge Laplacians from point clouds, proving spectral convergence and harmonic form consistency.

This paper refines understanding of decentralized learning by considering graph topology.

Improved spectral gap for MwG with adaptive RWM proposals.

A new framework tightens risk measure confidence bounds.

Study extends bounds on sample covariance matrices with general dependence.

New empirical PAC-Bayes bound for Markov chains with finite state space.

New matrix ensembles better match deep neural network spectral densities.

Spectral regularization improves learning over combinatorial spaces with limited data.

Study local geometry of mixture models via spectral theory, revealing transitions in training dynamics.

Paper connects neural networks to Gaussian processes for understanding double-descent.

The study reveals the spectral structure of attention layers and its implications for generalization.

Study reveals an equivalence principle for the spectrum of random inner-product kernel matrices in polynomial scaling.

Deep convolutional neural networks (CNNs) have been shown to be able to fit a random labeling over data while still being able to generalize well for normal labels. Describing CNN capacity through a posteriori measures of complexity has been recently proposed to tackle this apparent paradox. These complexity measures a…

This work analyzes how different layers in deep neural networks contribute to generalization error.

A new method for risk-sensitive reinforcement learning using Spectral Risk Measures.

Study spectral distribution of twisted Laplacian on high genus hyperbolic surfaces.

Study shows deterministic equivalent for neural network kernel convergence.

New spectral mixture representation for isotropic kernels simplifies random Fourier features.

SCOPE estimator improves covariance and precision matrix estimation.

New model for detecting communities in weighted bipartite networks.

We propose a novel approach for pixel classification in hyperspectral images, leveraging on both the spatial and spectral information in the data. The introduced method relies on a recently proposed framework for learning on distributions -- by representing them with mean elements in reproducing kernel Hilbert spaces (…

In this paper, we continue our previous work on the Dirichlet mixture model (DMM)-based VQ to derive the performance bound of the LSF VQ. The LSF parameters are transformed into the $Δ$LSF domain and the underlying distribution of the $Δ$LSF parameters are modelled by a DMM with finite number of mixture components. The…

New method estimates large matrices' spectra from small sub-matrices.

Spectral denoising recovers meaningful network structure from noisy financial correlations.

Unified framework explains why overfitting is benign in interpolating learning.

New theorem improves spectral gap for sampling from mixture distributions.

New estimates show spectral gap stability in RCD spaces, close to Beta distribution.

Random Fourier features is one of the most popular techniques for scaling up kernel methods, such as kernel ridge regression. However, despite impressive empirical results, the statistical properties of random Fourier features are still not well understood. In this paper we take steps toward filling this gap. Specifica…

The paper analyzes the generalization performance of spectral clustering algorithms and proposes new methods to improve their effectiveness.

State aggregation is a popular model reduction method rooted in optimal control. It reduces the complexity of engineering systems by mapping the system's states into a small number of meta-states. The choice of aggregation map often depends on the data analysts' knowledge and is largely ad hoc. In this paper, we propos…

COPT optimizes graph distances via simultaneous optimal transport.

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential eq…

Paper proposes AMP with spectral initialization for robust signal estimation.

Study shows non-spectrality of certain curves and line segments.

Study spectral density of neural networks using resolvent method.

Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related …

Combines linear and spectral estimators for signal recovery in generalized linear models.

This paper proves a generalization bound for complex-valued neural networks scaling with spectral complexity.

Optimizes risk measures given known marginal distributions of two unknown factors.