A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends spectral number variance convergence to random matrix ensembles for twisted Laplacians.
Method selects number of communities in weighted networks.
Improved spectral gap for MwG with adaptive RWM proposals.
Method estimates group structure in panel data using variance information.
This paper develops a new theory for ensemble learning beyond variance reduction.
Unified framework for spectral methods, kernel learning, and manifold unfolding.
We propose a metric, Layer Saturation, defined as the proportion of the number of eigenvalues needed to explain 99% of the variance of the latent representations, for analyzing the learned representations of neural network layers. Saturation is based on spectral analysis and can be computed efficiently, making live ana…
Analyzes how diffusion models learn, revealing a spectral bias in structure mastery.
Drago optimizes DRO problems with faster convergence.
The heuristic identification of peaks from noisy complex spectra often leads to misunderstanding of the physical and chemical properties of matter. In this paper, we propose a framework based on Bayesian inference, which enables us to separate multipeak spectra into single peaks statistically and consists of two steps.…
The paper analyzes the variance of different shuffling methods in stochastic gradient descent.
Study on variance of Laplace eigenfunctions on manifolds.
SpecGD mitigates misalignment in phase retrieval models with anisotropic inputs.
Due to the limited resources and the scale of the graphs in modern datasets, we often get to observe a sampled subgraph of a larger original graph of interest, whether it is the worldwide web that has been crawled or social connections that have been surveyed. Inferring a global property of the original graph from such…
Electroencephalographic (EEG) monitoring of neural activity is widely used for sleep disorder diagnostics and research. The standard of care is to manually classify 30-second epochs of EEG time-domain traces into 5 discrete sleep stages. Unfortunately, this scoring process is subjective and time-consuming, and the defi…
Spheres' spectral structure converges to Gaussian space's as dimensions grow.
Proves new inequality linking spectral numbers of Lagrangians and their reductions.
New theory shows how multi-head attention reduces variance and decorrelates outputs.
We obtain a sharp lower bound on the isoperimetric deficit of a general polygon in terms of the variance of its side lengths, the variance of its radii, and its deviation from being convex. Our technique involves a functional minimization problem on a suitably constructed compact manifold and is based on the spectral t…
Hybrid model combines risk measures for better portfolio allocation.
Study smooth linear statistics on random covers of hyperbolic surfaces, showing central limit and variance results.
Adaptive spectral RL method enhances RL performance and interpretability.
Estimates Gaussian location model with ridge regularization, comparing variational and spectral methods.
In this paper, we study an insurer's reinsurance-investment problem under a mean-variance criterion. We show that excess-loss is the unique equilibrium reinsurance strategy under a spectrally negative Lévy insurance model when the reinsurance premium is computed according to the expected value premium principle. Furthe…
New method trains neural networks in spectral domain for improved performance.
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can simultaneously handle European options, forward-starts, options on the realized variance and …
The study examines spectral dynamics in deep neural networks, predicting how outliers evolve during training.
Study geodesics on random hyperbolic surfaces, finding variance similar to prime number theory.
BBVI converges nearly dimensionally independent for log-concave targets.
Paper improves robust spectral clustering for noisy data.
Standard kernels such as Matérn or RBF kernels only encode simple monotonic dependencies within the input space. Spectral mixture kernels have been proposed as general-purpose, flexible kernels for learning and discovering more complicated patterns in the data. Spectral mixture kernels have recently been generalized in…
GOE statistics emerge from surface moduli space averages.
Spectral deconfounding improves machine learning models by reducing hidden confounding effects.
A large class of machine learning techniques requires the solution of optimization problems involving spectral functions of parametric matrices, e.g. log-determinant and nuclear norm. Unfortunately, computing the gradient of a spectral function is generally of cubic complexity, as such gradient descent methods are rath…
We perform a parallel analysis of the spectral density of (i) the logarithm of price and (ii) the daily number of trades of a set of stocks traded in the New York Stock Exchange. The stocks are selected to be representative of a wide range of stock capitalization. The observed spectral densities show a different power-…
Spectral portfolio theory links neural networks to wealth dynamics via SGD weight matrices.
New proof shows not all Salem numbers are growth rates of Coxeter groups.
We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our algorithm solves portfolio selection problems with multiple CVaR constraints. In e…
This paper presents a bias-variance tradeoff of graph Laplacian regularizer, which is widely used in graph signal processing and semi-supervised learning tasks. The scaling law of the optimal regularization parameter is specified in terms of the spectral graph properties and a novel signal-to-noise ratio parameter, whi…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can be computed one by one, repeatedly solving the single-component problem and def…
We consider the problem of clustering noisy finite-length observations of stationary ergodic random processes according to their nonparametric generative models without prior knowledge of the model statistics and the number of generative models. Two algorithms, both using the L1-distance between estimated power spectra…
We show that the page at which the Lee spectral sequence collapses gives a bound on the unknotting number, u(K). In particular, for knots with u(K)<3, we show that the Lee spectral sequence must collapse at the E_2 page. An immediate corollary is that the Knight Move Conjecture is true when u(K)<3.
Functional magnetic resonance imaging (fMRI) produces data about activity inside the brain, from which spatial maps can be extracted by independent component analysis (ICA). In datasets, there are n spatial maps that contain p voxels. The number of voxels is very high compared to the number of analyzed spatial maps. Cl…
We study sparse principal components analysis in high dimensions, where (the number of variables) can be much larger than (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We introduce two complementary not…
The paper tackles model collapse in GPLVMs by improving kernel flexibility and projection variance.
Essential principal components simplify spectral analysis with minimal training data.
Optimizes learning Hilbert-Schmidt operators between Sobolev spaces.
We investigate serial correlation, periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. Periodic, or calendar, components are dete…