相关论文: Noise dressing of the correlation matrix of factor…

In dealing with high-dimensional data sets, factor models are often useful for dimension reduction. The estimation of factor models has been actively studied in various fields. In the first part of this paper, we present a new approach to…

Random matrix theory is finding an increasing number of applications in the context of information theory and communication systems, especially in studying the properties of complex networks. Such properties include short-term and long-term…

Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…

The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…

We study the parametric resonance of the neutrino oscillation through the matter whose density varies spatially. The Fourier analysis of the matter effect enables us to clarify the parametric resonance condition, which is summarized in a…

Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the…

Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…

Random feature maps are ubiquitous in modern statistical machine learning, where they generalize random projections by means of powerful, yet often difficult to analyze nonlinear operators. In this paper, we leverage the "concentration"…

In a very high-dimensional vector space, two randomly-chosen vectors are almost orthogonal with high probability. Starting from this observation, we develop a statistical factor model, the random factor model, in which factors are chosen at…

In this paper, we study a new two-way factor model for high-dimensional matrix-variate time series. To estimate the number of factors in this two-way factor model, we decompose the series into two parts: one being a non-weakly correlated…

Matrix-variate data of high dimensions are frequently observed in finance and economics, spanning extended time periods, such as the long-term data on international trade flows among numerous countries. To address potential structural…

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…

We study the dependence of the spectral density of the covariance matrix ensemble on the power spectrum of the underlying multivariate signal. The white noise signal leads to the celebrated Marchenko-Pastur formula. We demonstrate results…

The objective function of a matrix factorization model usually aims to minimize the average of a regression error contributed by each element. However, given the existence of stochastic noises, the implicit deviations of sample data from…

In high-dimensional data, structured noise caused by observed and unobserved factors affecting multiple target variables simultaneously, imposes a serious challenge for modeling, by masking the often weak signal. Therefore, (1) explaining…

We analyze the spectral properties of large, time-lagged correlation matrices using the tools of random matrix theory. We compare predictions of the one-dimensional spectra, based on approaches already proposed in the literature. Employing…

We theoretically investigate the phenomena of generalization and memorization in diffusion models. Empirical studies suggest that these phenomena are influenced by model complexity and the size of the training dataset. In our experiments,…

Financial correlation matrices measure the unsystematic correlations between stocks. Such information is important for risk management. The correlation matrices are known to be ``noise dressed''. We develop a new and alternative method to…

We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the…