Related papers: Physics-Informed Singular-Value Learning for Cross…
We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and marginal volatilities and how to regularise the eigenvalues of large equity…
We give a new algorithm for the estimation of the cross-covariance matrix $\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in \mathbb{R}^p$ in the context where the number $T$ of observations of the pair $(X,Y)$ is…
Covariance matrix estimation and principal component analysis (PCA) are two cornerstones of multivariate analysis. Classic textbook solutions perform poorly when the dimension of the data is of a magnitude similar to the sample size, or…
We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues…
We introduce a novel covariance estimator for portfolio selection that adapts to the non-stationary or persistent heteroskedastic environments of financial time series by employing exponentially weighted averages and nonlinearly shrinking…
Some novel strategies have recently been proposed for single hidden layer neural network training that set randomly the weights from input to hidden layer, while weights from hidden to output layer are analytically determined by…
We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical…
The global minimum-variance portfolio is a typical choice for investors because of its simplicity and broad applicability. Although it requires only one input, namely the covariance matrix of asset returns, estimating the optimal solution…
One of the goals in scaling sequential machine learning methods pertains to dealing with high-dimensional data spaces. A key related challenge is that many methods heavily depend on obtaining the inverse covariance matrix of the data. It is…
CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other…
Solving inverse problems, such as parameter estimation and optimal control, is a vital part of science. Many experiments repeatedly collect data and rely on machine learning algorithms to quickly infer solutions to the associated inverse…
We study general singular value shrinkage estimators in high-dimensional regression and classification, when the number of features and the sample size both grow proportionally to infinity. We allow models with general covariance matrices…
We establish large sample approximations for an arbitray number of bilinear forms of the sample variance-covariance matrix of a high-dimensional vector time series using $ \ell_1$-bounded and small $\ell_2$-bounded weighting vectors.…
The comovement phenomenon in financial markets creates decision scenarios with positively correlated asset returns. This paper addresses covariance matrix estimation under such conditions, motivated by observations of significant positive…
Singular value decomposition is the key tool in the analysis and understanding of linear regularization methods. In the last decade nonlinear variational approaches such as $\ell^1$ or total variation regularizations became quite prominent…
Many machine learning algorithms require precise estimates of covariance matrices. The sample covariance matrix performs poorly in high-dimensional settings, which has stimulated the development of alternative methods, the majority based on…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
We propose two new Bayesian smoothing methods for general state-space models with unknown parameters. The first approach is based on the particle learning and smoothing algorithm, but with an adjustment in the backward resampling weights.…