Related papers: Geometric Deep Learning for Realized Covariance Ma…

Estimation of high dimensional covariance matrices is an interesting and important research topic. In this paper, we propose a dynamic structure and develop an estimation procedure for high dimensional covariance matrices. Asymptotic…

We suggest two classes of multivariate GARCH--models which are both easy to estimate and perform well in forecasting the covariance matrix of more than one hundred stocks. We apply methods from random matrix theory (RMT) to determine the…

While matrix factorisation models are ubiquitous in large scale recommendation and search, real time application of such models requires inner product computations over an intractably large set of item factors. In this manuscript we present…

We investigate learning of the differential geometric structure of a data manifold embedded in a high-dimensional Euclidean space. We first analyze kernel-based algorithms and show that under the usual regularizations, non-probabilistic…

We present a new class of Bayesian dynamic models for bivariate price-realized volatility time series in financial forecasting. A novel dynamic gamma process model adopted for realized volatility is integrated with traditional Bayesian…

This study aims to compare multiple deep learning-based forecasters for the task of predicting volatility using multivariate data. The paper evaluates a range of models, starting from simpler and shallower ones and progressing to deeper and…

This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…

Over the past few years, symmetric positive definite (SPD) matrices have been receiving considerable attention from computer vision community. Though various distance measures have been proposed in the past for comparing SPD matrices, the…

Data-driven Riemannian geometry has emerged as a powerful tool for interpretable representation learning, offering improved efficiency in downstream tasks. Moving forward, it is crucial to balance cheap manifold mappings with efficient…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

We investigate the predictive abilities of the heterogeneous autoregressive (HAR) model compared to machine learning (ML) techniques across an unprecedented dataset of 1,455 stocks. Our analysis focuses on the role of fitting schemes,…

Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…

Euclidean representations distort data with intrinsic non-Euclidean structure. While Riemannian representation learning offers a solution by embedding data onto matching manifolds, it typically relies on an encoder to estimate densities on…

The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

Deep learning models are often considered black boxes due to their complex hierarchical transformations. Identifying suitable architectures is crucial for maximizing predictive performance with limited data. Understanding the geometric…

In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr\'echet means on the manifold of symmetric positive definite matrices, commonly referred to as Karcher or geometric means.…

In this paper, the Riemannian gradient algorithm and the natural gradient algorithm are applied to solve descent direction problems on the manifold of positive definite Hermitian matrices, where the geodesic distance is considered as the…

We propose a novel computational procedure for quadratic hedging in high-dimensional incomplete markets, covering mean-variance hedging and local risk minimization. Starting from the observation that both quadratic approaches can be treated…

Global Covariance Pooling (GCP) has been demonstrated to improve the performance of Deep Neural Networks (DNNs) by exploiting second-order statistics of high-level representations. GCP typically performs classification of the covariance…