Related papers: Geometric Deep Learning for Realized Covariance Ma…
One of the main challenges in modern deep learning is to understand why such over-parameterized models perform so well when trained on finite data. A way to analyze this generalization concept is through the properties of the associated…
Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
Portfolio construction traditionally relies on separately estimating expected returns and covariance matrices using historical statistics, often leading to suboptimal allocation under time-varying market conditions. This paper proposes a…
In an environment of increasingly volatile financial markets, the accurate estimation of risk remains a major challenge. Traditional econometric models, such as GARCH and its variants, are based on assumptions that are often too rigid to…
Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…
This paper investigates an important problem of an appropriate variance-covariance matrix estimation in the Modern Portfolio Theory. We propose a novel framework for variancecovariance matrix estimation for purposes of the portfolio…
Graphical models and factor analysis are well-established tools in multivariate statistics. While these models can be both linked to structures exhibited by covariance and precision matrices, they are generally not jointly leveraged within…
Riemannian neural networks, which extend deep learning techniques to Riemannian spaces, have gained significant attention in machine learning. To better classify the manifold-valued features, researchers have started extending Euclidean…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially, recommender systems. Existing matrix completion models generally follow either a memory- or a…
We introduce the Historical and Dynamic Volatility Ratios (HVR/DVR) and show that equity and index volatilities are cointegrated at intraday and daily horizons. This allows us to construct a VECM to forecast portfolio volatility by…
Geometric data analysis and learning has emerged as a distinct and rapidly developing research area, increasingly recognized for its effectiveness across diverse applications. At the heart of this field lies curvature, a powerful and…
This paper shows a novel machine learning model for realized volatility (RV) prediction using a normalizing flow, an invertible neural network. Since RV is known to be skewed and have a fat tail, previous methods transform RV into values…
Multi-Task Learning (MTL) seeks to boost statistical power and learning efficiency by discovering structure shared across related tasks. State-of-the-art MTL representation methods, however, usually treat the latent representation matrix as…
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…
Adaptive stochastic gradient algorithms in the Euclidean space have attracted much attention lately. Such explorations on Riemannian manifolds, on the other hand, are relatively new, limited, and challenging. This is because of the…
The last decade has witnessed an experimental revolution in data science and machine learning, epitomised by deep learning methods. Indeed, many high-dimensional learning tasks previously thought to be beyond reach -- such as computer…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…