相关论文: Spectral Portfolio Theory: From SGD Weight Matrice…

Implicit bias induced by gradient-based algorithms is essential to the generalization of overparameterized models, yet its mechanisms can be subtle. This work leverages the Normalized Steepest Descent} (NSD) framework to investigate how…

Stochastic gradient descent (SGD) has been widely studied in the literature from different angles, and is commonly employed for solving many big data machine learning problems. However, the averaging technique, which combines all iterative…

We investigate how and when to diversify capital over assets, i.e., the portfolio selection problem, from a signal processing perspective. To this end, we first construct portfolios that achieve the optimal expected growth in i.i.d.…

Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it…

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but…

We show that the behavior of stochastic gradient descent is related to Bayesian statistics by showing that SGD is effectively diffusion on a fractal landscape, where the fractal dimension can be accounted for in a purely Bayesian way. By…

We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and it is optimal in the sense of…

In this study we suggest a portfolio selection framework based on option-implied information and multivariate non-Gaussian models. The proposed models incorporate skewness, kurtosis and more complex dependence structures among stocks…

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Stochastic gradient descent (SGD) and its variants enable modern artificial intelligence. However, theoretical understanding lags far behind their empirical success. It is widely believed that SGD has a curious ability to avoid sharp local…

This paper presents a comprehensive study on the convergence rates of the stochastic gradient descent (SGD) algorithm when applied to overparameterized two-layer neural networks. Our approach combines the Neural Tangent Kernel (NTK)…

Stochastic descent methods (of the gradient and mirror varieties) have become increasingly popular in optimization. In fact, it is now widely recognized that the success of deep learning is not only due to the special deep architecture of…

This study explores the use of Transformer-based models to predict both covariance and semi-covariance matrices for ETF portfolio optimization. Traditional portfolio optimization techniques often rely on static covariance estimates or…

A theoretical, and potentially also practical, problem with stochastic gradient descent is that trajectories may escape to infinity. In this note, we investigate uniform boundedness properties of iterates and function values along the…

We present and discuss a stochastic model of financial assets dynamics based on the idea of an inverse renormalization group strategy. With this strategy we construct the multivariate distributions of elementary returns based on the scaling…

Graph neural networks (GNNs) model nonlinear representations in graph data with applications in distributed agent coordination, control, and planning among others. Current GNN architectures assume ideal scenarios and ignore link…

Spectral features are widely incorporated within Graph Neural Networks (GNNs) to improve their expressive power, or their ability to distinguish among non-isomorphic graphs. One popular example is the usage of graph Laplacian eigenvectors…

We consider Random Matrix Theories with non-Gaussian potentials that have a rich phase structure in the large $N$ limit. We calculate the Spectral Form Factor (SFF) in such models and present them as interesting examples of dynamical models…

Stochastic gradient descent (SGD) and adaptive gradient methods, such as Adam and RMSProp, have been widely used in training deep neural networks. We empirically show that while the difference between the standard generalization performance…

Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that…