Learning to Learn Financial Networks for Optimising Momentum Strategies

Network momentum provides a novel type of risk premium, which exploits the interconnections among assets in a financial network to predict future returns. However, the current process of constructing financial networks relies heavily on expensive databases and financial expertise, limiting accessibility for small-sized and academic institutions. Furthermore, the traditional approach treats network construction and portfolio optimisation as separate tasks, potentially hindering optimal portfolio performance. To address these challenges, we propose L2GMOM, an end-to-end machine learning framework that simultaneously learns financial networks and optimises trading signals for network momentum strategies. The model of L2GMOM is a neural network with a highly interpretable forward propagation architecture, which is derived from algorithm unrolling. The L2GMOM is flexible and can be trained with diverse loss functions for portfolio performance, e.g. the negative Sharpe ratio. Backtesting on 64 continuous future contracts demonstrates a significant improvement in portfolio profitability and risk control, with a Sharpe ratio of 1.74 across a 20-year period.Comment: 9 page

Network Momentum across Asset Classes

We investigate the concept of network momentum, a novel trading signal derived from momentum spillover across assets. Initially observed within the confines of pairwise economic and fundamental ties, such as the stock-bond connection of the same company and stocks linked through supply-demand chains, momentum spillover implies a propagation of momentum risk premium from one asset to another. The similarity of momentum risk premium, exemplified by co-movement patterns, has been spotted across multiple asset classes including commodities, equities, bonds and currencies. However, studying the network effect of momentum spillover across these classes has been challenging due to a lack of readily available common characteristics or economic ties beyond the company level. In this paper, we explore the interconnections of momentum features across a diverse range of 64 continuous future contracts spanning these four classes. We utilise a linear and interpretable graph learning model with minimal assumptions to reveal the intricacies of the momentum spillover network. By leveraging the learned networks, we construct a network momentum strategy that exhibits a Sharpe ratio of 1.5 and an annual return of 22%, after volatility scaling, from 2000 to 2022. This paper pioneers the examination of momentum spillover across multiple asset classes using only pricing data, presents a multi-asset investment strategy based on network momentum, and underscores the effectiveness of this strategy through robust empirical analysis.Comment: 27 page

Kernel-based graph learning from smooth signals: a functional viewpoint

The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based representations and algorithms in the field of machine learning and graph signal processing. In this paper, we propose a novel graph learning framework that incorporates prior information along node and observation side, and in particular the covariates that help to explain the dependency structures in graph signals. To this end, we consider graph signals as functions in the reproducing kernel Hilbert space associated with a Kronecker product kernel, and integrate functional learning with smoothness-promoting graph learning to learn a graph representing the relationship between nodes. The functional learning increases the robustness of graph learning against missing and incomplete information in the graph signals. In addition, we develop a novel graph-based regularisation method which, when combined with the Kronecker product kernel, enables our model to capture both the dependency explained by the graph and the dependency due to graph signals observed under different but related circumstances, e.g. different points in time. The latter means the graph signals are free from the i.i.d. assumptions required by the classical graph learning models. Experiments on both synthetic and real-world data show that our methods outperform the state-of-the-art models in learning a meaningful graph topology from graph signals, in particular with heavy noise, missing values, and multiple dependency

Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint

The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role in the success of many graph-based representations and algorithms in the field of machine learning and graph signal processing. In this paper, we propose a novel graph learning framework that incorporates the node-side and observation-side information, and in particular the covariates that help to explain the dependency structures in graph signals. To this end, we consider graph signals as functions in the reproducing kernel Hilbert space associated with a Kronecker product kernel, and integrate functional learning with smoothness-promoting graph learning to learn a graph representing the relationship between nodes. The functional learning increases the robustness of graph learning against missing and incomplete information in the graph signals. In addition, we develop a novel graph-based regularisation method which, when combined with the Kronecker product kernel, enables our model to capture both the dependency explained by the graph and the dependency due to graph signals observed under different but related circumstances, e.g. different points in time. The latter means the graph signals are free from the i.i.d. assumptions required by the classical graph learning models. Experiments on both synthetic and real-world data show that our methods outperform the state-of-the-art models in learning a meaningful graph topology from graph signals, in particular under heavy noise, missing values, and multiple dependency.Comment: 13 pages, with extra 3-page appendice

Learning to Learn Graph Topologies

Learning a graph topology to reveal the underlying relationship between data entities plays an important role in various machine learning and data analysis tasks. Under the assumption that structured data vary smoothly over a graph, the problem can be formulated as a regularised convex optimisation over a positive semidefinite cone and solved by iterative algorithms. Classic methods require an explicit convex function to reflect generic topological priors, e.g. the $\ell_1$ penalty for enforcing sparsity, which limits the flexibility and expressiveness in learning rich topological structures. We propose to learn a mapping from node data to the graph structure based on the idea of learning to optimise (L2O). Specifically, our model first unrolls an iterative primal-dual splitting algorithm into a neural network. The key structural proximal projection is replaced with a variational autoencoder that refines the estimated graph with enhanced topological properties. The model is trained in an end-to-end fashion with pairs of node data and graph samples. Experiments on both synthetic and real-world data demonstrate that our model is more efficient than classic iterative algorithms in learning a graph with specific topological properties.Comment: Accepted at NeurIPS 202

3D suitability evaluation of urban underground space using a variable weight method and considering ground restrictions

The evaluation of urban underground space (UUS) suitability involves multiple indicators. Assigning weight to these indicators is crucial for accurate assessment. This paper presents a method for spatially variable weight assignment of indicators using the order relation analysis method (G1-method), the entropy weight method, an improved grey relational analysis (GRA) and a set of spatial weight adjustment coefficients. First, the subjective and objective weights of indicators for engineering geological and hydrogeological conditions were determined by the G1-method and entropy weight method, respectively, and their combined weights were then obtained using the principle of minimum discriminatory information. This study highlighted the impact of surface restrictions, such as buildings, on UUS, and the degree of the influence of these buildings gradually decreased with the increase in depth of the rock and soil mass in UUS, which resulted in changes in weights of indicators with depth. To address this issue, a coefficient was defined as the standardized value of the ratio of additional stress applied by restrictions to the self-weight stress of soil at the same depth to modify the combined weights so that all weights of indicators could vary in space. Finally, an improved GRA was used to determine the suitability level of each evaluation cell using the maximum correlation criterion. This method was applied to the 3D suitability evaluation of UUS in Sanlong Bay, Foshan City, Guangdong Province, China, including 16 evaluation indexes. This study comprehensively considered the influence of multiple factors, thereby providing reference for evaluating the suitability of UUS in big cities

Diffusion along perivascular spaces as marker for impairment of glymphatic system in Parkinson’s disease

Abstract The brain glymphatic system is involved in the clearance of misfolding α-synuclein, the impaired glymphatic system may contribute to the progression of Parkinson’s disease (PD). We aimed to analyze the diffusion tensor image along the perivascular space (DTI-ALPS) and perivascular space (PVS) burden to reveal the relationship between the glymphatic system and PD. A cross-sectional study using a 7 T MRI of 76 PD patients and 48 controls was performed to evaluate the brain’s glymphatic system. The DTI-ALPS and PVS burden in basal ganglia were calculated. Correlation analyses were conducted between DTI-ALPS, PVS burden and clinical features. We detected lower DTI-ALPS in the PD subgroup relative to controls, and the differences were more pronounced in patients with Hoehn & Yahr stage greater than two. The decreased DTI-ALPS was only evident in the left hemisphere in patients in the early stage but involved both hemispheres in more advanced PD patients. Decreased DTI-ALPS were also correlated with longer disease duration, higher Unified Parkinson’s Disease Rating Scale motor score (UPDRS III) and UPDRS total scores, as well as higher levodopa equivalent daily dose. Moreover, the decreased DTI-ALPS correlated with increased PVS burden, and both indexes correlated with PD disease severity. This study demonstrated decreased DTI-ALPS in PD, which might initiate from the left hemisphere and progressively involve right hemisphere with the disease progression. Decreased DTI-ALPS index correlated with increased PVS burden, indicating that both metrics could provide supporting evidence of an impaired glymphatic system. MRI evaluation of the PVS burden and diffusion along PVS are potential imaging biomarkers for PD for disease progression