Ni Zhan

Kevin Han Huang, Ni Zhan, Elif Ertekin et al.

Incorporating group symmetries into neural networks has been a cornerstone of success in many AI-for-science applications. Diagonal groups of isometries, which describe the invariance under a simultaneous movement of multiple objects, arise naturally in many-body quantum problems. Despite their importance, diagonal groups have received relatively little attention, as they lack a natural choice of invariant maps except in special cases. We study different ways of incorporating diagonal invariance in neural network ansätze trained via variational Monte Carlo methods, and consider specifically data augmentation, group averaging and canonicalization. We show that, contrary to standard ML setups, in-training symmetrization destabilizes training and can lead to worse performance. Our theoretical and numerical results indicate that this unexpected behavior may arise from a unique computational-statistical tradeoff not found in standard ML analyses of symmetrization. Meanwhile, we demonstrate that post hoc averaging is less sensitive to such tradeoffs and emerges as a simple, flexible and effective method for improving neural network solvers.

Ni Zhan

This paper examines deposits of individuals ("retail") and large companies ("wholesale") in the U.S. banking industry, and how these deposit types are impacted by macroeconomic factors, such as quantitative easing (QE). Actual data for deposits by holder are unavailable. We use a dataset on banks' financial information and probabilistic generative model to predict industry retail-wholesale deposit split from 2000 to 2020. Our model assumes account balances arise from separate retail and wholesale lognormal distributions and fit parameters of distributions by minimizing error between actual bank metrics and simulated metrics using the model's generative process. We use time-series regression to forward predict retail-wholesale deposits as function of loans, retail loans, and reserve balances at Fed banks. We find increase in reserves (representing QE) increases wholesale but not retail deposits, and increase in loans increase both wholesale and retail deposits evenly. The result shows that QE following the 2008 financial crisis benefited large companies more than average individuals, a relevant finding for economic decision making. In addition, this work benefits bank management strategy by providing forecasting capability for retail-wholesale deposits.

Ni Zhan, Yijia Sun, Aman Jakhar et al.

We examine a variety of graphical models to construct optimal portfolios. Graphical models such as PCA-KMeans, autoencoders, dynamic clustering, and structural learning can capture the time varying patterns in the covariance matrix and allow the creation of an optimal and robust portfolio. We compared the resulting portfolios from the different models with baseline methods. In many cases our graphical strategies generated steadily increasing returns with low risk and outgrew the S&P 500 index. This work suggests that graphical models can effectively learn the temporal dependencies in time series data and are proved useful in asset management.