Yulin Liu

Yulin Liu, Haoran Liu, Yingda Yin et al.

Normalizing flows (NFs) provide a powerful tool to construct an expressive distribution by a sequence of trackable transformations of a base distribution and form a probabilistic model of underlying data. Rotation, as an important quantity in computer vision, graphics, and robotics, can exhibit many ambiguities when occlusion and symmetry occur and thus demands such probabilistic models. Though much progress has been made for NFs in Euclidean space, there are no effective normalizing flows without discontinuity or many-to-one mapping tailored for SO(3) manifold. Given the unique non-Euclidean properties of the rotation manifold, adapting the existing NFs to SO(3) manifold is non-trivial. In this paper, we propose a novel normalizing flow on SO(3) by combining a Mobius transformation-based coupling layer and a quaternion affine transformation. With our proposed rotation normalizing flows, one can not only effectively express arbitrary distributions on SO(3), but also conditionally build the target distribution given input observations. Extensive experiments show that our rotation normalizing flows significantly outperform the baselines on both unconditional and conditional tasks.

Yulin Liu, Luyao Zhang

Currently, there are no convincing proxies for the fundamentals of cryptocurrency assets. We propose a new market-to-fundamental ratio, the price-to-utility (PU) ratio, utilizing unique blockchain accounting methods. We then proxy various existing fundamental-to-market ratios by Bitcoin historical data and find they have little predictive power for short-term bitcoin returns. However, PU ratio effectively predicts long-term bitcoin returns than alternative methods. Furthermore, we verify the explainability of PU ratio using machine learning. Finally, we present an automated trading strategy advised by the PU ratio that outperforms the conventional buy-and-hold and market-timing strategies. Our research contributes to explainable AI in finance from three facets: First, our market-to-fundamental ratio is based on classic monetary theory and the unique UTXO model of Bitcoin accounting rather than ad hoc; Second, the empirical evidence testifies the buy-low and sell-high implications of the ratio; Finally, we distribute the trading algorithms as open-source software via Python Package Index for future research, which is exceptional in finance research.

Luyao Zhang, Yulin Liu

Centralized monetary policy, leading to persistent inflation, is often inconsistent, untrustworthy, and unpredictable. Algorithmic stablecoins enabled by blockchain technology are promising in solving this problem. Algorithmic stablecoins utilize a monetary policy that is entirely rule-based. However, there is little understanding of how to optimize the rule. We propose a model that trade-off the price for supply stability. We further study the comparative statics by varying several design features. Finally, we discuss the empirical implications for designing stablecoins by the private sector and Central Bank Digital Currency (CBDC) by the public sector.

Yulin Liu, Mark Hansen

Reliable 4D aircraft trajectory prediction, whether in a real-time setting or for analysis of counterfactuals, is important to the efficiency of the aviation system. Toward this end, we first propose a highly generalizable efficient tree-based matching algorithm to construct image-like feature maps from high-fidelity meteorological datasets - wind, temperature and convective weather. We then model the track points on trajectories as conditional Gaussian mixtures with parameters to be learned from our proposed deep generative model, which is an end-to-end convolutional recurrent neural network that consists of a long short-term memory (LSTM) encoder network and a mixture density LSTM decoder network. The encoder network embeds last-filed flight plan information into fixed-size hidden state variables and feeds the decoder network, which further learns the spatiotemporal correlations from the historical flight tracks and outputs the parameters of Gaussian mixtures. Convolutional layers are integrated into the pipeline to learn representations from the high-dimension weather features. During the inference process, beam search, adaptive Kalman filter, and Rauch-Tung-Striebel smoother algorithms are used to prune the variance of generated trajectories.