Efficient Bayesian inference using physics-informed invertible neural networks for inverse problems

In the paper, we propose a novel approach for solving Bayesian inverse problems with physics-informed invertible neural networks (PI-INN). The architecture of PI-INN consists of two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The invertible map between the parametric input and the INN output with the aid of NB-Net is constructed to provide a tractable estimation of the posterior distribution, which enables efficient sampling and accurate density evaluation. Furthermore, the loss function of PI-INN includes two components: a residual-based physics-informed loss term and a new independence loss term. The presented independence loss term can Gaussianize the random latent variables and ensure statistical independence between two parts of INN output by effectively utilizing the estimated density function. Several numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed PI-INN, including inverse kinematics, inverse problems of the 1-d and 2-d diffusion equations, and seismic traveltime tomography

Computational Modeling and Design of Financial Markets: Towards Manipulation-Resistant and Expressive Markets

Electronic trading platforms have transformed the financial market landscape, supporting automation of trading and dissemination of information. With high volumes of data streaming at high velocity, market participants use algorithms to assist almost every aspect of their decision-making: they learn market state, identify trading opportunities, and express increasingly diverse and nuanced preferences. This growing automation motivates a reconsideration of market designs to support the new competence and prevent potential risks. This dissertation focuses on designing (1) manipulation-resistant markets that facilitate learning genuine market supply and demand, and (2) expressive markets that facilitate delivering preferences in greater detail and flexibility. Advances towards each may contribute to efficient resource allocation and information aggregation. Manipulation-Resistant Markets. Spoofing refers to the practice of submitting spurious orders to deceive others about supply and demand. To understand its effects, this dissertation develops an agent-based model of manipulating prices in limit-order markets. Empirical game-theoretic analysis on agent behavior in simulated markets with and without manipulation shows that spoofing hurts market surplus and decreases the proportion of learning traders who exploit order book information. That learning behavior typically persists in strategic equilibrium even in the presence of manipulation, indicating a consistently spoofable market. Built on this model, a cloaking mechanism is designed to deter spoofing via strategically concealing part of the order book. Simulated results demonstrate that the benefit of cloaking in mitigating manipulation outweighs its efficiency cost due to information loss. This dissertation explores variations of the learning-based trading strategy that reasonably compromise effectiveness in non-manipulated markets for robustness against manipulation. Regulators who deploy detection algorithms to catch manipulation face the challenge that an adversary may obfuscate strategy to evade. This dissertation proposes an adversarial learning framework to proactively reason about how a manipulator might mask behavior. Evasion is represented by a generative model, trained by augmenting manipulation order streams with examples of normal trading. The framework generates adapted manipulation order streams that mimic benign trading patterns and appear qualitatively different from prescribed manipulation strategies. Expressive Markets. Financial options are contracts that specify the right to buy or sell an underlying asset at a strike price in the future. Standard exchanges offer options of predetermined strike values and trade them independently, even for those written on the same asset. This dissertation proposes a mechanism to match orders on options related to the same asset, supporting trade of any custom strike. Combinatorial financial options---contracts that define future trades of any linear combination of underlying assets---are further introduced to enable the expression of demand based on predicted correlations among assets. Optimal clearing of such markets is coNP-hard, and a heuristic algorithm is proposed to find optimal matches through iterative constraint generation. Prediction markets that support betting on ranges (e.g., the price of S&P) offer predetermined intervals at a fixed resolution, limiting the ability to elicit fine-grained information. The logarithmic market scoring rule (LMSR) used in this setting presents two limitations that prevent its scaling to large outcome spaces: (1) operations run in time linear in the number of outcomes, and (2) loss suffered by the market can grow unbounded. By embedding the modularity properties of LMSR into a binary tree, this dissertation shows that operations can be expedited to logarithmic time. A constant worst-case loss can also be achieved by designing a liquidity scheme for intervals at different resolutions.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/167942/1/xintongw_1.pd

CrossSinger: A Cross-Lingual Multi-Singer High-Fidelity Singing Voice Synthesizer Trained on Monolingual Singers

It is challenging to build a multi-singer high-fidelity singing voice synthesis system with cross-lingual ability by only using monolingual singers in the training stage. In this paper, we propose CrossSinger, which is a cross-lingual singing voice synthesizer based on Xiaoicesing2. Specifically, we utilize International Phonetic Alphabet to unify the representation for all languages of the training data. Moreover, we leverage conditional layer normalization to incorporate the language information into the model for better pronunciation when singers meet unseen languages. Additionally, gradient reversal layer (GRL) is utilized to remove singer biases included in lyrics since all singers are monolingual, which indicates singer's identity is implicitly associated with the text. The experiment is conducted on a combination of three singing voice datasets containing Japanese Kiritan dataset, English NUS-48E dataset, and one internal Chinese dataset. The result shows CrossSinger can synthesize high-fidelity songs for various singers with cross-lingual ability, including code-switch cases.Comment: Accepted by ASRU202

Dual Relation Alignment for Composed Image Retrieval

Composed image retrieval, a task involving the search for a target image using a reference image and a complementary text as the query, has witnessed significant advancements owing to the progress made in cross-modal modeling. Unlike the general image-text retrieval problem with only one alignment relation, i.e., image-text, we argue for the existence of two types of relations in composed image retrieval. The explicit relation pertains to the reference image & complementary text-target image, which is commonly exploited by existing methods. Besides this intuitive relation, the observations during our practice have uncovered another implicit yet crucial relation, i.e., reference image & target image-complementary text, since we found that the complementary text can be inferred by studying the relation between the target image and the reference image. Regrettably, existing methods largely focus on leveraging the explicit relation to learn their networks, while overlooking the implicit relation. In response to this weakness, We propose a new framework for composed image retrieval, termed dual relation alignment, which integrates both explicit and implicit relations to fully exploit the correlations among the triplets. Specifically, we design a vision compositor to fuse reference image and target image at first, then the resulted representation will serve two roles: (1) counterpart for semantic alignment with the complementary text and (2) compensation for the complementary text to boost the explicit relation modeling, thereby implant the implicit relation into the alignment learning. Our method is evaluated on two popular datasets, CIRR and FashionIQ, through extensive experiments. The results confirm the effectiveness of our dual-relation learning in substantially enhancing composed image retrieval performance

A Correlation Information-based Spatiotemporal Network for Traffic Flow Forecasting

The technology of traffic flow forecasting plays an important role in intelligent transportation systems. Based on graph neural networks and attention mechanisms, most previous works utilize the transformer architecture to discover spatiotemporal dependencies and dynamic relationships. However, they have not considered correlation information among spatiotemporal sequences thoroughly. In this paper, based on the maximal information coefficient, we present two elaborate spatiotemporal representations, spatial correlation information (SCorr) and temporal correlation information (TCorr). Using SCorr, we propose a correlation information-based spatiotemporal network (CorrSTN) that includes a dynamic graph neural network component for integrating correlation information into spatial structure effectively and a multi-head attention component for modeling dynamic temporal dependencies accurately. Utilizing TCorr, we explore the correlation pattern among different periodic data to identify the most relevant data, and then design an efficient data selection scheme to further enhance model performance. The experimental results on the highway traffic flow (PEMS07 and PEMS08) and metro crowd flow (HZME inflow and outflow) datasets demonstrate that CorrSTN outperforms the state-of-the-art methods in terms of predictive performance. In particular, on the HZME (outflow) dataset, our model makes significant improvements compared with the ASTGNN model by 12.7%, 14.4% and 27.4% in the metrics of MAE, RMSE and MAPE, respectively.Comment: 19 pages, 13 figures, 5 table