arXiv subjects

Haotian Gu

Publications and source records attributed to Haotian Gu.

16 recordsLinked to original sources

arXiv2024

FedCore: Straggler-Free Federated Learning with Distributed Coresets

Federated learning (FL) is a machine learning paradigm that allows multiple clients to collaboratively train a shared model while keeping their data on-premise. However, the straggler issue, due to slow clients, often hinders the efficiency and scalability of FL. This paper presents FedCore, an algorithm that innovatively tackles the straggler problem via the decentralized selection of coresets, representative subsets of a dataset. Contrary to existing centralized coreset methods, FedCore creates coresets directly on each client in a distributed manner, ensuring privacy preservation in FL. FedCore translates the coreset optimization problem into a more tractable k-medoids clustering problem and operates distributedly on each client. Theoretical analysis confirms FedCore's convergence, and practical evaluations demonstrate an 8x reduction in FL training time, without compromising model accuracy. Our extensive evaluations also show that FedCore generalizes well to existing FL frameworks.

cs.DC↗

arXiv2024

Universality and Phase Transitions in Low Moments of Secular Coefficients of Critical Holomorphic Multiplicative Chaos

We investigate the low moments $\mathbb{E}[|A_N|^{2q}], 0 2q$. As a consequence, we establish the universality for the tightness of the normalized secular coefficients $A_N(\log(1+N))^{1/4}$, generalizing a result of Najnudel, Paquette, and Simm. Another corollary is the almost sure regularity of some critical non-Gaussian holomorphic chaos in appropriate Sobolev spaces. Moreover, we characterize the asymptotics of $\mathbb{E}[|A_N|^{2q}]$ for $|X_k|$ following a stretched exponential distribution with an arbitrary scale parameter, which exhibits a completely different behavior and underlying mechanism from the Gaussian universality regime. As a result, we unveil a double-layer phase transition around the critical case of exponential tails. Our proofs combine Harper's robust approach with a careful analysis of the (possibly random) leading terms in the monomial decomposition of $A_N$.

math.PR↗

arXiv2024

Transportation Marketplace Rate Forecast Using Signature Transform

Freight transportation marketplace rates are typically challenging to forecast accurately. In this work, we have developed a novel statistical technique based on signature transforms and have built a predictive and adaptive model to forecast these marketplace rates. Our technique is based on two key elements of the signature transform: one being its universal nonlinearity property, which linearizes the feature space and hence translates the forecasting problem into linear regression, and the other being the signature kernel, which allows for comparing computationally efficiently similarities between time series data. Combined, it allows for efficient feature generation and precise identification of seasonality and regime switching in the forecasting process. An algorithm based on our technique has been deployed by Amazon trucking operations, with far superior forecast accuracy and better interpretability versus commercially available industry models, even during the COVID-19 pandemic and the Ukraine conflict. Furthermore, our technique is able to capture the influence of business cycles and the heterogeneity of the marketplace, improving prediction accuracy by more than fivefold, with an estimated annualized saving of \$50MM.

cs.LG↗

arXiv2023

Risk of Transfer Learning and its Applications in Finance

Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. In this paper, we propose a novel concept of transfer risk and and analyze its properties to evaluate transferability of transfer learning. We apply transfer learning techniques and this concept of transfer risk to stock return prediction and portfolio optimization problems. Numerical results demonstrate a strong correlation between transfer risk and overall transfer learning performance, where transfer risk provides a computationally efficient way to identify appropriate source tasks in transfer learning, including cross-continent, cross-sector, and cross-frequency transfer for portfolio optimization.

q-fin.MF↗

arXiv2023

Transfer Learning for Portfolio Optimization

In this work, we explore the possibility of utilizing transfer learning techniques to address the financial portfolio optimization problem. We introduce a novel concept called "transfer risk", within the optimization framework of transfer learning. A series of numerical experiments are conducted from three categories: cross-continent transfer, cross-sector transfer, and cross-frequency transfer. In particular, 1. a strong correlation between the transfer risk and the overall performance of transfer learning methods is established, underscoring the significance of transfer risk as a viable indicator of "transferability"; 2. transfer risk is shown to provide a computationally efficient way to identify appropriate source tasks in transfer learning, enhancing the efficiency and effectiveness of the transfer learning approach; 3. additionally, the numerical experiments offer valuable new insights for portfolio management across these different settings.

q-fin.PM↗

arXiv2023

Adversarial Training for Gradient Descent: Analysis Through its Continuous-time Approximation

Adversarial training has gained great popularity as one of the most effective defenses for deep neural network and more generally for gradient-based machine learning models against adversarial perturbations on data points. This paper establishes a continuous-time approximation for the mini-max game of adversarial training. This approximation approach allows for precise and analytical comparisons between stochastic gradient descent and its adversarial training counterpart; and confirms theoretically the robustness of adversarial training from a new gradient-flow viewpoint. The analysis is then corroborated through various analytical and numerical examples.

cs.LG↗

arXiv2023

Feasibility of Transfer Learning: A Mathematical Framework

Transfer learning is a popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. It has enjoyed numerous empirical successes and inspired a growing number of theoretical studies. This paper addresses the feasibility issue of transfer learning. It begins by establishing the necessary mathematical concepts and constructing a mathematical framework for transfer learning. It then identifies and formulates the three-step transfer learning procedure as an optimization problem, allowing for the resolution of the feasibility issue. Importantly, it demonstrates that under certain technical conditions, such as appropriate choice of loss functions and data sets, an optimal procedure for transfer learning exists. This study of the feasibility issue brings additional insights into various transfer learning problems. It sheds light on the impact of feature augmentation on model performance, explores potential extensions of domain adaptation, and examines the feasibility of efficient feature extractor transfer in image classification.

cs.LG↗

arXiv2023

Feasibility and Transferability of Transfer Learning: A Mathematical Framework

Transfer learning is an emerging and popular paradigm for utilizing existing knowledge from previous learning tasks to improve the performance of new ones. Despite its numerous empirical successes, theoretical analysis for transfer learning is limited. In this paper we build for the first time, to the best of our knowledge, a mathematical framework for the general procedure of transfer learning. Our unique reformulation of transfer learning as an optimization problem allows for the first time, analysis of its feasibility. Additionally, we propose a novel concept of transfer risk to evaluate transferability of transfer learning. Our numerical studies using the Office-31 dataset demonstrate the potential and benefits of incorporating transfer risk in the evaluation of transfer learning performance.

cs.LG↗

arXiv2022

Automated Quality Controlled Analysis of 2D Phase Contrast Cardiovascular Magnetic Resonance Imaging

Flow analysis carried out using phase contrast cardiac magnetic resonance imaging (PC-CMR) enables the quantification of important parameters that are used in the assessment of cardiovascular function. An essential part of this analysis is the identification of the correct CMR views and quality control (QC) to detect artefacts that could affect the flow quantification. We propose a novel deep learning based framework for the fully-automated analysis of flow from full CMR scans that first carries out these view selection and QC steps using two sequential convolutional neural networks, followed by automatic aorta and pulmonary artery segmentation to enable the quantification of key flow parameters. Accuracy values of 0.958 and 0.914 were obtained for view classification and QC, respectively. For segmentation, Dice scores were $>$0.969 and the Bland-Altman plots indicated excellent agreement between manual and automatic peak flow values. In addition, we tested our pipeline on an external validation data set, with results indicating good robustness of the pipeline. This work was carried out using multivendor clinical data consisting of 986 cases, indicating the potential for the use of this pipeline in a clinical setting.

eess.IV↗

arXiv2022

Multi-level Adaptation for Automatic Landing with Engine Failure under Turbulent Weather

This paper addresses efficient feasibility evaluation of possible emergency landing sites, online navigation, and path following for automatic landing under engine-out failure subject to turbulent weather. The proposed Multi-level Adaptive Safety Control framework enables unmanned aerial vehicles (UAVs) under large uncertainties to perform safety maneuvers traditionally reserved for human pilots with sufficient experience. In this framework, a simplified flight model is first used for time-efficient feasibility evaluation of a set of landing sites and trajectory generation. Then, an online path following controller is employed to track the selected landing trajectory. We used a high-fidelity simulation environment for a fixed-wing aircraft to test and validate the proposed approach under various weather uncertainties. For the case of emergency landing due to engine failure under severe weather conditions, the simulation results show that the proposed automatic landing framework is robust to uncertainties and adaptable at different landing stages while being computationally inexpensive for planning and tracking tasks.

cs.RO↗

arXiv2022

AI-enabled Assessment of Cardiac Systolic and Diastolic Function from Echocardiography

Left ventricular (LV) function is an important factor in terms of patient management, outcome, and long-term survival of patients with heart disease. The most recently published clinical guidelines for heart failure recognise that over reliance on only one measure of cardiac function (LV ejection fraction) as a diagnostic and treatment stratification biomarker is suboptimal. Recent advances in AI-based echocardiography analysis have shown excellent results on automated estimation of LV volumes and LV ejection fraction. However, from time-varying 2-D echocardiography acquisition, a richer description of cardiac function can be obtained by estimating functional biomarkers from the complete cardiac cycle. In this work we propose for the first time an AI approach for deriving advanced biomarkers of systolic and diastolic LV function from 2-D echocardiography based on segmentations of the full cardiac cycle. These biomarkers will allow clinicians to obtain a much richer picture of the heart in health and disease. The AI model is based on the 'nn-Unet' framework and was trained and tested using four different databases. Results show excellent agreement between manual and automated analysis and showcase the potential of the advanced systolic and diastolic biomarkers for patient stratification. Finally, for a subset of 50 cases, we perform a correlation analysis between clinical biomarkers derived from echocardiography and CMR and we show excellent agreement between the two modalities.

physics.med-ph↗

arXiv2022

Dynamic Programming Principles for Mean-Field Controls with Learning

Dynamic programming principle (DPP) is fundamental for control and optimization, including Markov decision problems (MDPs), reinforcement learning (RL), and more recently mean-field controls (MFCs). However, in the learning framework of MFCs, DPP has not been rigorously established, despite its critical importance for algorithm designs. In this paper, we first present a simple example in MFCs with learning where DPP fails with a mis-specified Q function; and then propose the correct form of Q function in an appropriate space for MFCs with learning. This particular form of Q function is different from the classical one and is called the IQ function. In the special case when the transition probability and the reward are independent of the mean-field information, it integrates the classical Q function for single-agent RL over the state-action distribution. In other words, MFCs with learning can be viewed as lifting the classical RLs by replacing the state-action space with its probability distribution space. This identification of the IQ function enables us to establish precisely the DPP in the learning framework of MFCs. Finally, we illustrate through numerical experiments the time consistency of this IQ function.

math.OC↗

arXiv2022

Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approach

One of the challenges for multi-agent reinforcement learning (MARL) is designing efficient learning algorithms for a large system in which each agent has only limited or partial information of the entire system. While exciting progress has been made to analyze decentralized MARL with the network of agents for social networks and team video games, little is known theoretically for decentralized MARL with the network of states for modeling self-driving vehicles, ride-sharing, and data and traffic routing. This paper proposes a framework of localized training and decentralized execution to study MARL with network of states. Localized training means that agents only need to collect local information in their neighboring states during the training phase; decentralized execution implies that agents can execute afterwards the learned decentralized policies, which depend only on agents' current states. The theoretical analysis consists of three key components: the first is the reformulation of the MARL system as a networked Markov decision process with teams of agents, enabling updating the associated team Q-function in a localized fashion; the second is the Bellman equation for the value function and the appropriate Q-function on the probability measure space; and the third is the exponential decay property of the team Q-function, facilitating its approximation with efficient sample efficiency and controllable error. The theoretical analysis paves the way for a new algorithm LTDE-Neural-AC, where the actor-critic approach with over-parameterized neural networks is proposed. The convergence and sample complexity is established and shown to be scalable with respect to the sizes of both agents and states. To the best of our knowledge, this is the first neural network based MARL algorithm with network structure and provably convergence guarantee.

cs.LG↗

arXiv2021

Mean-Field Controls with Q-learning for Cooperative MARL: Convergence and Complexity Analysis

Multi-agent reinforcement learning (MARL), despite its popularity and empirical success, suffers from the curse of dimensionality. This paper builds the mathematical framework to approximate cooperative MARL by a mean-field control (MFC) approach, and shows that the approximation error is of $\mathcal{O}(\frac{1}{\sqrt{N}})$. By establishing an appropriate form of the dynamic programming principle for both the value function and the Q function, it proposes a model-free kernel-based Q-learning algorithm (MFC-K-Q), which is shown to have a linear convergence rate for the MFC problem, the first of its kind in the MARL literature. It further establishes that the convergence rate and the sample complexity of MFC-K-Q are independent of the number of agents $N$, which provides an $\mathcal{O}(\frac{1}{\sqrt{N}})$ approximation to the MARL problem with $N$ agents in the learning environment. Empirical studies for the network traffic congestion problem demonstrate that MFC-K-Q outperforms existing MARL algorithms when $N$ is large, for instance when $N>50$.

cs.LG↗

arXiv2020

Error estimates for a POD method for solving viscous G-equations in incompressible cellular flows

The G-equation is a well-known model for studying front propagation in turbulent combustion. In this paper, we develop an efficient model reduction method for computing \textcolor{black}{regular solutions} of viscous G-equations in incompressible steady and time-periodic cellular flows. Our method is based on the Galerkin proper orthogonal decomposition (POD) method. To facilitate the algorithm design and convergence analysis, we decompose the solution of the viscous G-equation into a mean-free part and a mean part, where their evolution equations can be derived accordingly. We construct the POD basis from the solution snapshots of the mean-free part. With the POD basis, we can efficiently solve the evolution equation for the mean-free part of the solution to the viscous G-equation. After we get the mean-free part of the solution, the mean of the solution can be recovered. We also provide rigorous convergence analysis for our method. Numerical results for \textcolor{black}{viscous G-equations and curvature G-equations} are presented to demonstrate the accuracy and efficiency of the proposed method. In addition, we study the turbulent flame speeds of the viscous G-equations in incompressible cellular flows.

math.NA↗

arXiv2018

Analysis on hybrid fractals

We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski gasket, for which we construct explicitly an energy form with the property that it does not "capture" the $3$-level Sierpinski gasket structure. This characteristic type of energy forms that "miss" parts of the structure of the underlying space are investigated in the more general framework of finitely ramified cell structures. The spectrum of the associated Laplacian and its asymptotic behavior in two different hybrids is analyzed theoretically and numerically. A website with further numerical data analysis is available at http://www.math.cornell.edu/~harry970804/.

math.FA↗