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Yidong Zhou

Publications and source records attributed to Yidong Zhou.

34 records · Page 2Linked to original sources
arXiv2025

Wasserstein Transfer Learning

Transfer learning is a powerful paradigm for leveraging knowledge from source domains to enhance learning in a target domain. However, traditional transfer learning approaches often focus on scalar or multivariate data within Euclidean spaces, limiting their applicability to complex data structures such as probability distributions. To address this limitation, we introduce a novel transfer learning framework for regression models whose outputs are probability distributions residing in the Wasserstein space. When the informative subset of transferable source domains is known, we propose an estimator with provable asymptotic convergence rates, quantifying the impact of domain similarity on transfer efficiency. For cases where the informative subset is unknown, we develop a data-driven transfer learning procedure designed to mitigate negative transfer. The proposed methods are supported by rigorous theoretical analysis and are validated through extensive simulations and real-world applications. The code is available at https://github.com/h7nian/WaTL

cs.LG↗
arXiv2025

Sliced Wasserstein Regression

While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance, commonly used in distributional data analysis, poses challenges for multivariate distributions. A promising alternative is the sliced Wasserstein distance, which offers a computationally simpler solution. We propose distributional regression models with multivariate distributions as responses paired with Euclidean vector predictors. The foundation of our methodology is a slicing transform from the multivariate distribution space to the sliced distribution space for which we establish a theoretical framework, with the Radon transform as a prominent example. We introduce and study the asymptotic properties of sample-based estimators for two regression approaches, one based on utilizing the sliced Wasserstein distance directly in the multivariate distribution space, and a second approach based on a new slice-wise distance, employing a univariate distribution regression for each slice. Both global and local Fréchet regression methods are deployed for these approaches and illustrated in simulations and through applications. These include joint distributions of excess winter death rates and winter temperature anomalies in European countries as a function of base winter temperature and also data from finance.

stat.ME↗
arXiv2025

Fréchet Geodesic Boosting

Gradient boosting has become a cornerstone of machine learning, enabling base learners such as decision trees to achieve exceptional predictive performance. While existing algorithms primarily handle scalar or Euclidean outputs, increasingly prevalent complex-structured data, such as distributions, networks, and manifold-valued outputs, present challenges for traditional methods. Such non-Euclidean data lack algebraic structures such as addition, subtraction, or scalar multiplication required by standard gradient boosting frameworks. To address these challenges, we introduce Fréchet geodesic boosting (FGBoost), a novel approach tailored for outputs residing in geodesic metric spaces. FGBoost leverages geodesics as proxies for residuals and constructs ensembles in a way that respects the intrinsic geometry of the output space. Through theoretical analysis, extensive simulations, and real-world applications, we demonstrate the strong performance and adaptability of FGBoost, showcasing its potential for modeling complex data.

stat.ML↗
arXiv2025

Deep Fréchet Regression

Advancements in modern science have led to the increasing availability of non-Euclidean data in metric spaces. This paper addresses the challenge of modeling relationships between non-Euclidean responses and multivariate Euclidean predictors. We propose a flexible regression model capable of handling high-dimensional predictors without imposing parametric assumptions. Two primary challenges are addressed: the curse of dimensionality in nonparametric regression and the absence of linear structure in general metric spaces. The former is tackled using deep neural networks, while for the latter we demonstrate the feasibility of mapping the metric space where responses reside to a low-dimensional Euclidean space using manifold learning. We introduce a reverse mapping approach, employing local Fréchet regression, to map the low-dimensional manifold representations back to objects in the original metric space. We develop a theoretical framework, investigating the convergence rate of deep neural networks under dependent sub-Gaussian noise with bias. The convergence rate of the proposed regression model is then obtained by expanding the scope of local Fréchet regression to accommodate multivariate predictors in the presence of errors in predictors. Simulations and case studies show that the proposed model outperforms existing methods for non-Euclidean responses, focusing on the special cases of probability distributions and networks.

stat.ME↗
arXiv2025

Trisimplicial vertices in (fork, odd parachute)-free graphs

An {\em odd hole} in a graph is an induced subgraph which is a cycle of odd length at least five. An {\em odd parachute} is a graph obtained from an odd hole $H$ by adding a new edge $uv$ such that $x$ is adjacent to $u$ but not to $v$ for each $x\in V(H)$. A graph $G$ is perfectly divisible if for each induced subgraph $H$ of $G$, $V(H)$ can be partitioned into $A$ and $B$ such that $H[A]$ is perfect and $ω(H[B])<ω(H)$. A vertex of a graph is {\em trisimplicial} if its neighbourhood is the union of three cliques. In this paper, we prove that $χ(G)\leq \binom{ω(G)+1}{2}$ if $G$ is a (fork, odd parachute)-free graph by showing that $G$ contains a trisimplicial vertex when $G$ is nonperfectly divisible. This generalizes some results of Karthick, Kaufmann and Sivaraman [{\em Electron. J. Combin.} \textbf{29} (2022) \#P3.19], and Wu and Xu [{\em Discrete Math.} \textbf{347} (2024) 114121]. As a corollary, every nonperfectly divisible claw-free graph contains a trisimplicial vertex.

math.CO↗
arXiv2024

Leveraging Hardware Power through Optimal Pulse Profiling for Each Qubit Pair

In the scaling development of quantum computers, the calibration process emerges as a critical challenge. Existing calibration methods, utilizing the same pulse waveform for two-qubit gates across the device, overlook hardware differences among physical qubits and lack efficient parallel calibration. In this paper, we enlarge the pulse candidates for two-qubit gates to three pulse waveforms, and introduce a fine-grained calibration protocol. In the calibration protocol, three policies are proposed to profile each qubit pair with its optimal pulse waveform. Afterwards, calibration subgraphs are introduced to enable parallel calibraton through identifying compatible calibration operations. The protocol is validated on real machine with up to 127 qubits. Real-machine experiments demonstrates a minimum gate error of 0.001 with a median error of 0.006 which is 1.84x reduction compared to default pulse waveform provided by IBM. On device level, a double fold increase in quantum volume as well as 2.3x reduction in error per layered gate are achieved. The proposed protocol leverages the potential current hardware and could server as an important step toward fault-tolerant quantum computing.

quant-ph↗
arXiv2024

ECDQC: Efficient Compilation for Distributed Quantum Computing with Linear Layout

In this paper, we propose an efficient compilation method for distributed quantum computing (DQC) using the Linear Nearest Neighbor (LNN) architecture. By exploiting the LNN topology's symmetry, we optimize quantum circuit compilation for High Local Connectivity, Sparse Full Connectivity (HLC-SFC) algorithms like Quantum Approximate Optimization Algorithm (QAOA) and Quantum Fourier Transform (QFT). We also utilize dangling qubits to minimize non-local interactions and reduce SWAP gates. Our approach significantly decreases compilation time, gate count, and circuit depth, improving scalability and robustness for large-scale quantum computations.

quant-ph↗
arXiv2024

A comparison on constrain encoding methods for quantum approximate optimization algorithm

The Quantum Approximate Optimization Algorithm (QAOA) represents a significant opportunity for practical quantum computing applications, particularly in the era before error correction is fully realized. This algorithm is especially relevant for addressing constraint satisfaction problems (CSPs), which are critical in various fields such as supply chain management, energy distribution, and financial modeling. In our study, we conduct a numerical comparison of three different strategies for incorporating linear constraints into QAOA: transforming them into an unconstrained format, introducing penalty dephasing, and utilizing the quantum Zeno effect. We assess the efficiency and effectiveness of these methods using the knapsack problem as a case study. Our findings provide insights into the potential applicability of different encoding methods for various use cases.

quant-ph↗
arXiv2024

Coqa: Blazing Fast Compiler Optimizations for QAOA

The Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage over classical computers. However, existing compilers lack specialized methods for optimizing QAOA circuits. There are circuit patterns inside the QAOA circuits, and current quantum hardware has specific qubit connectivity topologies. Therefore, we propose Coqa to optimize QAOA circuit compilation tailored to different types of quantum hardware. Our method integrates a linear nearest-neighbor (LNN) topology and efficiently map the patterns of QAOA circuits to the LNN topology by heuristically checking the interaction based on the weight of problem Hamiltonian. This approach allows us to reduce the number of SWAP gates during compilation, which directly impacts the circuit depth and overall fidelity of the quantum computation. By leveraging the inherent patterns in QAOA circuits, our approach achieves more efficient compilation compared to general-purpose compilers. With our proposed method, we are able to achieve an average of 30% reduction in gate count and a 39x acceleration in compilation time across our benchmarks.

quant-ph↗
arXiv2024

Dynamic Modeling of Sparse Longitudinal Data and Functional Snippets With Stochastic Differential Equations

Sparse functional/longitudinal data have attracted widespread interest due to the prevalence of such data in social and life sciences. A prominent scenario where such data are routinely encountered are accelerated longitudinal studies, where subjects are enrolled in the study at a random time and are only tracked for a short amount of time relative to the domain of interest. The statistical analysis of such functional snippets is challenging since information for the far-off-diagonal regions of the covariance structure is missing. Our main methodological contribution is to address this challenge by bypassing covariance estimation and instead modeling the underlying process as the solution of a data-adaptive stochastic differential equation. Taking advantage of the interface between Gaussian functional data and stochastic differential equations makes it possible to efficiently reconstruct the target process by estimating its dynamic distribution. The proposed approach allows one to consistently recover forward sample paths from functional snippets at the subject level. We establish the existence and uniqueness of the solution to the proposed data-driven stochastic differential equation and derive rates of convergence for the corresponding estimators. The finite-sample performance is demonstrated with simulation studies and functional snippets arising from a growth study and spinal bone mineral density data.

stat.ME↗
arXiv2024

EPOC: A Novel Pulse Generation Framework Incorporating Advanced Synthesis Techniques for Quantum Circuits

In this paper we propose EPOC, an efficient pulse generation framework for quantum circuits that combines ZX-Calculus, circuit partitioning, and circuit synthesis to accelerate pulse generation. Unlike previous works that focus on generating pulses from unitary matrices without exploring equivalent representations, EPOC employs a finer granularity approach by grouping quantum gates and decomposing the resulting unitary matrices into smaller ones using synthesis techniques. This enables increased parallelism and decreased latency in quantum pulses. EPOC also continuously optimizes the circuit by identifying equivalent representations, leading to further reductions in circuit latency while minimizing the computational overhead associated with quantum optimal control. We introduce circuit synthesis into the workflow of quantum optimal control for the first time and achieve a 31.74% reduction in latency compared to previous work and a 76.80% reduction compared to the gate-based method for creating pulses. The approach demonstrates the potential for significant performance improvements in quantum circuits while minimizing computational overhead.

quant-ph↗
arXiv2023

Graphs with girth $2\ell+1$ and without longer odd holes that contain an odd $K_4$-subdivision

We say that a graph $G$ has an {\em odd $K_4$-subdivision} if some subgraph of $G$ is isomorphic to a $K_4$-subdivision and whose faces are all odd holes of $G$. For a number $\ell\geq 2$, let $\mathcal{G}_{\ell}$ denote the family of graphs which have girth $2\ell+1$ and have no odd hole with length greater than $2\ell+1$. Wu, Xu and Xu conjectured that every graph in $\bigcup_{\ell\geq2}\mathcal{G}_{\ell}$ is 3-colorable. Recently, Chudnovsky et al. and Wu et al., respectively, proved that every graph in $\mathcal{G}_2$ and $\mathcal{G}_3$ is 3-colorable. In this paper, we prove that no $4$-vertex-critical graph in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ has an odd $K_4$-subdivision. Using this result, Chen proved that all graphs in $\bigcup_{\ell\geq5}\mathcal{G}_{\ell}$ are 3-colorable.

math.CO↗
arXiv2023

Wasserstein Regression with Empirical Measures and Density Estimation for Sparse Data

The problem of modeling the relationship between univariate distributions and one or more explanatory variables has found increasing interest. Traditional functional data methods cannot be applied directly to distributional data because of their inherent constraints. Modeling distributions as elements of the Wasserstein space, a geodesic metric space equipped with the Wasserstein metric that is related to optimal transport, is attractive for statistical applications. Existing approaches proceed by substituting proxy estimated distributions for the typically unknown response distributions. These estimates are obtained from available data but are problematic when for some of the distributions only few data are available. Such situations are common in practice and cannot be addressed with available approaches, especially when one aims at density estimates. We show how this and other problems associated with density estimation such as tuning parameter selection and bias issues can be side-stepped when covariates are available. We also introduce a novel version of distribution-response regression that is based on empirical measures. By avoiding the preprocessing step of recovering complete individual response distributions, the proposed approach is applicable when the sample size available for some of the distributions is small. In this case, one can still obtain consistent distribution estimates even for distributions with only few data by gaining strength across the entire sample of distributions, while traditional approaches where distributions or densities are estimated individually fail, since sparsely sampled densities cannot be consistently estimated. The proposed model is demonstrated to outperform existing approaches through simulations. Its efficacy is corroborated in two case studies on Environmental Influences on Child Health Outcomes (ECHO) data and eBay auction data.

stat.ME↗
arXiv2022

Network Regression with Graph Laplacians

Network data are increasingly available in various research fields, motivating statistical analysis for populations of networks where a network as a whole is viewed as a data point. Due to the non-Euclidean nature of networks, basic statistical tools available for scalar and vector data are no longer applicable when one aims to relate networks as outcomes to Euclidean covariates, while the study of how a network changes in dependence on covariates is often of paramount interest. This motivates to extend the notion of regression to the case of responses that are network data. Here we propose to adopt conditional Fréchet means implemented with both global least squares regression and local weighted least squares smoothing, extending the Fréchet regression concept to networks that are quantified by their graph Laplacians. The challenge is to characterize the space of graph Laplacians so as to justify the application of Fréchet regression. This characterization then leads to asymptotic rates of convergence for the corresponding M-estimators by applying empirical process methods. We demonstrate the usefulness and good practical performance of the proposed framework with simulations and with network data arising from resting-state fMRI in neuroimaging, as well as New York taxi records.

stat.ME↗
arXiv2021

Learning delay dynamics for multivariate stochastic processes, with application to the prediction of the growth rate of COVID-19 cases in the United States

Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasing attention in recent years. Motivated by the challenge to predict the COVID-19 caseload trajectories for individual states in the U.S., we target here the inverse problem. Given a sample of observed random trajectories obeying an unknown random differential equation model with delay, we use a functional data analysis framework to learn the model parameters that govern the underlying dynamics from the data. We show existence and uniqueness of the analytical solutions of the population delay random differential equation model when one has discrete time delays in the functional concurrent regression model and also for a second scenario where one has a delay continuum or distributed delay. The latter involves a functional linear regression model with history index. The derivative of the process of interest is modeled using the process itself as predictor and also other functional predictors with predictor-specific delayed impacts. This dynamics learning approach is shown to be well suited to model the growth rate of COVID-19 for the states that are part of the U.S., by pooling information from the individual states, using the case process and concurrently observed economic and mobility data as predictors.

math.AP↗