Zezhong Zhang

Zezhong Zhang, Feng Bao, Guannan Zhang

The Ensemble Score Filter (EnSF) is a score-based diffusion model approach for solving high-dimensional and nonlinear data assimilation problems. While initial applications of EnSF to the Lorenz-96 model and the quasi-geostrophic system showed potential, the current method employs a heuristic weighted sum to combine the prior and the likelihood score functions. This introduces a structural error into the estimation of the posterior score function in the nonlinear setting. This work addresses this challenge by developing an iterative ensemble score filter (IEnSF) that applies an iterative algorithm as an outer loop around the reverse-time stochastic differential equation solver. When the state dynamics or the observation operator is nonlinear, the iterative algorithm can gradually reduce the posterior score estimation error by improving the accuracy of approximating the conditional expectation of the likelihood score function. The number of iterations required depends on the distance between the prior and posterior distributions. Numerical experiments demonstrate that the IEnSF algorithm substantially reduces the error in posterior score estimation in the nonlinear setting and thus improves the accuracy of tracking high-dimensional dynamical systems.

Zezhong Zhang, Guangxu Zhu, Shuguang Cui

In recent years, the exponential increase in the demand of wireless data transmission rises the urgency for accurate spectrum sensing approaches to improve spectrum efficiency. The unreliability of conventional spectrum sensing methods by using measurements from a single secondary user (SU) has motivated research on cooperative spectrum sensing (CSS). In this work, we propose a vertical federated learning (VFL) framework to exploit the distributed features across multiple SUs without compromising data privacy. However, the repetitive training process in VFL faces the issue of high communication latency. To accelerate the training process, we propose a truncated vertical federated learning (T-VFL) algorithm, where the training latency is highly reduced by integrating the standard VFL algorithm with a channel-aware user scheduling policy. The convergence performance of T-VFL is provided via mathematical analysis and justified by simulation results. Moreover, to guarantee the convergence performance of the T-VFL algorithm, we conclude three design rules on the neural architectures used under the VFL framework, whose effectiveness is proved through simulations.

Shanfeng Huang, Zezhong Zhang, Shuai Wang et al.

Federated edge learning (FEEL) is envisioned as a promising paradigm to achieve privacy-preserving distributed learning. However, it consumes excessive learning time due to the existence of straggler devices. In this paper, a novel topology-optimized federated edge learning (TOFEL) scheme is proposed to tackle the heterogeneity issue in federated learning and to improve the communication-and-computation efficiency. Specifically, a problem of jointly optimizing the aggregation topology and computing speed is formulated to minimize the weighted summation of energy consumption and latency. To solve the mixed-integer nonlinear problem, we propose a novel solution method of penalty-based successive convex approximation, which converges to a stationary point of the primal problem under mild conditions. To facilitate real-time decision making, an imitation-learning based method is developed, where deep neural networks (DNNs) are trained offline to mimic the penalty-based method, and the trained imitation DNNs are deployed at the edge devices for online inference. Thereby, an efficient imitate-learning based approach is seamlessly integrated into the TOFEL framework. Simulation results demonstrate that the proposed TOFEL scheme accelerates the federated learning process, and achieves a higher energy efficiency. Moreover, we apply the scheme to 3D object detection with multi-vehicle point cloud datasets in the CARLA simulator. The results confirm the superior learning performance of the TOFEL scheme over conventional designs with the same resource and deadline constraints.

Sumin Shen, Huiying Mao, Zezhong Zhang et al.

In online experimentation, appropriate metrics (e.g., purchase) provide strong evidence to support hypotheses and enhance the decision-making process. However, incomplete metrics are frequently occurred in the online experimentation, making the available data to be much fewer than the planned online experiments (e.g., A/B testing). In this work, we introduce the concept of dropout buyers and categorize users with incomplete metric values into two groups: visitors and dropout buyers. For the analysis of incomplete metrics, we propose a clustering-based imputation method using $k$-nearest neighbors. Our proposed imputation method considers both the experiment-specific features and users' activities along their shopping paths, allowing different imputation values for different users. To facilitate efficient imputation of large-scale data sets in online experimentation, the proposed method uses a combination of stratification and clustering. The performance of the proposed method is compared to several conventional methods in both simulation studies and a real online experiment at eBay.

Zezhong Zhang, Feng Bao, Lili Ju et al.

Transfer learning for partial differential equations (PDEs) is to develop a pre-trained neural network that can be used to solve a wide class of PDEs. Existing transfer learning approaches require much information of the target PDEs such as its formulation and/or data of its solution for pre-training. In this work, we propose to construct transferable neural feature spaces from purely function approximation perspectives without using PDE information. The construction of the feature space involves re-parameterization of the hidden neurons and uses auxiliary functions to tune the resulting feature space. Theoretical analysis shows the high quality of the produced feature space, i.e., uniformly distributed neurons. Extensive numerical experiments verify the outstanding performance of our method, including significantly improved transferability, e.g., using the same feature space for various PDEs with different domains and boundary conditions, and the superior accuracy, e.g., several orders of magnitude smaller mean squared error than the state of the art methods.

Yanfang Liu, Minglei Yang, Zezhong Zhang et al.

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require to use reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the UCI repository.

Ted Tao Yuan, Zezhong Zhang

To recommend relevant merchandises for seasonal retail events, we rely on item retrieval from marketplace inventory. With feedback to expand query scope, we discuss keyword expansion candidate selection using word embedding similarity, and an enhanced tf-idf formula for expanded words in search ranking.

Xiucheng Wang, Qiming Zhang, Nan Cheng et al.

Radio maps (RMs) serve as a critical foundation for enabling environment-aware wireless communication, as they provide the spatial distribution of wireless channel characteristics. Despite recent progress in RM construction using data-driven approaches, most existing methods focus solely on pathloss prediction in a fixed 2D plane, neglecting key parameters such as direction of arrival (DoA), time of arrival (ToA), and vertical spatial variations. Such a limitation is primarily due to the reliance on static learning paradigms, which hinder generalization beyond the training data distribution. To address these challenges, we propose UrbanRadio3D, a large-scale, high-resolution 3D RM dataset constructed via ray tracing in realistic urban environments. UrbanRadio3D is over 37$\times$3 larger than previous datasets across a 3D space with 3 metrics as pathloss, DoA, and ToA, forming a novel 3D$\times$33D dataset with 7$\times$3 more height layers than prior state-of-the-art (SOTA) dataset. To benchmark 3D RM construction, a UNet with 3D convolutional operators is proposed. Moreover, we further introduce RadioDiff-3D, a diffusion-model-based generative framework utilizing the 3D convolutional architecture. RadioDiff-3D supports both radiation-aware scenarios with known transmitter locations and radiation-unaware settings based on sparse spatial observations. Extensive evaluations on UrbanRadio3D validate that RadioDiff-3D achieves superior performance in constructing rich, high-dimensional radio maps under diverse environmental dynamics. This work provides a foundational dataset and benchmark for future research in 3D environment-aware communication. The dataset is available at https://github.com/UNIC-Lab/UrbanRadio3D.

Ming Fan, Zezhong Zhang, Dan Lu et al.

We introduce GenAI4UQ, a software package for inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting in scientific applications. GenAI4UQ leverages a generative artificial intelligence (AI) based conditional modeling framework to address the limitations of traditional inverse modeling techniques, such as Markov Chain Monte Carlo methods. By replacing computationally intensive iterative processes with a direct, learned mapping, GenAI4UQ enables efficient calibration of model input parameters and generation of output predictions directly from observations. The software's design allows for rapid ensemble forecasting with robust uncertainty quantification, while maintaining high computational and storage efficiency. GenAI4UQ simplifies the model training process through built-in auto-tuning of hyperparameters, making it accessible to users with varying levels of expertise. Its conditional generative framework ensures versatility, enabling applicability across a wide range of scientific domains. At its core, GenAI4UQ transforms the paradigm of inverse modeling by providing a fast, reliable, and user-friendly solution. It empowers researchers and practitioners to quickly estimate parameter distributions and generate model predictions for new observations, facilitating efficient decision-making and advancing the state of uncertainty quantification in computational modeling. (The code and data are available at https://github.com/patrickfan/GenAI4UQ).

Zezhong Zhang, Feng Bao, Guannan Zhang

The impressive expressive power of deep neural networks (DNNs) underlies their widespread applicability. However, while the theoretical capacity of deep architectures is high, the practical expressive power achieved through successful training often falls short. Building on the insights gained from Neural ODEs, which explore the depth of DNNs as a continuous variable, in this work, we generalize the traditional fully connected DNN through the concept of continuous width. In the Generalized Deep Neural Network (GDNN), the traditional notion of neurons in each layer is replaced by a continuous state function. Using the finite rank parameterization of the weight integral kernel, we establish that GDNN can be obtained by employing the Integral Activation Transform (IAT) as activation layers within the traditional DNN framework. The IAT maps the input vector to a function space using some basis functions, followed by nonlinear activation in the function space, and then extracts information through the integration with another collection of basis functions. A specific variant, IAT-ReLU, featuring the ReLU nonlinearity, serves as a smooth generalization of the scalar ReLU activation. Notably, IAT-ReLU exhibits a continuous activation pattern when continuous basis functions are employed, making it smooth and enhancing the trainability of the DNN. Our numerical experiments demonstrate that IAT-ReLU outperforms regular ReLU in terms of trainability and better smoothness.

Feng Bao, Zezhong Zhang, Guannan Zhang

We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low accuracy in handling high-dimensional and highly nonlinear problems. EnSF attacks this challenge by exploiting the score-based diffusion model, defined in a pseudo-temporal domain, to characterizing the evolution of the filtering density. EnSF stores the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). Unlike existing diffusion models that train neural networks to approximate the score function, we develop a training-free score estimation that uses a mini-batch-based Monte Carlo estimator to directly approximate the score function at any pseudo-spatial-temporal location, which provides sufficient accuracy in solving high-dimensional nonlinear problems as well as saves a tremendous amount of time spent on training neural networks. High-dimensional Lorenz-96 systems are used to demonstrate the performance of our method. EnSF provides surprising performance, compared with the state-of-the-art Local Ensemble Transform Kalman Filter method, in reliably and efficiently tracking extremely high-dimensional Lorenz systems (up to 1,000,000 dimensions) with highly nonlinear observation processes.

Zezhong Zhang, Ted Yuan

Online controlled experiments have emerged as industry gold standard for assessing new web features. As new web algorithms proliferate, experimentation platform faces an increasing demand on the velocity of online experiments, which encourages adaptive traffic testing methods to speed up identifying best variant by efficiently allocating traffic. This paper proposed four Bayesian batch bandit algorithms (NB-TS, WB-TS, NB-TTTS, WB-TTTS) for eBay's experimentation platform, using summary batch statistics of a goal metric without incurring new engineering technical debts. The novel WB-TTTS, in particular, demonstrates as an efficient, trustworthy and robust alternative to fixed horizon A/B testing. Another novel contribution is to bring trustworthiness of best arm identification algorithms into evaluation criterion and highlight the existence of severe false positive inflation with equivalent best arms. To gain the trust of experimenters, experimentation platform must consider both efficiency and trustworthiness; However, to the best of authors' knowledge, trustworthiness as an important topic is rarely discussed. This paper shows that Bayesian bandits without neutral posterior reshaping, particularly naive Thompson sampling (NB-TS), are untrustworthy because they can always identify an arm as the best from equivalent best arms. To restore trustworthiness, a novel finding uncovers connections between convergence distribution of posterior optimal probabilities of equivalent best arms and neutral posterior reshaping, which controls false positives. Lastly, this paper presents lessons learned from eBay's experience, as well as thorough evaluations. We hope this work is useful to other industrial practitioners and inspires academic researchers interested in the trustworthiness of adaptive traffic experimentation.

Zezhong Zhang, Guangxu Zhu, Rui Wang et al.

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the linear structure of a dataset, which is useful for feature extraction and data compression. In this work, we propose the deployment of distributed PCA over a multi-access channel based on the algorithm of stochastic gradient descent to learn the dominant feature space of a distributed dataset at multiple devices. Over-the-air aggregation is adopted to reduce the multi-access latency, giving the name over-the-air PCA. The novelty of this design lies in exploiting channel noise to accelerate the descent in the region around each saddle point encountered by gradient descent, thereby increasing the convergence speed of over-the-air PCA. The idea is materialized by proposing a power-control scheme which detects the type of descent region and controlling the level of channel noise accordingly. The scheme is proved to achieve a faster convergence rate than in the case without power control.

Zezhong Zhang, Keyu Nie, Ted Tao Yuan

At eBay, there are thousands of product health metrics for different domain teams to monitor. We built a two-phase alerting system to notify users with actionable alerts based on anomaly detection and alert retrieval. In the first phase, we developed an efficient anomaly detection algorithm, called Moving Metric Detector (MMD), to identify potential alerts among metrics with distribution agnostic criteria. In the second alert retrieval phase, we built additional logic with feedbacks to select valid actionable alerts with point-wise ranking model and business rules. Compared with other trend and seasonality decomposition methods, our decomposer is faster and better to detect anomalies in unsupervised cases. Our two-phase approach dramatically improves alert precision and avoids alert spamming in eBay production.

Keyu Nie, Zezhong Zhang, Ted Tao Yuan et al.

In this paper, we solve the arms exponential exploding issue in multivariate Multi-Armed Bandit (Multivariate-MAB) problem when the arm dimension hierarchy is considered. We propose a framework called path planning (TS-PP) which utilizes decision graph/trees to model arm reward success rate with m-way dimension interaction, and adopts Thompson sampling (TS) for heuristic search of arm selection. Naturally, it is quite straightforward to combat the curse of dimensionality using a serial processes that operates sequentially by focusing on one dimension per each process. For our best acknowledge, we are the first to solve Multivariate-MAB problem using graph path planning strategy and deploying alike Monte-Carlo tree search ideas. Our proposed method utilizing tree models has advantages comparing with traditional models such as general linear regression. Simulation studies validate our claim by achieving faster convergence speed, better efficient optimal arm allocation and lower cumulative regret.