arXiv subjects

Shixiang Zhu

Publications and source records attributed to Shixiang Zhu.

At least 55 records · Page 3Linked to original sources

arXiv2023

Multi-resolution spatio-temporal prediction with application to wind power generation

Wind energy is becoming an increasingly crucial component of a sustainable grid, but its inherent variability and limited predictability present challenges for grid operators. The energy sector needs novel forecasting techniques that can precisely predict the generation of renewable power and offer precise quantification of prediction uncertainty. This will facilitate well-informed decision-making by operators who wish to integrate renewable energy into the power grid. This paper presents a novel approach to wind speed prediction with uncertainty quantification using a multi-resolution spatio-temporal Gaussian process. By leveraging information from multiple sources of predictions with varying accuracies and uncertainties, the joint framework provides a more accurate and robust prediction of wind speed while measuring the uncertainty in these predictions. We assess the effectiveness of our proposed framework using real-world wind data obtained from the Midwest region of the United States. Our results demonstrate that the framework enables predictors with varying data resolutions to learn from each other, leading to an enhancement in overall predictive performance. The proposed framework shows a superior performance compared to other state-of-the-art methods. The goal of this research is to improve grid operation and management by aiding system operators and policymakers in making better-informed decisions related to energy demand management, energy storage system deployment, and energy supply scheduling. This results in potentially further integration of renewable energy sources into the existing power systems.

stat.AP↗

arXiv2023

Sequential Adversarial Anomaly Detection for One-Class Event Data

We consider the sequential anomaly detection problem in the one-class setting when only the anomalous sequences are available and propose an adversarial sequential detector by solving a minimax problem to find an optimal detector against the worst-case sequences from a generator. The generator captures the dependence in sequential events using the marked point process model. The detector sequentially evaluates the likelihood of a test sequence and compares it with a time-varying threshold, also learned from data through the minimax problem. We demonstrate our proposed method's good performance using numerical experiments on simulations and proprietary large-scale credit card fraud datasets. The proposed method can generally apply to detecting anomalous sequences.

stat.ML↗

arXiv2023

Non-stationary spatio-temporal point process modeling for high-resolution COVID-19 data

Most COVID-19 studies commonly report figures of the overall infection at a state- or county-level. This aggregation tends to miss out on fine details of virus propagation. In this paper, we analyze a high-resolution COVID-19 dataset in Cali, Colombia, that records the precise time and location of every confirmed case. We develop a non-stationary spatio-temporal point process equipped with a neural network-based kernel to capture the heterogeneous correlations among COVID-19 cases. The kernel is carefully crafted to enhance expressiveness while maintaining model interpretability. We also incorporate some exogenous influences imposed by city landmarks. Our approach outperforms the state-of-the-art in forecasting new COVID-19 cases with the capability to offer vital insights into the spatio-temporal interaction between individuals concerning the disease spread in a metropolis.

stat.AP↗

arXiv2022

Distributionally Robust Weighted $k$-Nearest Neighbors

Learning a robust classifier from a few samples remains a key challenge in machine learning. A major thrust of research has been focused on developing $k$-nearest neighbor ($k$-NN) based algorithms combined with metric learning that captures similarities between samples. When the samples are limited, robustness is especially crucial to ensure the generalization capability of the classifier. In this paper, we study a minimax distributionally robust formulation of weighted $k$-nearest neighbors, which aims to find the optimal weighted $k$-NN classifiers that hedge against feature uncertainties. We develop an algorithm, \texttt{Dr.k-NN}, that efficiently solves this functional optimization problem and features in assigning minimax optimal weights to training samples when performing classification. These weights are class-dependent, and are determined by the similarities of sample features under the least favorable scenarios. When the size of the uncertainty set is properly tuned, the robust classifier has a smaller Lipschitz norm than the vanilla $k$-NN, and thus improves the generalization capability. We also couple our framework with neural-network-based feature embedding. We demonstrate the competitive performance of our algorithm compared to the state-of-the-art in the few-training-sample setting with various real-data experiments.

stat.ML↗

arXiv2022

Neural Spectral Marked Point Processes

Self- and mutually-exciting point processes are popular models in machine learning and statistics for dependent discrete event data. To date, most existing models assume stationary kernels (including the classical Hawkes processes) and simple parametric models. Modern applications with complex event data require more general point process models that can incorporate contextual information of the events, called marks, besides the temporal and location information. Moreover, such applications often require non-stationary models to capture more complex spatio-temporal dependence. To tackle these challenges, a key question is to devise a versatile influence kernel in the point process model. In this paper, we introduce a novel and general neural network-based non-stationary influence kernel with high expressiveness for handling complex discrete events data while providing theoretical performance guarantees. We demonstrate the superior performance of our proposed method compared with the state-of-the-art on synthetic and real data.

cs.LG↗

arXiv2021

Data-Driven Optimization for Atlanta Police Zone Design

We present a data-driven optimization framework for redesigning police patrol zones in an urban environment. The objectives are to rebalance police workload among geographical areas and to reduce response time to emergency calls. We develop a stochastic model for police emergency response by integrating multiple data sources, including police incidents reports, demographic surveys, and traffic data. Using this stochastic model, we optimize zone redesign plans using mixed-integer linear programming. Our proposed design was implemented by the Atlanta Police Department in March 2019. By analyzing data before and after the zone redesign, we show that the new design has reduced the response time to high priority 911 calls by 5.8\% and the imbalance of police workload among different zones by 43\%.

math.OC↗

arXiv2021

Early Detection of COVID-19 Hotspots Using Spatio-Temporal Data

Recently, the Centers for Disease Control and Prevention (CDC) has worked with other federal agencies to identify counties with increasing coronavirus disease 2019 (COVID-19) incidence (hotspots) and offers support to local health departments to limit the spread of the disease. Understanding the spatio-temporal dynamics of hotspot events is of great importance to support policy decisions and prevent large-scale outbreaks. This paper presents a spatio-temporal Bayesian framework for early detection of COVID-19 hotspots (at the county level) in the United States. We assume both the observed number of cases and hotspots depend on a class of latent random variables, which encode the underlying spatio-temporal dynamics of the transmission of COVID-19. Such latent variables follow a zero-mean Gaussian process, whose covariance is specified by a non-stationary kernel function. The most salient feature of our kernel function is that deep neural networks are introduced to enhance the model's representative power while still enjoying the interpretability of the kernel. We derive a sparse model and fit the model using a variational learning strategy to circumvent the computational intractability for large data sets. Our model demonstrates better interpretability and superior hotspot-detection performance compared to other baseline methods.

stat.ML↗

arXiv2021

Spatial-Temporal-Textual Point Processes for Crime Linkage Detection

Crimes emerge out of complex interactions of human behaviors and situations. Linkages between crime incidents are highly complex. Detecting crime linkage given a set of incidents is a highly challenging task since we only have limited information, including text descriptions, incident times, and locations. In practice, there are very few labels. We propose a new statistical modeling framework for {\it spatio-temporal-textual} data and demonstrate its usage on crime linkage detection. We capture linkages of crime incidents via multivariate marked spatio-temporal Hawkes processes and treat embedding vectors of the free-text as {\it marks} of the incident, inspired by the notion of {\it modus operandi} (M.O.) in crime analysis. Numerical results using real data demonstrate the good performance of our method as well as reveals interesting patterns in the crime data: the joint modeling of space, time, and text information enhances crime linkage detection compared with the state-of-the-art, and the learned spatial dependence from data can be useful for police operations.

stat.ML↗

arXiv2021

Data-Driven Optimization for Police Beat Design in South Fulton, Georgia

We redesign the police patrol beat in South Fulton, Georgia, in collaboration with the South Fulton Police Department (SFPD), using a predictive data-driven optimization approach. Due to rapid urban development and population growth, the existing police beat design done in the 1970s was far from efficient, which leads to low policing efficiency and long 911 call response time. We balance the police workload among different city regions, improve operational efficiency, and reduce 911 call response time by redesigning beat boundaries for the SFPD. We discretize the city into small geographical atoms, which correspond to our decision variables; the decision is to map the atoms into "beats", the basic unit of the police operation. We first analyze workload and trend in each atom using the rich dataset, including police incidents reports and U.S. census data; We then predict future police workload for each atom using spatial statistical regression models; Lastly, we formulate the optimal beat design as a mixed-integer programming (MIP) program with continuity and compactness constraints on the beats' shape. The optimization problem is solved using simulated annealing due to its large-scale and non-convex nature. The simulation results suggest that our proposed beat design can reduce workload variance among beats significantly by over 90\%.

math.OC↗

arXiv2021

High-resolution Spatio-temporal Model for County-level COVID-19 Activity in the U.S

We present an interpretable high-resolution spatio-temporal model to estimate COVID-19 deaths together with confirmed cases one-week ahead of the current time, at the county-level and weekly aggregated, in the United States. A notable feature of our spatio-temporal model is that it considers the (a) temporal auto- and pairwise correlation of the two local time series (confirmed cases and death of the COVID-19), (b) dynamics between locations (propagation between counties), and (c) covariates such as local within-community mobility and social demographic factors. The within-community mobility and demographic factors, such as total population and the proportion of the elderly, are included as important predictors since they are hypothesized to be important in determining the dynamics of COVID-19. To reduce the model's high-dimensionality, we impose sparsity structures as constraints and emphasize the impact of the top ten metropolitan areas in the nation, which we refer (and treat within our models) as hubs in spreading the disease. Our retrospective out-of-sample county-level predictions were able to forecast the subsequently observed COVID-19 activity accurately. The proposed multi-variate predictive models were designed to be highly interpretable, with clear identification and quantification of the most important factors that determine the dynamics of COVID-19. Ongoing work involves incorporating more covariates, such as education and income, to improve prediction accuracy and model interpretability.

stat.AP↗

arXiv2021

Signal Processing Challenges and Examples for {\it in-situ} Transmission Electron Microscopy

Transmission Electron Microscopy (TEM) is a powerful tool for imaging material structure and characterizing material chemistry. Recent advances in data collection technology for TEM have enabled high-volume and high-resolution data collection at a microsecond frame rate. Taking advantage of these advances in data collection rates requires the development and application of data processing tools, including image analysis, feature extraction, and streaming data processing techniques. In this paper, we highlight a few areas in materials science that have benefited from combining signal processing and statistical analysis with data collection capabilities in TEM and present a future outlook on opportunities of integrating signal processing with automated TEM data analysis.

cs.CV↗

arXiv2021

Spatio-Temporal Point Processes with Attention for Traffic Congestion Event Modeling

We present a novel framework for modeling traffic congestion events over road networks. Using multi-modal data by combining count data from traffic sensors with police reports that report traffic incidents, we aim to capture two types of triggering effect for congestion events. Current traffic congestion at one location may cause future congestion over the road network, and traffic incidents may cause spread traffic congestion. To model the non-homogeneous temporal dependence of the event on the past, we use a novel attention-based mechanism based on neural networks embedding for point processes. To incorporate the directional spatial dependence induced by the road network, we adapt the "tail-up" model from the context of spatial statistics to the traffic network setting. We demonstrate our approach's superior performance compared to the state-of-the-art methods for both synthetic and real data.

cs.LG↗

arXiv2021

Deep Fourier Kernel for Self-Attentive Point Processes

We present a novel attention-based model for discrete event data to capture complex non-linear temporal dependence structures. We borrow the idea from the attention mechanism and incorporate it into the point processes' conditional intensity function. We further introduce a novel score function using Fourier kernel embedding, whose spectrum is represented using neural networks, which drastically differs from the traditional dot-product kernel and can capture a more complex similarity structure. We establish our approach's theoretical properties and demonstrate our approach's competitive performance compared to the state-of-the-art for synthetic and real data.

stat.ML↗

arXiv2021

Goodness-of-Fit Test for Mismatched Self-Exciting Processes

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative model captures the nature or ground-truth since it is usually unknown. The challenge typically lies in the fact that the generative models typically provide, at most, good approximations to the ground-truth (e.g., through the rich representative power of neural networks), but they cannot be precisely the ground-truth. We thus cannot use the classic goodness-of-fit (GOF) test framework to evaluate their performance. In this paper, we develop a GOF test for generative models of self-exciting processes by making a new connection to this problem with the classical statistical theory of Quasi-maximum-likelihood estimator (QMLE). We present a non-parametric self-normalizing statistic for the GOF test: the Generalized Score (GS) statistics, and explicitly capture the model misspecification when establishing the asymptotic distribution of the GS statistic. Numerical simulation and real-data experiments validate our theory and demonstrate the proposed GS test's good performance.

math.ST↗

arXiv2021

Balanced Districting on Grid Graphs with Provable Compactness and Contiguity

Given a graph $G = (V,E)$ with vertex weights $w(v)$ and a desired number of parts $k$, the goal in graph partitioning problems is to partition the vertex set V into parts $V_1,\ldots,V_k$. Metrics for compactness, contiguity, and balance of the parts $V_i$ are frequent objectives, with much existing literature focusing on compactness and balance. Revisiting an old method known as striping, we give the first polynomial-time algorithms with guaranteed contiguity and provable bicriteria approximations for compactness and balance for planar grid graphs. We consider several types of graph partitioning, including when vertex weights vary smoothly or are stochastic, reflecting concerns in various real-world instances. We show significant improvements in experiments for balancing workloads for the fire department and reducing over-policing using 911 call data from South Fulton, GA.

cs.DS↗

arXiv2021

Imitation Learning of Neural Spatio-Temporal Point Processes

We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete event data, the study of spatial-temporal aspects of such data is relatively scarce. Our model captures complex spatio-temporal dependence between discrete events by carefully design a mixture of heterogeneous Gaussian diffusion kernels, whose parameters are parameterized by neural networks. This new kernel is the key that our model can capture intricate spatial dependence patterns and yet still lead to interpretable results as we examine maps of Gaussian diffusion kernel parameters. The imitation learning model fitting for the NEST is more robust than the maximum likelihood estimate. It directly measures the divergence between the empirical distributions between the training data and the model-generated data. Moreover, our imitation learning-based approach enjoys computational efficiency due to the explicit characterization of the reward function related to the likelihood function; furthermore, the likelihood function under our model enjoys tractable expression due to Gaussian kernel parameterization. Experiments based on real data show our method's good performance relative to the state-of-the-art and the good interpretability of NEST's result.

cs.LG↗

arXiv2020

Learning Temporal Point Processes via Reinforcement Learning

Social goods, such as healthcare, smart city, and information networks, often produce ordered event data in continuous time. The generative processes of these event data can be very complex, requiring flexible models to capture their dynamics. Temporal point processes offer an elegant framework for modeling event data without discretizing the time. However, the existing maximum-likelihood-estimation (MLE) learning paradigm requires hand-crafting the intensity function beforehand and cannot directly monitor the goodness-of-fit of the estimated model in the process of training. To alleviate the risk of model-misspecification in MLE, we propose to generate samples from the generative model and monitor the quality of the samples in the process of training until the samples and the real data are indistinguishable. We take inspiration from reinforcement learning (RL) and treat the generation of each event as the action taken by a stochastic policy. We parameterize the policy as a flexible recurrent neural network and gradually improve the policy to mimic the observed event distribution. Since the reward function is unknown in this setting, we uncover an analytic and nonparametric form of the reward function using an inverse reinforcement learning formulation. This new RL framework allows us to derive an efficient policy gradient algorithm for learning flexible point process models, and we show that it performs well in both synthetic and real data.

cs.LG↗

arXiv2018

Crime Event Embedding with Unsupervised Feature Selection

We present a novel event embedding algorithm for crime data that can jointly capture time, location, and the complex free-text component of each event. The embedding is achieved by regularized Restricted Boltzmann Machines (RBMs), and we introduce a new way to regularize by imposing a $\ell_1$ penalty on the conditional distributions of the observed variables of RBMs. This choice of regularization performs feature selection and it also leads to efficient computation since the gradient can be computed in a closed form. The feature selection forces embedding to be based on the most important keywords, which captures the common modus operandi (M. O.) in crime series. Using numerical experiments on a large-scale crime dataset, we show that our regularized RBMs can achieve better event embedding and the selected features are highly interpretable from human understanding.

stat.ML↗