arXiv subjects

Ning Ning

Publications and source records attributed to Ning Ning.

At least 37 records · Page 2Linked to original sources

arXiv2024

An Assessment of Ensemble Kalman Filter and Azouani-Olson-Titi Algorithms for Data Assimilation: A Comparative Study

Continuous data assimilation (CDA) is a method that continuously integrates observational data into a dynamical system to improve model accuracy in real-time. The AOT algorithm is one of the most widely used methods in CDA due to its efficiency in incorporating observational data to enhance model accuracy. However, no research to date has evaluated the performance of the AOT algorithm compared to the most widely used DA method, the ensemble Kalman filter (EnKF). Hence, in this paper, we conduct an extensive numerical examination to evaluate and compare these two algorithms for CDA problems with measurement error, addressing this gap. By analyzing the one-dimensional Kuramoto-Sivashinsky equation and the two-dimensional Navier-Stokes equation, which are central to many applications and representative in CDA problems, we found a significant computational advantage of the AOT algorithm.

math.OC↗

arXiv2024

VT-MRF-SPF: Variable Target Markov Random Field Scalable Particle Filter

Markov random fields (MRFs) are invaluable tools across diverse fields, and spatiotemporal MRFs (STMRFs) amplify their effectiveness by integrating spatial and temporal dimensions. However, modeling spatiotemporal data introduces additional hurdles, including dynamic spatial dimensions and partial observations, prevalent in scenarios like disease spread analysis and environmental monitoring. Tracking high-dimensional targets with complex spatiotemporal interactions over extended periods poses significant challenges in accuracy, efficiency, and computational feasibility. To tackle these obstacles, we introduce the variable target MRF scalable particle filter (VT-MRF-SPF), a fully online learning algorithm designed for high-dimensional target tracking over STMRFs with varying dimensions under partial observation. We rigorously guarantee algorithm performance, explicitly indicating overcoming the curse of dimensionality. Additionally, we provide practical guidelines for tuning graphical parameters, leading to superior performance in extensive examinations.

stat.ME↗

arXiv2024

Understanding Human-COVID-19 Dynamics using Geospatial Big Data: A Systematic Literature Review

The COVID-19 pandemic has changed human life. To mitigate the pandemic's impacts, different regions implemented various policies to contain COVID-19 and residents showed diverse responses. These human responses in turn shaped the uneven spatial-temporal spread of COVID-19. Consequently, the human-pandemic interaction is complex, dynamic, and interconnected. Delineating the reciprocal effects between human society and the pandemic is imperative for mitigating risks from future epidemics. Geospatial big data acquired through mobile applications and sensor networks have facilitated near-real-time tracking and assessment of human responses to the pandemic, enabling a surge in researching human-pandemic interactions. However, these investigations involve inconsistent data sources, human activity indicators, relationship detection models, and analysis methods, leading to a fragmented understanding of human-pandemic dynamics. To assess the current state of human-pandemic interactions research, we conducted a synthesis study based on 67 selected publications between March 2020 and January 2023. We extracted key information from each article across six categories, e.g., research area and time, data, methodological framework, and results and conclusions. Results reveal that regression models were predominant in relationship detection, featured in 67.16% of papers. Only two papers employed spatial-temporal models, notably underrepresented in the existing literature. Studies examining the effects of policies and human mobility on the pandemic's health impacts were the most prevalent, each comprising 12 articles (17.91%). Only 3 papers (4.48%) delved into bidirectional interactions between human responses and the COVID-19 spread. These findings shed light on the need for future research to spatially and temporally model the long-term, bidirectional causal relationships within human-pandemic systems.

physics.soc-ph↗

arXiv2024

Doubly Reflected Backward SDEs Driven by G-Brownian Motions and Fully Nonlinear PDEs with Double Obstacles

In this paper, we introduce a new method to study the doubly reflected backward stochastic differential equation driven by G-Brownian motion (G-BSDE). Our approach involves approximating the solution through a family of penalized reflected G-BSDEs with a lower obstacle that are monotone decreasing. By employing this approach, we establish the well-posedness of the solution of the doubly reflected G-BSDE with the weakest known conditions, and uncover its relationship with the fully nonlinear partial differential equation with double obstacles for the first time.

math.PR↗

arXiv2024

A&B BNN: Add&Bit-Operation-Only Hardware-Friendly Binary Neural Network

Binary neural networks utilize 1-bit quantized weights and activations to reduce both the model's storage demands and computational burden. However, advanced binary architectures still incorporate millions of inefficient and nonhardware-friendly full-precision multiplication operations. A&B BNN is proposed to directly remove part of the multiplication operations in a traditional BNN and replace the rest with an equal number of bit operations, introducing the mask layer and the quantized RPReLU structure based on the normalizer-free network architecture. The mask layer can be removed during inference by leveraging the intrinsic characteristics of BNN with straightforward mathematical transformations to avoid the associated multiplication operations. The quantized RPReLU structure enables more efficient bit operations by constraining its slope to be integer powers of 2. Experimental results achieved 92.30%, 69.35%, and 66.89% on the CIFAR-10, CIFAR-100, and ImageNet datasets, respectively, which are competitive with the state-of-the-art. Ablation studies have verified the efficacy of the quantized RPReLU structure, leading to a 1.14% enhancement on the ImageNet compared to using a fixed slope RLeakyReLU. The proposed add&bit-operation-only BNN offers an innovative approach for hardware-friendly network architecture.

cs.LG↗

arXiv2024

Inference on spatiotemporal dynamics for networks of biological populations

Mathematical models in ecology and epidemiology must be consistent with observed data in order to generate reliable knowledge and evidence-based policy. Metapopulation systems, which consist of a network of connected sub-populations, pose technical challenges in statistical inference due to nonlinear, stochastic interactions. Numerical difficulties encountered in conducting inference can obstruct the core scientific questions concerning the link between the mathematical models and the data. Recently, an algorithm has been developed which enables effective likelihood-based inference for the high-dimensional partially observed stochastic dynamic models arising in metapopulation systems. The COVID-19 pandemic provides a situation where mathematical models and their policy implications were widely visible, and we use the new inferential technology to revisit an influential metapopulation model used to inform basic epidemiological understanding early in the pandemic. Our methods support self-critical data analysis, enabling us to identify and address model limitations, and leading to a new model with substantially improved statistical fit and parameter identifiability. Our results suggest that the lockdown initiated on January 23, 2020 in China was more effective than previously thought. We proceed to recommend statistical analysis standards for future metapopulation system modeling.

stat.AP↗

arXiv2024

One-Dimensional McKean-Vlasov Stochastic Variational Inequalities and Coupled BSDEs with Locally Holder Noise Coefficients

In this article, we investigate three classes of equations: the McKean-Vlasov stochastic differential equation (MVSDE), the MVSDE with a subdifferential operator referred to as the McKean-Vlasov stochastic variational inequality (MVSVI), and the coupled forward-backward MVSVI. The latter class encompasses the FBSDE with reflection in a convex domain as a special case. We establish the well-posedness, in terms of the existence and uniqueness of a strong solution, for these three classes in their general forms. Importantly, we consider stochastic coefficients with locally Holder continuity and employ different strategies to achieve that for each class.

math.PR↗

arXiv2024

Propagation of chaos for doubly mean reflected BSDEs

In this paper, we establish propagation of chaos (POC) for doubly mean reflected backward stochastic differential equations (MRBSDEs). MRBSDEs differentiate the typical RBSDEs in that the constraint is not on the paths of the solution but on its law. This unique property has garnered significant attention since the inception of MRBSDEs. Rather than directly investigating these equations, we focus on approximating them by interacting particle systems (IPS). We propose two sets of IPS having mean-field Skorokhod problems, capturing the dynamics of IPS reflected in a mean-field way. As the dimension of the IPS tends to infinity, the POC phenomenon emerges, indicating that the system converges to a limit with independent particles, where each solves the MRBSDE. Beyond establishing the first POC result for doubly MRBSDEs, we achieve distinct convergence speeds under different scenarios.

math.PR↗

arXiv2023

Statistical Machine Learning Meets High-Dimensional Spatiotemporal Challenges -- A Case Study of COVID-19 Modeling

Diverse non-pharmacological interventions (NPIs), serving as the primary approach for COVID-19 control prior to pharmaceutical interventions, showed heterogeneous spatiotemporal effects on pandemic management. Investigating the dynamic compounding impacts of NPIs on pandemic spread is imperative. However, the challenges posed by data availability of high-dimensional human behaviors and the complexity of modeling changing and interrelated factors are substantial. To address these challenges, this study analyzed social media data, COVID-19 case rates, Apple mobility data, and the stringency of stay-at-home policies in the United States throughout the year 2020, aiming to (1) uncover the spatiotemporal variations in NPIs during the COVID-19 pandemic utilizing geospatial big data; (2) develop a statistical machine learning model that incorporates spatiotemporal dependencies and temporal lag effects for the detection of relationships; (3) dissect the impacts of NPIs on the pandemic across space and time. Three indices were computed based on Twitter (currently known as X) data: the Negative and Positive Sentiments Adjusted by Demographics (N-SAD and P-SAD) and the Ratio Adjusted by Demographics (RAD), representing negative sentiment, positive sentiment, and public awareness of COVID-19, respectively. The Multivariate Bayesian Structural Time Series Time Lagged model (MBSTS-TL) was proposed to investigate the effects of NPIs, accounting for spatial dependencies and temporal lag effects. The developed MBSTS-TL model exhibited a high degree of accuracy. Determinants of COVID-19 health impacts transitioned from an emphasis on human mobility during the initial outbreak period to a combination of human mobility and stay-at-home policies during the rapid spread phase, and ultimately to the compound of human mobility, stay-at-home policies, and public awareness of COVID-19.

stat.AP↗

arXiv2023

Bayesian Feature Selection in Joint Quantile Time Series Analysis

Quantile feature selection over correlated multivariate time series data has always been a methodological challenge and is an open problem. In this paper, we propose a general Bayesian dimension reduction methodology for feature selection in high-dimensional joint quantile time series analysis, under the name of the quantile feature selection time series (QFSTS) model. The QFSTS model is a general structural time series model, where each component yields an additive contribution to the time series modeling with direct interpretations. Its flexibility is compound in the sense that users can add/deduct components for each time series and each time series can have its own specific valued components of different sizes. Feature selection is conducted in the quantile regression component, where each time series has its own pool of contemporaneous external predictors allowing nowcasting. Bayesian methodology in extending feature selection to the quantile time series research area is developed using multivariate asymmetric Laplace distribution, spike-and-slab prior setup, the Metropolis-Hastings algorithm, and the Bayesian model averaging technique, all implemented consistently in the Bayesian paradigm. The QFSTS model requires small datasets to train and converges fast. Extensive examinations confirmed that the QFSTS model has superior performance in feature selection, parameter estimation, and forecast.

stat.ML↗

arXiv2023

Spike and slab Bayesian sparse principal component analysis

Sparse principal component analysis (SPCA) is a popular tool for dimensionality reduction in high-dimensional data. However, there is still a lack of theoretically justified Bayesian SPCA methods that can scale well computationally. One of the major challenges in Bayesian SPCA is selecting an appropriate prior for the loadings matrix, considering that principal components are mutually orthogonal. We propose a novel parameter-expanded coordinate ascent variational inference (PX-CAVI) algorithm. This algorithm utilizes a spike and slab prior, which incorporates parameter expansion to cope with the orthogonality constraint. Besides comparing to two popular SPCA approaches, we introduce the PX-EM algorithm as an EM analogue to the PX-CAVI algorithm for comparison. Through extensive numerical simulations, we demonstrate that the PX-CAVI algorithm outperforms these SPCA approaches, showcasing its superiority in terms of performance. We study the posterior contraction rate of the variational posterior, providing a novel contribution to the existing literature. The PX-CAVI algorithm is then applied to study a lung cancer gene expression dataset. The R package VBsparsePCA with an implementation of the algorithm is available on the Comprehensive R Archive Network (CRAN).

stat.ME↗

arXiv2023

Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality

Parameter learning for high-dimensional, partially observed, and nonlinear stochastic processes is a methodological challenge. Spatiotemporal disease transmission systems provide examples of such processes giving rise to open inference problems. We propose the iterated block particle filter (IBPF) algorithm for learning high-dimensional parameters over graphical state space models with general state spaces, measures, transition densities and graph structure. Theoretical performance guarantees are obtained on beating the curse of dimensionality (COD), algorithm convergence, and likelihood maximization. Experiments on a highly nonlinear and non-Gaussian spatiotemporal model for measles transmission reveal that the iterated ensemble Kalman filter algorithm (Li et al. (2020)) is ineffective and the iterated filtering algorithm (Ionides et al. (2015)) suffers from the COD, while our IBPF algorithm beats COD consistently across various experiments with different metrics.

stat.ML↗

arXiv2023

The mbsts package: Multivariate Bayesian Structural Time Series Models in R

The multivariate Bayesian structural time series (MBSTS) model is a general machine learning model that deals with inference and prediction for multiple correlated time series, where one also has the choice of using a different candidate pool of contemporaneous predictors for each target series. The MBSTS model has wide applications and is ideal for feature selection, time series forecasting, nowcasting, inferring causal impact, and others. This paper demonstrates how to use the R package mbsts for MBSTS modeling, establishing a bridge between user-friendly and developer-friendly functions in the package and the corresponding methodology. Object-oriented functions in the package are explained in the way that enables users to flexibly add or deduct some components, as well as to simplify or complicate some settings.

stat.ME↗

arXiv2022

An iterated block particle filter for inference on coupled dynamic systems with shared and unit-specific parameters

We consider inference for a collection of partially observed, stochastic, interacting, nonlinear dynamic processes. Each process is identified with a label called its unit, and our primary motivation arises in biological metapopulation systems where a unit corresponds to a spatially distinct sub-population. Metapopulation systems are characterized by strong dependence through time within a single unit and relatively weak interactions between units, and these properties make block particle filters an effective tool for simulation-based likelihood evaluation. Iterated filtering algorithms can facilitate likelihood maximization for simulation-based filters. We introduce an iterated block particle filter applicable when parameters are unit-specific or shared between units. We demonstrate this algorithm by performing inference on a coupled epidemiological model describing spatiotemporal measles case report data for twenty towns.

stat.ME↗

arXiv2022

Systemic Infinitesimal Over-dispersion on Graphical Dynamic Models

Stochastic models for collections of interacting populations have crucial roles in scientific fields such as epidemiology and ecology, yet the standard approach to extending an ordinary differential equation model to a Markov chain does not have sufficient flexibility in the mean-variance relationship to match data. To handle that, over-dispersed Markov chains have previously been constructed using gamma white noise on the rates. We develop new approaches using Dirichlet noise to construct collections of independent or dependent noise processes. This permits the modeling of high-frequency variation in transition rates both within and between the populations under study. Our theory is developed in a general framework of time-inhomogeneous Markov processes equipped with a graphical structure, for which ecological and epidemiological models provide motivating examples. We demonstrate our approach on a widely analyzed measles dataset, adding Dirichlet noise to a classical SEIR (Susceptible-Exposed-Infected-Recovered) model. Our methodology shows improved statistical fit measured by log-likelihood and provides new insights into the dynamics of this biological system.

stat.ME↗

arXiv2020

Scalable Monte Carlo Inference and Rescaled Local Asymptotic Normality

In this paper, we generalize the property of local asymptotic normality (LAN) to an enlarged neighborhood, under the name of rescaled local asymptotic normality (RLAN). We obtain sufficient conditions for a regular parametric model to satisfy RLAN. We show that RLAN supports the construction of a statistically efficient estimator which maximizes a cubic approximation to the log-likelihood on this enlarged neighborhood. In the context of Monte Carlo inference, we find that this maximum cubic likelihood estimator can maintain its statistical efficiency in the presence of asymptotically increasing Monte Carlo error in likelihood evaluation.

math.ST↗

arXiv2020

Well-posedness and Stability Analysis of Two Classes of Generalized Stochastic Volatility Models

In this paper, to cope with the shortage of sufficient theoretical support resulted from the fast-growing quantitative financial modeling, we investigate two classes of generalized stochastic volatility models, establish their well-posedness of strong solutions, and conduct the stability analysis with respect to small perturbations. In the first class, a multidimensional path-dependent process is driven by another multidimensional path-dependent process. The second class is a generalized one-dimensional stochastic volatility model with Hölder continuous coefficients. What greatly differentiates those two classes of models is that both the process and its correlated driving process have their own subdifferential operators, whose one special case is the general reflection operators for multi-sided barriers. Hence, the models investigated fully cover various newly explored variants of stochastic volatility models whose well-posedness is unknown, and naturally serve as the rigorous mathematical foundation for new stochastic volatility model development in terms of multi-dimension, path-dependence, and multi-sided barrier reflection.

math.PR↗

arXiv2020

Impact of positive ion energy on carbon-surface production of negative ions in deuterium plasmas

This work focuses on the production of negative-ions on graphite and diamond surfaces bombarded by positive ions in a low pressure (2 Pa) low power (20 W) capacitively coupled deuterium plasma. A sample is placed opposite a mass spectrometer and negatively biased so that surface produced negative ions can be self-extracted from the plasma and measured by the mass spectrometer. The ratio between negative-ion counts at mass spectrometer and positive ion current at sample surface defines a relative negative-ion yield. Changes in negative-ion production yields versus positive ion energy in the range 10-60 eV are analysed. While the negative-ion production yield is decreasing for diamond surfaces when increasing the positive ion impact energy, it is strongly increasing for graphite. This increase is attributed to the onset of the sputtering mechanisms between 20 and 40 eV which creates negative ions at rather low energy that are efficiently collected by the mass spectrometer. The same mechanism occurs for diamond but is mitigated by a strong decrease of the ionization probability due to defect creation and loss of diamond electronic properties.

physics.plasm-ph↗