arXiv subjects

Bingqing Hu

Publications and source records attributed to Bingqing Hu.

5 recordsLinked to original sources

arXiv2026

RAGTIMER 1.0: Rapid Rare-Event Partial State Space Construction for Stochastic VAS (extended version)

Transient reachability analysis of rare events in Continuous-Time Stochastic Vector Addition Systems (CTSVAS) such as Chemical Reaction Networks (CRNs) has proven a formidable challenge to cutting-edge tools. Underlying a CTSVAS is a continuous-time Markov chain (CTMC), and CTMC transient reachability analysis calls for Probabilistic Model Checking (PMC). This analysis requires the explicit representation of a model's entire state space. Rare events occur with extremely low probability, compounding the challenge of probabilistic analysis. In CRNs, it is imperative to verify the probability of rare events; even a low concentration of a species can have pathological consequences. This paper presents the RAGTIMER 1.0 tool, which efficiently builds a partial state space for a CTSVAS by enumerating traces to a rare event of interest and expanding them to exploit concurrency and cycles, providing a guaranteed lower bound on the probability of a rare event. Guaranteed lower bounds are particularly useful in synthetic biological applications because they indicate how and when a rare event can be experimentally observed. RAGTIMER is an attractive alternative to existing rare event analysis methods for CTSVAS models. It outperforms existing PMC tools and refutes multiple probability estimates from rare-event stochastic simulation on multiple challenging CRN models. RAGTIMER uses optimized data structures, a simple input format, and memory-safe Rust code to improve the scalability and accessibility of PMC for industry professionals.

cs.FL↗

arXiv2026

Conditional Distribution Estimation Given Functional Covariates Using Deep Operator Networks

Functional linear models are commonly used for analyzing functional data with scalar responses, particularly for modeling the conditional mean of the response given functional covariates. In this work, we extend the traditional scalar-on-function regression in two major aspects: 1. estimating the conditional distribution function instead of a particular characteristic such as the conditional mean; 2. considering an arbitrary operator without imposing functional linearity or any model assumption. We use a likelihood approach for the conditional hazard function and apply convolutional neural networks to approximate the effects of functional inputs and estimate the conditional distribution using deep operator networks. Through simulations and a real world data example, we show the desirable robustness of the proposed method in comparison with the mean regression neural networks, demonstrating that our approach achieves better conditional distribution estimation and interval prediction in complex data settings.

stat.ME↗

arXiv2025

Reasoning about Rare-Event Reachability in Stochastic Vector Addition Systems via Affine Vector Spaces

Rare events in Stochastic Vector Addition System (VAS) are of significant interest because, while extremely unlikely, they may represent undesirable behavior that can have adverse effects. Their low probabilities and potentially extremely large state spaces challenge existing probabilistic model checking and stochastic rare-event simulation techniques. In particular, in Chemical Reaction Networks (CRNs), a chemical kinetic language often represented as VAS, rare event effects may be pathological. We present two novel heuristics for priority-first partial state space expansion and trace generation tuned to the transient analysis of rare-event probability in VAS: Iterative Subspace Reduction (ISR) and Single Distance Priority (SDP). Both methods construct a closed vector space containing all solution states. SDP then simply prioritizes shorter distances to this ``solution space'', while ISR constructs a set of nested subspaces, where short and highly-probable satisfying traces are likely to pass through in sequence. The resulting partial state graph from each method contains likely traces to rare-event states, allowing efficient probabilistic model checking to compute a lower-bound probability of a rare event of interest. These methods are deterministic, fast, and demonstrate marked performance on challenging CRN models.

cs.FL↗

arXiv2025

Nonparametric Estimation of Conditional Survival Function with Time-Varying Covariates Using DeepONet

Traditional survival models often rely on restrictive assumptions such as proportional hazards or instantaneous effects of time-varying covariates on the hazard function, which limit their applicability in real-world settings. We consider the nonparametric estimation of the conditional survival function, which leverages the flexibility of neural networks to capture the complex, potentially long-term non-instantaneous effects of time-varying covariates. In this work, we use Deep Operator Networks (DeepONet), a deep learning architecture designed for operator learning, to model the arbitrary effects of both time-varying and time-invariant covariates. Specifically, our method relaxes commonly used assumptions in hazard regressions by modeling the conditional hazard function as an unknown nonlinear operator of entire histories of time-varying covariates. The estimation is based on a loss function constructed from the nonparametric full likelihood for censored survival data. Simulation studies demonstrate that our method performs well, whereas the Cox model yields biased results when the assumption of instantaneous time-varying covariate effects is violated. We further illustrate its utility with the ADNI data, for which it yields a lower integrated Brier score than the Cox model.

stat.ME↗

arXiv2022

Conditional Distribution Function Estimation Using Neural Networks for Censored and Uncensored Data

Most work in neural networks focuses on estimating the conditional mean of a continuous response variable given a set of covariates.In this article, we consider estimating the conditional distribution function using neural networks for both censored and uncensored data. The algorithm is built upon the data structure particularly constructed for the Cox regression with time-dependent covariates. Without imposing any model assumption, we consider a loss function that is based on the full likelihood where the conditional hazard function is the only unknown nonparametric parameter, for which unconstraint optimization methods can be applied. Through simulation studies, we show the proposed method possesses desirable performance, whereas the partial likelihood method and the traditional neural networks with $L_2$ loss yield biased estimates when model assumptions are violated. We further illustrate the proposed method with several real-world data sets. The implementation of the proposed methods is made available at https://github.com/bingqing0729/NNCDE.

stat.ME↗