arXiv subjects

Ruijian Han

Publications and source records attributed to Ruijian Han.

24 records · Page 2Linked to original sources

arXiv2023

An approximate control variates approach to multifidelity distribution estimation

Forward simulation-based uncertainty quantification that studies the distribution of quantities of interest (QoI) is a crucial component for computationally robust engineering design and prediction. There is a large body of literature devoted to accurately assessing statistics of QoIs, and in particular, multilevel or multifidelity approaches are known to be effective, leveraging cost-accuracy tradeoffs between a given ensemble of models. However, effective algorithms that can estimate the full distribution of QoIs are still under active development. In this paper, we introduce a general multifidelity framework for estimating the cumulative distribution function (CDF) of a vector-valued QoI associated with a high-fidelity model under a budget constraint. Given a family of appropriate control variates obtained from lower-fidelity surrogates, our framework involves identifying the most cost-effective model subset and then using it to build an approximate control variates estimator for the target CDF. We instantiate the framework by constructing a family of control variates using intermediate linear approximators and rigorously analyze the corresponding algorithm. Our analysis reveals that the resulting CDF estimator is uniformly consistent and asymptotically optimal as the budget tends to infinity, with only mild moment and regularity assumptions on the joint distribution of QoIs. The approach provides a robust multifidelity CDF estimator that is adaptive to the available budget, does not require \textit{a priori} knowledge of cross-model statistics or model hierarchy, and applies to multiple dimensions. We demonstrate the efficiency and robustness of the approach using test examples of parametric PDEs and stochastic differential equations including both academic instances and more challenging engineering problems.

stat.CO↗

arXiv2022

Probabilistic methods for approximate archetypal analysis

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided the data is approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of archetypal analysis. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of archetypal analysis. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets.

stat.CO↗

arXiv2022

A General Pairwise Comparison Model for Extremely Sparse Networks

Statistical inference using pairwise comparison data is an effective approach to analyzing large-scale sparse networks. In this paper, we propose a general framework to model the mutual interactions in a network, which enjoys ample flexibility in terms of model parametrization. Under this setup, we show that the maximum likelihood estimator for the latent score vector of the subjects is uniformly consistent under a near-minimal condition on network sparsity. This condition is sharp in terms of the leading order asymptotics describing the sparsity. Our analysis utilizes a novel chaining technique and illustrates an important connection between graph topology and model consistency. Our results guarantee that the maximum likelihood estimator is justified for estimation in large-scale pairwise comparison networks where data are asymptotically deficient. Simulation studies are provided in support of our theoretical findings.

stat.ML↗

arXiv2021

Online Debiased Lasso for Streaming Data

We propose an online debiased lasso (ODL) method for statistical inference in high-dimensional linear models with streaming data. The proposed ODL consists of an efficient computational algorithm for streaming data and approximately normal estimators for the regression coefficients. Its implementation only requires the availability of the current data batch in the data stream and sufficient statistics of the historical data at each stage of the analysis. A dynamic procedure is developed to select and update the tuning parameters upon the arrival of each new data batch so that we can adjust the amount of regularization adaptively along the data stream. The asymptotic normality of the ODL estimator is established under the conditions similar to those in an offline setting and mild conditions on the size of data batches in the stream, which provides theoretical justification for the proposed online statistical inference procedure. We conduct extensive numerical experiments to evaluate the performance of ODL. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. An air quality dataset and an index fund dataset from Hong Kong Stock Exchange are analyzed to illustrate the application of the proposed method.

math.ST↗

arXiv2021

Statistical Inference in High-dimensional Generalized Linear Models with Streaming Data

In this paper we develop an online statistical inference approach for high-dimensional generalized linear models with streaming data for real-time estimation and inference. We propose an online debiased lasso (ODL) method to accommodate the special structure of streaming data. ODL differs from offline debiased lasso in two important aspects. First, in computing the estimate at the current stage, it only uses summary statistics of the historical data. Second, in addition to debiasing an online lasso estimator, ODL corrects an approximation error term arising from nonlinear online updating with streaming data. We show that the proposed online debiased estimators for the GLMs are consistent and asymptotically normal. This result provides a theoretical basis for carrying out real-time interim statistical inference with streaming data. Extensive numerical experiments are conducted to evaluate the performance of the proposed ODL method. These experiments demonstrate the effectiveness of our algorithm and support the theoretical results. A streaming dataset from the National Automotive Sampling System-Crashworthiness Data System is analyzed to illustrate the application of the proposed method.

math.ST↗

arXiv2019

Curiosity-Driven Recommendation Strategy for Adaptive Learning via Deep Reinforcement Learning

The design of recommendations strategies in the adaptive learning system focuses on utilizing currently available information to provide individual-specific learning instructions for learners. As a critical motivate for human behaviors, curiosity is essentially the drive to explore knowledge and seek information. In a psychologically inspired view, we aim to incorporate the element of curiosity for guiding learners to study spontaneously. In this paper, a curiosity-driven recommendation policy is proposed under the reinforcement learning framework, allowing for a both efficient and enjoyable personalized learning mode. Given intrinsic rewards from a well-designed predictive model, we apply the actor-critic method to approximate the policy directly through neural networks. Numeric analyses with a large continuous knowledge state space and concrete learning scenarios are used to further demonstrate the power of the proposed method.

cs.CY↗