arXiv subjects

Chencheng Cai

Publications and source records attributed to Chencheng Cai.

10 recordsLinked to original sources

arXiv2024

Semi-parametric TEnsor Factor Analysis by Iteratively Projected Singular Value Decomposition

This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.

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arXiv2023

Independent-Set Design of Experiments for Estimating Treatment and Spillover Effects under Network Interference

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm , and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations.

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arXiv2022

Bullwhip Effect of Supply Networks: Joint Impact of Network Structure and Market Demand

The progressive amplification of fluctuations in demand as the demand travels upstream the supply chains is known as the bullwhip effect. We first analytically characterize the bullwhip effect in general supply chain networks in two cases: (i) all suppliers have a unique layer position, where our method is founded on the control-theoretic approach, and (ii) not all suppliers have a unique layer position due to the presence of intra-layer links or inter-layer links between suppliers that are not positioned in consecutive layers, where we use both the absorbing Markov chain and the control-theoretic approach. We then investigate how network structures impact the BWE of supply chain networks. In particular, we analytically show that (i) if the market demand is generated from the same stationary process, the structure of supply networks does not affect the layer-wise bullwhip effect of supply networks, and (ii) if the market demand is generated from different stationary or non-stationary market processes, wider supply networks lead to a lower level of layer-wise bullwhip effect. Finally, numerical simulations are used to validate our propositions.

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arXiv2022

Optimizing Randomized and Deterministic Saturation Designs under Interference

Randomized saturation designs are a family of designs which assign a possibly different treatment proportion to each cluster of a population at random. As a result, they generalize the well-known (stratified) completely randomized designs and the cluster-based randomized designs, which are included as special cases. We show that, under the stable unit treatment value assumption, either the cluster-based or the stratified completely randomized design are in fact optimal for the bias and variance of the difference-in-means estimator among randomized saturation designs. However, this is no longer the case when interference is present. We provide the closed form of the bias and variance of the difference-in-means estimator under a linear model of interference and investigate the optimization of each of these objectives. In addition to the randomized saturation designs, we propose a deterministic saturation design, where the treatment proportion for clusters are fixed, rather than randomized, in order to further improve the estimator under correct model specification. Through simulations, we illustrate the merits of optimizing randomized saturation designs to the graph and potential outcome structure, as well as showcasing the additional improvements yielded by well-chosen deterministic saturation designs.

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arXiv2020

Matrix Completion using Kronecker Product Approximation

A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an alternative and more general form of the underlying complete matrix, which assumes a low Kronecker rank instead of a low regular rank, but includes the latter as a special case. The extra flexibility allows for a much more parsimonious representation of the underlying matrix, but also raises the challenge of determining the proper Kronecker product configuration to be used. We find that the configuration can be identified using the mean squared error criterion as well as a modified cross-validation criterion. We establish the consistency of this procedure under suitable conditions on the signal-to-noise ratio. A aggregation procedure is also proposed to deal with special missing patterns and complex underlying structures. Both numerical and empirical studies are carried out to demonstrate the performance of the new method.

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arXiv2020

KoPA: Automated Kronecker Product Approximation

We consider the problem of matrix approximation and denoising induced by the Kronecker product decomposition. Specifically, we propose to approximate a given matrix by the sum of a few Kronecker products of matrices, which we refer to as the Kronecker product approximation (KoPA). Because the Kronecker product is an extension of the outer product from vectors to matrices, KoPA extends the low rank matrix approximation, and includes it as a special case. Comparing with the latter, KoPA also offers a greater flexibility, since it allows the user to choose the configuration, which are the dimensions of the two smaller matrices forming the Kronecker product. On the other hand, the configuration to be used is usually unknown, and needs to be determined from the data in order to achieve the optimal balance between accuracy and parsimony. We propose to use extended information criteria to select the configuration. Under the paradigm of high dimensional analysis, we show that the proposed procedure is able to select the true configuration with probability tending to one, under suitable conditions on the signal-to-noise ratio. We demonstrate the superiority of KoPA over the low rank approximations through numerical studies, and several benchmark image examples.

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arXiv2019

Hybrid Kronecker Product Decomposition and Approximation

Discovering the underlying low dimensional structure of high dimensional data has attracted a significant amount of researches recently and has shown to have a wide range of applications. As an effective dimension reduction tool, singular value decomposition is often used to analyze high dimensional matrices, which are traditionally assumed to have a low rank matrix approximation. In this paper, we propose a new approach. We assume a high dimensional matrix can be approximated by a sum of a small number of Kronecker products of matrices with potentially different configurations, named as a hybird Kronecker outer Product Approximation (hKoPA). It provides an extremely flexible way of dimension reduction compared to the low-rank matrix approximation. Challenges arise in estimating a hKoPA when the configurations of component Kronecker products are different or unknown. We propose an estimation procedure when the set of configurations are given and a joint configuration determination and component estimation procedure when the configurations are unknown. Specifically, a least squares backfitting algorithm is used when the configuration is given. When the configuration is unknown, an iterative greedy algorithm is used. Both simulation and real image examples show that the proposed algorithms have promising performances. The hybrid Kronecker product approximation may have potentially wider applications in low dimensional representation of high dimensional data

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arXiv2019

State Space Emulation and Annealed Sequential Monte Carlo for High Dimensional Optimization

Many high dimensional optimization problems can be reformulated into a problem of finding theoptimal state path under an equivalent state space model setting. In this article, we present a general emulation strategy for developing a state space model whose likelihood function (or posterior distribution) shares the same general landscape as the objective function of the original optimization problem. Then the solution of the optimization problem is the same as the optimal state path that maximizes the likelihood function or the posterior distribution under the emulated system. To find such an optimal path, we adapt a simulated annealing approach by inserting a temperature control into the emulated dynamic system and propose a novel annealed Sequential Monte Carlo (SMC) method that effectively generating Monte Carlo sample paths utilizing samples obtained on the high temperature scale. Compared to the vanilla simulated annealing implementation, annealed SMC is an iterative algorithm for state space model optimization that directly generates state paths from the equilibrium distributions with a decreasing sequence of temperatures through sequential importance sampling which does not require burn-in or mixing iterations to ensure quasi-equilibrium condition. Several applications of state space model emulation and the corresponding annealed SMC results are demonstrated.

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arXiv2019

Individualized Group Learning

Many massive data are assembled through collections of information of a large number of individuals in a population. The analysis of such data, especially in the aspect of individualized inferences and solutions, has the potential to create significant value for practical applications. Traditionally, inference for an individual in the data set is either solely relying on the information of the individual or from summarizing the information about the whole population. However, with the availability of big data, we have the opportunity, as well as a unique challenge, to make a more effective individualized inference that takes into consideration of both the population information and the individual discrepancy. To deal with the possible heterogeneity within the population while providing effective and credible inferences for individuals in a data set, this article develops a new approach called the individualized group learning (iGroup). The iGroup approach uses local nonparametric techniques to generate an individualized group by pooling other entities in the population which share similar characteristics with the target individual, even when individual estimates are biased due to limited number of observations. Three general cases of iGroup are discussed, and their asymptotic performances are investigated. Both theoretical results and empirical simulations reveal that, by applying iGroup, the performance of statistical inference on the individual level are ensured and can be substantially improved from inference based on either solely individual information or entire population information. The method has a broad range of applications. Two examples in financial statistics and maritime anomaly detection are presented.

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arXiv2018

Resampling Strategy in Sequential Monte Carlo for Constrained Sampling Problems

Sequential Monte Carlo (SMC) methods are a class of Monte Carlo methods that are used to obtain random samples of a high dimensional random variable in a sequential fashion. Many problems encountered in applications often involve different types of constraints. These constraints can make the problem much more challenging. In this paper, we formulate a general framework of using SMC for constrained sampling problems based on forward and backward pilot resampling strategies. We review some existing methods under the framework and develop several new algorithms. It is noted that all information observed or imposed on the underlying system can be viewed as constraints. Hence the approach outlined in this paper can be useful in many applications.

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