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Jinzhu Jia

Publications and source records attributed to Jinzhu Jia.

At least 19 recordsLinked to original sources
arXiv2025

Causal Estimation and Inference in Nonlinear Mendelian Randomization Studies

Mendelian randomization (MR) is widely used to uncover causal relationships in the presence of unmeasured confounders. However, most existing MR methods presuppose linear causality, risking bias when the true relationships are nonlinear, which is a common empirical scenario. In this paper, we compared two prevalent instrumental variable techniques (the two-stage prediction method and the control function method) under both linear and nonlinear settings, and addressed key issues such as horizontal pleiotropy and violations of classical assumptions in control function method. Most notably, we proposed a flexible semiparametric approach that estimates the causal function without a priori specification, reducing the risk of model misspecification, and extended our methods to binary outcomes, broadening its applicability. For all approaches, we provided estimators, standard errors, and test statistics, to facilitate robust causal inference. Extensive numerical simulations demonstrated that our proposed methods exhibited both accuracy and robustness across diverse scenarios. Applying our methods to UK Biobank data uncovered significant nonlinear causal effects missed by linear MR approaches. We offer an R package implementation for broader and more convenient use.

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arXiv2025

Hypothesis Testing for Progressive Kernel Estimation and VCM Framework

Identifying an appropriate radius for unbiased kernel estimation is crucial for the efficiency of radiance estimation. However, determining both the radius and unbiasedness still faces big challenges. In this paper, we first propose a statistical model of photon samples and associated contributions for progressive kernel estimation, under which the kernel estimation is unbiased if the null hypothesis of this statistical model stands. Then, we present a method to decide whether to reject the null hypothesis about the statistical population (i.e., photon samples) by the F-test in the Analysis of Variance. Hereby, we implement a progressive photon mapping (PPM) algorithm, wherein the kernel radius is determined by this hypothesis test for unbiased radiance estimation. Secondly, we propose VCM+, a reinforcement of Vertex Connection and Merging (VCM), and derive its theoretically unbiased formulation. VCM+ combines hypothesis testing-based PPM with bidirectional path tracing (BDPT) via multiple importance sampling (MIS), wherein our kernel radius can leverage the contributions from PPM and BDPT. We test our new algorithms, improved PPM and VCM+, on diverse scenarios with different lighting settings. The experimental results demonstrate that our method can alleviate light leaks and visual blur artifacts of prior radiance estimate algorithms. We also evaluate the asymptotic performance of our approach and observe an overall improvement over the baseline in all testing scenarios.

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arXiv2024

Integrated Sensing and Communication Channel Modeling: A Survey

Integrated sensing and communication (ISAC) is expected to play a crucial role in the sixth-generation (6G) mobile communication systems, offering potential applications in the scenarios of intelligent transportation, smart factories, etc. The performance of radar sensing in ISAC systems is closely related to the characteristics of radar sensing and communication channels. Therefore, ISAC channel modeling serves as a fundamental cornerstone for evaluating and optimizing ISAC systems. This article provides a comprehensive survey on the ISAC channel modeling methods. Furthermore, the methods of target radar cross section (RCS) modeling and clutter RCS modeling are summarized. Finally, we discuss the future research trends related to ISAC channel modeling in various scenarios.

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arXiv2023

Integrated Sensing and Communication enabled Doppler Frequency Shift Estimation and Compensation

Despite the millimeter wave technology fulfills the low-latency and high data transmission, it will cause severe Doppler Frequency Shift (DFS) for high-speed vehicular network, which tremendously damages the communication performance. In this paper, we propose an Integrated Sensing and Communication (ISAC) enabled DFS estimation and compensation algorithm. Firstly, the DFS is coarsely estimated and compensated using radar detection. Then, the designed preamble sequence is used to accurately estimate and compensate DFS. In addition, an adaptive DFS estimator is designed to reduce the computational complexity. Compared with the traditional DFS estimation algorithm, the improvement of the proposed algorithm is verified in bit error rate and mean square error performance by simulation results.

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arXiv2022

Te Test: A New Non-asymptotic T-test for Behrens-Fisher Problems

The Behrens-Fisher Problem is a classical statistical problem. It is to test the equality of the means of two normal populations using two independent samples, when the equality of the population variances is unknown. Linnik (1968) has shown that this problem has no exact fixed-level tests based on the complete sufficient statistics. However, exact conventional solutions based on other statistics and approximate solutions based the complete sufficient statistics do exist. Existing methods are mainly asymptotic tests, and usually don't perform well when the variances or sample sizes differ a lot. In this paper, we propose a new method to find an exact t-test (Te) to solve this classical Behrens-Fisher Problem. Confidence intervals for the difference between two means are provided. We also use detailed analysis to show that Te test reaches the maximum of degree of freedom and to give a weak version of proof that Te test has the shortest confidence interval length expectation. Some simulations are performed to show the advantages of our new proposed method compared to available conventional methods like Welch's test, paired t-test and so on. We will also compare it to unconventional method, like two-stage test.

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arXiv2021

Variance Reduction for Causal Inference

Propensity score methods have been shown to be powerful in obtaining efficient estimators of average treatment effect (ATE) from observational data, especially under the existence of confounding factors. When estimating, deciding which type of covariates need to be included in the propensity score function is important, since incorporating some unnecessary covariates may amplify both bias and variance of estimators of ATE. In this paper, we show that including additional instrumental variables that satisfy the exclusion restriction for outcome will do harm to the statistical efficiency. Also, we prove that, controlling for covariates that appear as outcome predictors, i.e. predict the outcomes and are irrelevant to the exposures, can help reduce the asymptotic variance of ATE estimation. We also note that, efficiently estimating the ATE by non-parametric or semi-parametric methods require the estimated propensity score function, as described in Hirano et al. (2003)\cite{Hirano2003}. Such estimation procedure usually asks for many regularity conditions, Rothe (2016)\cite{Rothe2016} also illustrated this point and proposed a known propensity score (KPS) estimator that requires mild regularity conditions and is still fully efficient. In addition, we introduce a linearly modified (LM) estimator that is nearly efficient in most general settings and need not estimation of the propensity score function, hence convenient to calculate. The construction of this estimator borrows idea from the interaction estimator of Lin (2013)\cite{Lin2013}, in which regression adjustment with interaction terms are applied to deal with data arising from a completely randomized experiment. As its name suggests, the LM estimator can be viewed as a linear modification on the IPW estimator using known propensity scores. We will also investigate its statistical properties both analytically and numerically.

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arXiv2021

Propensity Score Adapted Covariate Selection for Causal Inference

In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $\sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the "linear association" conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.

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arXiv2021

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signals Detection

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracle inequality is for the random design and can be extended to many $\ell_1 + \ell_2$ regularized M-estimations, with the corresponding empirical process having stochastic Lipschitz properties. We derive the concentration inequality for the suprema empirical processes for the weighted sum of negative binomial variables to show some high--probability events. We apply the method by showing the sign consistency, provided that the nonzero components in the true sparse vector are larger than a proper choice of the weakest signal detection threshold. In the second application, we show the grouping effect inequality with high probability. Third, under some assumptions for a design matrix, we can recover the true variable set with a high probability if the weakest signal detection threshold is large than the turning parameter up to a known constant. Lastly, we briefly discuss the de-biased elastic-net estimator, and numerical studies are given to support the proposal.

stat.ML↗
arXiv2021

Directional FDR Control for Sub-Gaussian Sparse GLMs

High-dimensional sparse generalized linear models (GLMs) have emerged in the setting that the number of samples and the dimension of variables are large, and even the dimension of variables grows faster than the number of samples. False discovery rate (FDR) control aims to identify some small number of statistically significantly nonzero results after getting the sparse penalized estimation of GLMs. Using the CLIME method for precision matrix estimations, we construct the debiased-Lasso estimator and prove the asymptotical normality by minimax-rate oracle inequalities for sparse GLMs. In practice, it is often needed to accurately judge each regression coefficient's positivity and negativity, which determines whether the predictor variable is positively or negatively related to the response variable conditionally on the rest variables. Using the debiased estimator, we establish multiple testing procedures. Under mild conditions, we show that the proposed debiased statistics can asymptotically control the directional (sign) FDR and directional false discovery variables at a pre-specified significance level. Moreover, it can be shown that our multiple testing procedure can approximately achieve a statistical power of 1. We also extend our methods to the two-sample problems and propose the two-sample test statistics. Under suitable conditions, we can asymptotically achieve directional FDR control and directional FDV control at the specified significance level for two-sample problems. Some numerical simulations have successfully verified the FDR control effects of our proposed testing procedures, which sometimes outperforms the classical knockoff method.

math.ST↗
arXiv2017

Sparse Poisson Regression with Penalized Weighted Score Function

We proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We show that under mild conditions, our estimator is $\ell_1$ consistent and the tuning parameter can be pre-specified, which shares the same good property of the square-root Lasso.

math.ST↗
arXiv2017

Main and Interaction Effects Selection for Quadratic Discriminant Analysis via Penalized Linear Regression

Discriminant analysis is a useful classification method. Variable selection for discriminant analysis is becoming more and more im- portant in a high-dimensional setting. This paper is concerned with the binary-class problems of main and interaction effects selection for the quadratic discriminant analysis. We propose a new penalized quadratic discriminant analysis (QDA) for variable selection in binary classification. Under sparsity assumption on the relevant variables, we conduct a penalized liner regression to derive sparse QDA by plug- ging the main and interaction effects in the model. Then the QDA problem is converted to a penalized sparse ordinary least squares op- timization by using the composite absolute penalties (CAP). Coor- dinate descent algorithm is introduced to solve the convex penalized least squares. The penalized linear regression can simultaneously se- lect the main and interaction effects, and also conduct classification. Compared with the existing methods of variable selection in QDA, the extensive simulation studies and two real data analyses demon- strate that our proposed method works well and is robust in the performance of variable selection and classification.

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arXiv2015

Vanilla Lasso for sparse classification under single index models

This paper study sparse classification problems. We show that under single-index models, vanilla Lasso could give good estimate of unknown parameters. With this result, we see that even if the model is not linear, and even if the response is not continuous, we could still use vanilla Lasso to train classifiers. Simulations confirm that vanilla Lasso could be used to get a good estimation when data are generated from a logistic regression model.

math.ST↗
arXiv2015

Mixed and missing data: a unified treatment with latent graphical models

We propose to learn latent graphical models when data have mixed variables and missing values. This model could be used for further data analysis, including regression, classification, ranking etc. It also could be used for imputing missing values. We specify a latent Gaussian model for the data, where the categorical variables are generated by discretizing an unobserved variable and the latent variables are multivariate Gaussian. The observed data consists of two parts: observed Gaussian variables and observed categorical variables, where the latter part is considered as partially missing Gaussian variables. We use the Expectation-Maximization algorithm to fit the model. To prevent overfitting we use sparse inverse covariance estimation to obtain sparse estimate of the latent covariance matrix, equivalently, the graphical model. The fitted model then could be used for problems including re- gression, classification and ranking. Such an approach is applied to a medical data set where our method outperforms the state-of-the-art methods. Simulation studies and real data results suggest that our proposed model performs better than random forest in terms of prediction error when the model is correctly specified, and is a better imputation method than hot deck imputation even if the model is not correctly specified.

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arXiv2014

Concise comparative summaries (CCS) of large text corpora with a human experiment

In this paper we propose a general framework for topic-specific summarization of large text corpora and illustrate how it can be used for the analysis of news databases. Our framework, concise comparative summarization (CCS), is built on sparse classification methods. CCS is a lightweight and flexible tool that offers a compromise between simple word frequency based methods currently in wide use and more heavyweight, model-intensive methods such as latent Dirichlet allocation (LDA). We argue that sparse methods have much to offer for text analysis and hope CCS opens the door for a new branch of research in this important field. For a particular topic of interest (e.g., China or energy), CSS automatically labels documents as being either on- or off-topic (usually via keyword search), and then uses sparse classification methods to predict these labels with the high-dimensional counts of all the other words and phrases in the documents. The resulting small set of phrases found as predictive are then harvested as the summary. To validate our tool, we, using news articles from the New York Times international section, designed and conducted a human survey to compare the different summarizers with human understanding. We demonstrate our approach with two case studies, a media analysis of the framing of "Egypt" in the New York Times throughout the Arab Spring and an informal comparison of the New York Times' and Wall Street Journal's coverage of "energy." Overall, we find that the Lasso with $L^2$ normalization can be effectively and usefully used to summarize large corpora, regardless of document size.

cs.CL↗
arXiv2014

Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with currently known algorithms, sampling over such classes is only feasible for graphs with fewer than approximately 20 vertices. In this paper, we design reversible irreducible Markov chains on the space of Markov equivalent classes by proposing a perfect set of operators that determine the transitions of the Markov chain. The stationary distribution of a proposed Markov chain has a closed form and can be computed easily. Specifically, we construct a concrete perfect set of operators on sparse Markov equivalence classes by introducing appropriate conditions on each possible operator. Algorithms and their accelerated versions are provided to efficiently generate Markov chains and to explore properties of Markov equivalence classes of sparse directed acyclic graphs (DAGs) with thousands of vertices. We find experimentally that in most Markov equivalence classes of sparse DAGs, (1) most edges are directed, (2) most undirected subgraphs are small and (3) the number of these undirected subgraphs grows approximately linearly with the number of vertices. The article contains supplement arXiv:1303.0632, http://dx.doi.org/10.1214/13-AOS1125SUPP

stat.ML↗
arXiv2012

On pattern recovery of the fused Lasso

We study the property of the Fused Lasso Signal Approximator (FLSA) for estimating a blocky signal sequence with additive noise. We transform the FLSA to an ordinary Lasso problem. By studying the property of the design matrix in the transformed Lasso problem, we find that the irrepresentable condition might not hold, in which case we show that the FLSA might not be able to recover the signal pattern. We then apply the newly developed preconditioning method -- Puffer Transformation [Jia and Rohe, 2012] on the transformed Lasso problem. We call the new method the preconditioned fused Lasso and we give non-asymptotic results for this method. Results show that when the signal jump strength (signal difference between two neighboring groups) is big and the noise level is small, our preconditioned fused Lasso estimator gives the correct pattern with high probability. Theoretical results give insight on what controls the signal pattern recovery ability -- it is the noise level {instead of} the length of the sequence. Simulations confirm our theorems and show significant improvement of the preconditioned fused Lasso estimator over the vanilla FLSA.

stat.ML↗
arXiv2012

Preconditioning to comply with the Irrepresentable Condition

Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in sparse linear regression. Given $X \in R^{n \times p}$ and $Y \in R^n$ that satisfy the standard regression equation, this paper demonstrates that even if the design matrix $X$ does not satisfy the irrepresentable condition for the Lasso, the design matrix $F X$ often does, where $F \in R^{n\times n}$ is a preconditioning matrix defined in this paper. By computing the Lasso on $(F X, F Y)$, instead of on $(X, Y)$, the necessary assumptions on $X$ become much less stringent. Our preconditioner $F$ ensures that the singular values of the design matrix are either zero or one. When $n\ge p$, the columns of $F X$ are orthogonal and the preconditioner always circumvents the stringent assumptions. When $p\ge n$, $F$ projects the design matrix onto the Stiefel manifold; the rows of $F X$ are orthogonal. We give both theoretical results and simulation results to show that, in the high dimensional case, the preconditioner helps to circumvent the stringent assumptions, improving the statistical performance of a broad class of model selection techniques in linear regression. Simulation results are particularly promising.

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