arXiv subjects

Lucy Xia

Publications and source records attributed to Lucy Xia.

13 recordsLinked to original sources

arXiv2025

Model-robust Inference for Seamless II/III Trials with Covariate Adaptive Randomization

Seamless phase II/III trials have become a cornerstone of modern drug development, offering a means to accelerate evaluation while maintaining statistical rigor. However, most existing inference procedures are model-based, designed primarily for continuous outcomes, and often neglect the stratification used in covariate-adaptive randomization (CAR), limiting their practical relevance. In this paper, we propose a unified, model-robust framework for seamless phase II/III trials grounded in generalized linear models (GLMs), enabling valid inference across diverse outcome types, estimands, and CAR schemes. Using Z-estimation, we derive the asymptotic properties of treatment effect estimators and explicitly characterize how their variance depends on the underlying randomization procedure. Based on these results, we develop adjusted Wald tests that, together with Dunnett's multiple-comparison procedure and the inverse chi-square combination method, ensure valid overall Type I error. Extensive simulation studies and a trial example demonstrate that the proposed model-robust tests achieve superior power and reliable inference compared to conventional approaches.

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arXiv2025

Tensor Neyman-Pearson Classification: Theory, Algorithms, and Error Control

Biochemical discovery increasingly relies on classifying molecular structures when the consequences of different errors are highly asymmetric. In mutagenicity and carcinogenicity, misclassifying a harmful compound as benign can trigger substantial scientific, regulatory, and health risks, whereas false alarms primarily increase laboratory workload. Modern representations transform molecular graphs into persistence image tensors that preserve multiscale geometric and topological structure, yet existing tensor classifiers and deep tensor neural networks provide no finite-sample guarantees on type I error and often exhibit severe error inflation in practice. We develop the first Tensor Neyman-Pearson (Tensor-NP) classification framework that achieves finite-sample control of type I error while exploiting the multi-mode structure of tensor data. Under a tensor-normal mixture model, we derive the oracle NP discriminant, characterize its Tucker low-rank manifold geometry, and establish tensor-specific margin and conditional detection conditions enabling high-probability bounds on excess type II error. We further propose a Discriminant Tensor Iterative Projection estimator and a Tensor-NP Neural Classifier combining deep learning with Tensor-NP umbrella calibration, yielding the first distribution-free NP-valid methods for multiway data. Across four biochemical datasets, Tensor-NP classifiers maintain type I errors at prespecified levels while delivering competitive type II error performance, providing reliable tools for asymmetric-risk decisions with complex molecular tensors.

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arXiv2024

Covariate Selection for Optimizing Balance with an Innovative Adaptive Randomization Approach

Balancing influential covariates is crucial for valid treatment comparisons in clinical studies. While covariate-adaptive randomization is commonly used to achieve balance, its performance can be inadequate when the number of baseline covariates is large. It is therefore essential to identify the influential factors associated with the outcome and ensure balance among these critical covariates. In this article, we propose a novel adaptive randomization approach that integrates the patients' responses and covariates information to select sequentially significant covariates and maintain their balance. We establish theoretically the consistency of our covariate selection method and demonstrate that the improved covariate balancing, as evidenced by a faster convergence rate of the imbalance measure, leads to higher efficiency in estimating treatment effects. Furthermore, we provide extensive numerical and empirical studies to illustrate the benefits of our proposed method across various settings.

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arXiv2023

Neyman-Pearson and equal opportunity: when efficiency meets fairness in classification

Organizations often rely on statistical algorithms to make socially and economically impactful decisions. We must address the fairness issues in these important automated decisions. On the other hand, economic efficiency remains instrumental in organizations' survival and success. Therefore, a proper dual focus on fairness and efficiency is essential in promoting fairness in real-world data science solutions. Among the first efforts towards this dual focus, we incorporate the equal opportunity (EO) constraint into the Neyman-Pearson (NP) classification paradigm. Under this new NP-EO framework, we (a) derive the oracle classifier, (b) propose finite-sample based classifiers that satisfy population-level fairness and efficiency constraints with high probability, and (c) demonstrate statistical and social effectiveness of our algorithms on simulated and real datasets.

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arXiv2022

Robust Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models

Unsupervised learning has been widely used in many real-world applications. One of the simplest and most important unsupervised learning models is the Gaussian mixture model (GMM). In this work, we study the multi-task learning problem on GMMs, which aims to leverage potentially similar GMM parameter structures among tasks to obtain improved learning performance compared to single-task learning. We propose a multi-task GMM learning procedure based on the EM algorithm that effectively utilizes unknown similarities between related tasks and is robust against a fraction of outlier tasks from arbitrary distributions. The proposed procedure is shown to achieve the minimax optimal rate of convergence for both parameter estimation error and the excess mis-clustering error, in a wide range of regimes. Moreover, we generalize our approach to tackle the problem of transfer learning for GMMs, where similar theoretical results are derived. Additionally, iterative unsupervised multi-task and transfer learning methods may suffer from an initialization alignment problem, and two alignment algorithms are proposed to resolve the issue. Finally, we demonstrate the effectiveness of our methods through simulations and real data examples. To the best of our knowledge, this is the first work studying multi-task and transfer learning on GMMs with theoretical guarantees.

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arXiv2022

Non-splitting Neyman-Pearson Classifiers

The Neyman-Pearson (NP) binary classification paradigm constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). This paradigm is suitable for applications such as severe disease diagnosis, fraud detection, among others. A series of NP classifiers have been developed to guarantee the type I error control with high probability. However, these existing classifiers involve a sample splitting step: a mixture of class 0 and class 1 observations to construct a scoring function and some left-out class 0 observations to construct a threshold. This splitting enables classifier construction built upon independence, but it amounts to insufficient use of data for training and a potentially higher type II error. Leveraging a canonical linear discriminant analysis model, we derive a quantitative CLT for a certain functional of quadratic forms of the inverse of sample and population covariance matrices, and based on this result, develop for the first time NP classifiers without splitting the training sample. Numerical experiments have confirmed the advantages of our new non-splitting parametric strategy.

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arXiv2020

Intentional Control of Type I Error over Unconscious Data Distortion: a Neyman-Pearson Approach to Text Classification

This paper addresses the challenges in classifying textual data obtained from open online platforms, which are vulnerable to distortion. Most existing classification methods minimize the overall classification error and may yield an undesirably large type I error (relevant textual messages are classified as irrelevant), particularly when available data exhibit an asymmetry between relevant and irrelevant information. Data distortion exacerbates this situation and often leads to fallacious prediction. To deal with inestimable data distortion, we propose the use of the Neyman-Pearson (NP) classification paradigm, which minimizes type II error under a user-specified type I error constraint. Theoretically, we show that the NP oracle is unaffected by data distortion when the class conditional distributions remain the same. Empirically, we study a case of classifying posts about worker strikes obtained from a leading Chinese microblogging platform, which are frequently prone to extensive, unpredictable and inestimable censorship. We demonstrate that, even though the training and test data are susceptible to different distortion and therefore potentially follow different distributions, our proposed NP methods control the type I error on test data at the targeted level. The methods and implementation pipeline proposed in our case study are applicable to many other problems involving data distortion.

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arXiv2020

Neyman-Pearson classification: parametrics and sample size requirement

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $α$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people have clear priorities among the two error types. Recently, Tong, Feng and Li (2018) proposed a nonparametric umbrella algorithm that adapts all scoring-type classification methods (e.g., logistic regression, support vector machines, random forest) to respect the given type I error upper bound $α$ with high probability, without specific distributional assumptions on the features and the responses. Universal the umbrella algorithm is, it demands an explicit minimum sample size requirement on class $0$, which is often the more scarce class, such as in rare disease diagnosis applications. In this work, we employ the parametric linear discriminant analysis (LDA) model and propose a new parametric thresholding algorithm, which does not need the minimum sample size requirements on class $0$ observations and thus is suitable for small sample applications such as rare disease diagnosis. Leveraging both the existing nonparametric and the newly proposed parametric thresholding rules, we propose four LDA-based NP classifiers, for both low- and high-dimensional settings. On the theoretical front, we prove NP oracle inequalities for one proposed classifier, where the rate for excess type II error benefits from the explicit parametric model assumption. Furthermore, as NP classifiers involve a sample splitting step of class $0$ observations, we construct a new adaptive sample splitting scheme that can be applied universally to NP classifiers, and this adaptive strategy reduces the type II error of these classifiers.

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arXiv2019

A Projection Based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding conditional independence test is developed with the asymptotic null distribution unveiled where the number of factors could be high-dimensional. It is also shown that the new test has control over the asymptotic significance level and can be calculated efficiently. A generic method for building dependency graphs without Gaussian assumption using the new test is elaborated. Numerical results and real data analysis show the superiority of the new method.

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arXiv2018

Unifying approach to selective inference with applications to cross-validation

We develop tools to do valid post-selective inference for a family of model selection procedures, including choosing a model via cross-validated Lasso. The tools apply universally when the following random vectors are jointly asymptotically multivariate Gaussian: 1. the vector composed of each model's quality value evaluated under certain model selection criteria (e.g. cross-validation errors across folds, AIC, prediction errors etc.) 2. the test statistics from which we make inference on the parameters; it is worth noting that the parameters here are chosen after model selection methods are performed. Under these assumptions, we derive a pivotal quantity that has an asymptotically Unif(0,1) distribution which can be used to perform tests and construct confidence intervals. Both the tests and confidence intervals are selectively valid for the chosen parameter. While the above assumptions may not be satisfied in some applications, we propose a novel variation to these model selection procedures by adding Gaussian randomizations to either one of the two vectors. As a result, the joint distribution of the above random vectors is multivariate Gaussian and our general tools apply. We illustrate our method by applying it to four important procedures for which very few selective inference results have been developed: cross-validated Lasso, cross-validated randomized Lasso, AIC-based model selection among a fixed set of models and inference for a newly introduced novel marginal LOCO parameter, inspired by the LOCO parameter of Rinaldo et al (2016); and we provide complete results for these cases. For randomized model selection procedures, we develop Markov chain Monte Carlo sampling scheme to construct valid post-selective confidence intervals empirically.

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arXiv2017

Inferactive data analysis

We describe inferactive data analysis, so-named to denote an interactive approach to data analysis with an emphasis on inference after data analysis. Our approach is a compromise between Tukey's exploratory (roughly speaking "model free") and confirmatory data analysis (roughly speaking classical and "model based"), also allowing for Bayesian data analysis. We view this approach as close in spirit to current practice of applied statisticians and data scientists while allowing frequentist guarantees for results to be reported in the scientific literature, or Bayesian results where the data scientist may choose the statistical model (and hence the prior) after some initial exploratory analysis. While this approach to data analysis does not cover every scenario, and every possible algorithm data scientists may use, we see this as a useful step in concrete providing tools (with frequentist statistical guarantees) for current data scientists. The basis of inference we use is selective inference [Lee et al., 2016, Fithian et al., 2014], in particular its randomized form [Tian and Taylor, 2015a]. The randomized framework, besides providing additional power and shorter confidence intervals, also provides explicit forms for relevant reference distributions (up to normalization) through the {\em selective sampler} of Tian et al. [2016]. The reference distributions are constructed from a particular conditional distribution formed from what we call a DAG-DAG -- a Data Analysis Generative DAG. As sampling conditional distributions in DAGs is generally complex, the selective sampler is crucial to any practical implementation of inferactive data analysis. Our principal goal is in reviewing the recent developments in selective inference as well as describing the general philosophy of selective inference.

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arXiv2015

QUADRO: A supervised dimension reduction method via Rayleigh quotient optimization

We propose a novel Rayleigh quotient based sparse quadratic dimension reduction method - named QUADRO (Quadratic Dimension Reduction via Rayleigh Optimization) - for analyzing high- dimensional data. Unlike in the linear setting where Rayleigh quotient optimization coincides with classification, these two problems are very different under nonlinear settings. In this paper, we clarify this difference and show that Rayleigh quotient optimization may be of independent scientific interests. One major challenge of Rayleigh quotient optimization is that the variance of quadratic statistics involves all fourth cross-moments of predictors, which are infeasible to compute for high-dimensional applications and may accumulate too many stochastic errors. This issue is resolved by considering a family of elliptical models. Moreover, for heavy-tail distributions, robust estimates of mean vectors and covariance matrices are employed to guarantee uniform convergence in estimating nonpolynomially many parameters, even though only the fourth moments are assumed. Methodologically, QUADRO is based on elliptical models which allow us to formulate the Rayleigh quotient maximization as a convex optimization problem. Computationally, we propose an efficient linearized augmented Lagrangian method to solve the constrained optimization problem. Theoretically, we provide explicit rates of convergence in terms of Rayleigh quotient under both Gaussian and general elliptical models. Thorough numerical results on both synthetic and real datasets are also provided to back up our theoretical results.

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arXiv2013

Aggregation of Affine Estimators

We consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares estimators. Dalalyan and Salmon (2012) have established that, for this problem, exponentially weighted (EW) model selection aggregation leads to sharp oracle inequalities in expectation, but similar bounds in deviation were not previously known. While results indicate that the same aggregation scheme may not satisfy sharp oracle inequalities with high probability, we prove that a weaker notion of oracle inequality for EW that holds with high probability. Moreover, using a generalization of the newly introduced $Q$-aggregation scheme we also prove sharp oracle inequalities that hold with high probability. Finally, we apply our results to universal aggregation and show that our proposed estimator leads simultaneously to all the best known bounds for aggregation, including $\ell_q$-aggregation, $q \in (0,1)$, with high probability.

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