arXiv subjects

Huazhen Lin

Publications and source records attributed to Huazhen Lin.

14 recordsLinked to original sources

arXiv2026

Minimal Sufficient Representations for Self-interpretable Deep Neural Networks

Deep neural networks (DNNs) achieve remarkable predictive performance but remain difficult to interpret, largely due to overparameterization that obscures the minimal structure required for interpretation. Here we introduce DeepIn, a self-interpretable neural network framework that adaptively identifies and learns the minimal representation necessary for preserving the full expressive capacity of standard DNNs. We show that DeepIn can correctly identify the minimal representation dimension, select relevant variables, and recover the minimal sufficient network architecture for prediction. The resulting estimator achieves optimal non-asymptotic error rates that adapt to the learned minimal dimension, demonstrating that recovering minimal sufficient structure fundamentally improves generalization error. Building on these guarantees, we further develop hypothesis testing procedures for both selected variables and learned representations, bridging deep representation learning with formal statistical inference. Across biomedical and vision benchmarks, DeepIn improves both predictive accuracy and interpretability, reducing error by up to 30% on real-world datasets while automatically uncovering human-interpretable discriminative patterns. Our results suggest that interpretability and statistical rigor can be embedded directly into deep architectures without sacrificing performance.

stat.ME↗

arXiv2026

Beyond the Prompt in Large Language Models: Comprehension, In-Context Learning, and Chain-of-Thought

Large Language Models (LLMs) have demonstrated remarkable proficiency across diverse tasks, exhibiting emergent properties such as semantic prompt comprehension, In-Context Learning (ICL), and Chain-of-Thought (CoT) reasoning. Despite their empirical success, the theoretical mechanisms driving these phenomena remain poorly understood. This study dives into the foundations of these observations by addressing three critical questions: (1) How do LLMs accurately decode prompt semantics despite being trained solely on a next-token prediction objective? (2) Through what mechanism does ICL facilitate performance gains without explicit parameter updates? and (3) Why do intermediate reasoning steps in CoT prompting effectively unlock capabilities for complex, multi-step problems? Our results demonstrate that, through the autoregressive process, LLMs are capable of exactly inferring the transition probabilities between tokens across distinct tasks using provided prompts. We show that ICL enhances performance by reducing prompt ambiguity and facilitating posterior concentration on the intended task. Furthermore, we find that CoT prompting activates the model's capacity for task decomposition, breaking complex problems into a sequence of simpler sub-tasks that the model has mastered during the pretraining phase. By comparing their individual error bounds, we provide novel theoretical insights into the statistical superiority of advanced prompt engineering techniques.

cs.CL↗

arXiv2025

Olica: Efficient Structured Pruning of Large Language Models without Retraining

Most existing structured pruning methods for Large Language Models (LLMs) require substantial computational and data resources for retraining to reestablish the corrupted correlations, making them prohibitively expensive. To address this, we propose a pruning framework for LLMs called Orthogonal decomposition and Linear Calibration (Olica), which eliminates the need for retraining. A key observation is that the multi-head attention (MHA) layer depends on two types of matrix products. By treating these matrix products as unified entities and applying principal component analysis (PCA), we extract the most important information to compress LLMs without sacrificing accuracy or disrupting their original structure. Consequently, retraining becomes unnecessary. A fast decomposition method is devised, reducing the complexity of PCA by a factor of the square of the number of attention heads. Additionally, to mitigate error accumulation problem caused by pruning the feed-forward network (FFN) layer, we introduce a linear calibration method to reconstruct the residual errors of pruned layers using low-rank matrices. By leveraging singular value decomposition (SVD) on the solution of the least-squares problem, these matrices are obtained without requiring retraining. Extensive experiments show that the proposed Olica is efficient in terms of data usage, GPU memory, and running time, while delivering superior performance across multiple benchmarks.

cs.CL↗

arXiv2024

Deep Transfer Learning: Model Framework and Error Analysis

This paper presents a framework for deep transfer learning, which aims to leverage information from multi-domain upstream data with a large number of samples $n$ to a single-domain downstream task with a considerably smaller number of samples $m$, where $m \ll n$, in order to enhance performance on downstream task. Our framework offers several intriguing features. First, it allows the existence of both shared and domain-specific features across multi-domain data and provides a framework for automatic identification, achieving precise transfer and utilization of information. Second, the framework explicitly identifies upstream features that contribute to downstream tasks, establishing clear relationships between upstream domains and downstream tasks, thereby enhancing interpretability. Error analysis shows that our framework can significantly improve the convergence rate for learning Lipschitz functions in downstream supervised tasks, reducing it from $\tilde{O}(m^{-\frac{1}{2(d+2)}}+n^{-\frac{1}{2(d+2)}})$ ("no transfer") to $\tilde{O}(m^{-\frac{1}{2(d^*+3)}} + n^{-\frac{1}{2(d+2)}})$ ("partial transfer"), and even to $\tilde{O}(m^{-1/2}+n^{-\frac{1}{2(d+2)}})$ ("complete transfer"), where $d^* \ll d$ and $d$ is the dimension of the observed data. Our theoretical findings are supported by empirical experiments on image classification and regression datasets.

cs.LG↗

arXiv2024

Adv-SSL: Adversarial Self-Supervised Representation Learning with Theoretical Guarantees

Learning transferable data representations from abundant unlabeled data remains a central challenge in machine learning. Although numerous self-supervised learning methods have been proposed to address this challenge, a significant class of these approaches aligns the covariance or correlation matrix with the identity matrix. Despite impressive performance across various downstream tasks, these methods often suffer from biased sample risk, leading to substantial optimization shifts in mini-batch settings and complicating theoretical analysis. In this paper, we introduce a novel \underline{\bf Adv}ersarial \underline{\bf S}elf-\underline{\bf S}upervised Representation \underline{\bf L}earning (Adv-SSL) for unbiased transfer learning with no additional cost compared to its biased counterparts. Our approach not only outperforms the existing methods across multiple benchmark datasets but is also supported by comprehensive end-to-end theoretical guarantees. Our analysis reveals that the minimax optimization in Adv-SSL encourages representations to form well-separated clusters in the embedding space, provided there is sufficient upstream unlabeled data. As a result, our method achieves strong classification performance even with limited downstream labels, shedding new light on few-shot learning.

stat.ML↗

arXiv2024

Generative adversarial learning with optimal input dimension and its adaptive generator architecture

We investigate the impact of the input dimension on the generalization error in generative adversarial networks (GANs). In particular, we first provide both theoretical and practical evidence to validate the existence of an optimal input dimension (OID) that minimizes the generalization error. Then, to identify the OID, we introduce a novel framework called generalized GANs (G-GANs), which includes existing GANs as a special case. By incorporating the group penalty and the architecture penalty developed in the paper, G-GANs have several intriguing features. First, our framework offers adaptive dimensionality reduction from the initial dimension to a dimension necessary for generating the target distribution. Second, this reduction in dimensionality also shrinks the required size of the generator network architecture, which is automatically identified by the proposed architecture penalty. Both reductions in dimensionality and the generator network significantly improve the stability and the accuracy of the estimation and prediction. Theoretical support for the consistent selection of the input dimension and the generator network is provided. Third, the proposed algorithm involves an end-to-end training process, and the algorithm allows for dynamic adjustments between the input dimension and the generator network during training, further enhancing the overall performance of G-GANs. Extensive experiments conducted with simulated and benchmark data demonstrate the superior performance of G-GANs. In particular, compared to that of off-the-shelf methods, G-GANs achieves an average improvement of 45.68% in the CT slice dataset, 43.22% in the MNIST dataset and 46.94% in the FashionMNIST dataset in terms of the maximum mean discrepancy or Frechet inception distance. Moreover, the features generated based on the input dimensions identified by G-GANs align with visually significant features.

cs.LG↗

arXiv2024

Latent Schr{\"o}dinger Bridge Diffusion Model for Generative Learning

This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for theoretical exploration in this domain. Our approach commences with the pre-training of an encoder-decoder architecture using data originating from a distribution that may diverge from the target distribution, thus facilitating the accommodation of a large sample size through the utilization of pre-existing large-scale models. Subsequently, we develop a diffusion model within the latent space utilizing the Schr{\"o}dinger bridge framework. Our theoretical analysis encompasses the establishment of end-to-end error analysis for learning distributions via the latent Schr{\"o}dinger bridge diffusion model. Specifically, we control the second-order Wasserstein distance between the generated distribution and the target distribution. Furthermore, our obtained convergence rates effectively mitigate the curse of dimensionality, offering robust theoretical support for prevailing diffusion models.

stat.ML↗

arXiv2023

Evaluation of transplant benefits with the U.S. Scientific Registry of Transplant Recipients by semiparametric regression of mean residual life

Kidney transplantation is the most effective renal replacement therapy for end stage renal disease patients. With the severe shortage of kidney supplies and for the clinical effectiveness of transplantation, patient's life expectancy post transplantation is used to prioritize patients for transplantation; however, severe comorbidity conditions and old age are the most dominant factors that negatively impact post-transplantation life expectancy, effectively precluding sick or old patients from receiving transplants. It would be crucial to design objective measures to quantify the transplantation benefit by comparing the mean residual life with and without a transplant, after adjusting for comorbidity and demographic conditions. To address this urgent need, we propose a new class of semiparametric covariate-dependent mean residual life models. Our method estimates covariate effects semiparametrically efficiently and the mean residual life function nonparametrically, enabling us to predict the residual life increment potential for any given patient. Our method potentially leads to a more fair system that prioritizes patients who would have the largest residual life gains. Our analysis of the kidney transplant data from the U.S. Scientific Registry of Transplant Recipients also suggests that a single index of covariates summarize well the impacts of multiple covariates, which may facilitate interpretations of each covariate's effect. Our subgroup analysis further disclosed inequalities in survival gains across groups defined by race, gender and insurance type (reflecting socioeconomic status).

stat.ME↗

arXiv2023

Deep regression learning with optimal loss function

In this paper, we develop a novel efficient and robust nonparametric regression estimator under a framework of feedforward neural network. There are several interesting characteristics for the proposed estimator. First, the loss function is built upon an estimated maximum likelihood function, who integrates the information from observed data, as well as the information from data structure. Consequently, the resulting estimator has desirable optimal properties, such as efficiency. Second, different from the traditional maximum likelihood estimation (MLE), the proposed method avoid the specification of the distribution, hence is flexible to any kind of distribution, such as heavy tails, multimodal or heterogeneous distribution. Third, the proposed loss function relies on probabilities rather than direct observations as in least squares, contributing the robustness in the proposed estimator. Finally, the proposed loss function involves nonparametric regression function only. This enables a direct application of existing packages, simplifying the computation and programming. We establish the large sample property of the proposed estimator in terms of its excess risk and minimax near-optimal rate. The theoretical results demonstrate that the proposed estimator is equivalent to the true MLE in which the density function is known. Our simulation studies show that the proposed estimator outperforms the existing methods in terms of prediction accuracy, efficiency and robustness. Particularly, it is comparable to the true MLE, and even gets better as the sample size increases. This implies that the adaptive and data-driven loss function from the estimated density may offer an additional avenue for capturing valuable information. We further apply the proposed method to four real data examples, resulting in significantly reduced out-of-sample prediction errors compared to existing methods.

stat.ME↗

arXiv2022

Factor-guided functional PCA for high-dimensional functional data

The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method to consider both temporal dependence and correlation of variables so that the extracted features are as sufficient as possible. In particular, we use a factor process to consider the correlation among high-dimensional functional variables and then apply functional principal component analysis (FPCA) to the factor processes to address the dependence over time. Furthermore, to solve the computational problem arising from triple-infinite dimensions, we creatively build some moment equations to estimate loading, scores and eigenfunctions in closed form without rotation. Theoretically, we establish the asymptotical properties of the proposed estimator. Extensive simulation studies demonstrate that our proposed method outperforms other competitors in terms of accuracy and computational cost. The proposed method is applied to analyze the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, resulting in higher prediction accuracy and 41 important ROIs that are associated with Alzheimer's disease, 23 of which have been confirmed by the literature.

stat.ME↗

arXiv2020

Two-directional simultaneous inference for high-dimensional models

This paper proposes a general two directional simultaneous inference (TOSI) framework for high-dimensional models with a manifest variable or latent variable structure, for example, high-dimensional mean models, high-dimensional sparse regression models, and high-dimensional latent factors models. TOSI performs simultaneous inference on a set of parameters from two directions, one to test whether the assumed zero parameters indeed are zeros and one to test whether exist zeros in the parameter set of nonzeros. As a result, we can exactly identify whether the parameters are zeros, thereby keeping the data structure fully and parsimoniously expressed. We theoretically prove that the proposed TOSI method asymptotically controls the Type I error at the prespecified significance level and that the testing power converges to one. Simulations are conducted to examine the performance of the proposed method in finite sample situations and two real datasets are analyzed. The results show that the TOSI method is more predictive and has more interpretable estimators than existing methods.

stat.ME↗

arXiv2020

Semiparametric regression of mean residual life with censoring and covariate dimension reduction

We propose a new class of semiparametric regression models of mean residual life for censored outcome data. The models, which enable us to estimate the expected remaining survival time and generalize commonly used mean residual life models, also conduct covariate dimension reduction. Using the geometric approaches in semiparametrics literature and the martingale properties with survival data, we propose a flexible inference procedure that relaxes the parametric assumptions on the dependence of mean residual life on covariates and how long a patient has lived. We show that the estimators for the covariate effects are root-$n$ consistent, asymptotically normal, and semiparametrically efficient. With the unspecified mean residual life function, we provide a nonparametric estimator for predicting the residual life of a given subject, and establish the root-$n$ consistency and asymptotic normality for this estimator. Numerical experiments are conducted to illustrate the feasibility of the proposed estimators. We apply the method to analyze a national kidney transplantation dataset to further demonstrate the utility of the work.

math.ST↗

arXiv2018

Covariance-Insured Screening

Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors far greater than the sample size. In order to identify more novel biomarkers and understand biological mechanisms, it is vital to detect signals weakly associated with outcomes among ultrahigh-dimensional predictors. However, existing screening methods, which typically ignore correlation information, are likely to miss these weak signals. By incorporating the inter-feature dependence, we propose a covariance-insured screening methodology to identify predictors that are jointly informative but only marginally weakly associated with outcomes. The validity of the method is examined via extensive simulations and real data studies for selecting potential genetic factors related to the onset of cancer.

stat.ML↗

arXiv2006

Local partial-likelihood estimation for lifetime data

This paper considers a proportional hazards model, which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable, for analysis of lifetime data. A local partial-likelihood technique is proposed to estimate nonlinear interactions. Asymptotic normality of the proposed estimator is established. The baseline hazard function, the bias and the variance of the local likelihood estimator are consistently estimated. In addition, a one-step local partial-likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial-likelihood estimator. Furthermore, a penalized local likelihood estimator is proposed to select important risk variables in the model. Numerical examples are used to illustrate the effectiveness of the proposed procedures.

math.ST↗