arXiv subjects

Yihong Gu

Publications and source records attributed to Yihong Gu.

17 recordsLinked to original sources

arXiv2026

Optimal use of a black-box learner in semiparametric estimation

Consider the partial linear model $Y = \mu_0(X) + \beta_0 \cdot T + \varepsilon$ and $T = \pi_0(X) + u$ in the structure-agnostic setting, where we are blind to the structure $\mu_0$ and $\pi_0$ and estimate the nuisances by a black-box hypothesis class. The learnability of the class is characterized by the estimation error $\delta_s$ in the absence of model misspecification and its $L_2$ mis-specification error $\delta_{a, \mu}$ and $\delta_{a, \pi}$ for $\mu_0$ and $\pi_0$, respectively. We propose a novel estimator of the target linear coefficient $\theta_0 = \beta_0$ with error rate \[ \frac{1}{\sqrt{n}} + \delta_{a, \mu} \cdot \delta_{a, \pi} + [\delta_s]^2. \] A matching lower bound is also established, implying that this rate is unimprovable. Compared with the product rate yielded by double machine learning (DML), our estimator removes the suboptimal term $\max(\delta_{a, \mu}, \delta_{a, \pi})\cdot \delta_s$ at no extra cost or assumption. Building on the underlying insights, which are neither tailored to the one-learner setting nor the partial linear model, we propose Transductive Adversarial Moment-calibrated Editing (TAME), which locally edits debiasing weights induced by black-box regression estimates on the inference sample through adversarial conditional moment calibration. TAME can be combined with any initial black-box estimates and can strictly improve on DML guarantees when the nuisance difficulties are imbalanced. We discuss how to fully exploit the advantages introduced by TAME, including the gains from using two learners, the resulting under-smoothing principle for model selection, and extensions to other linear functional estimation problems.

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arXiv2026

Unveiling Invariant and Transferable Latent Factors Across Heterogeneous Environments via ATLAS

This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings. Such a model is motivated by transfer learning and latent factor regression, where one seeks stable low-dimensional representations for both interpretation and robust out-of-sample prediction of the response $Y$. Leveraging the invariance principle, we show that the invariant and heterogeneous factors are disentangled under a minimal structural condition. Based on this, we propose ATLAS, an Auxiliary-label and invariance-guided Transfer via Latent Alignment across heterogeneous environmentS. ATLAS is a unified procedure that leverages the invariance principle to separate aligned invariant and unaligned heterogeneous factors, and further exploits supervision from auxiliary labels to extract prediction-invariant and transferable factors from those unaligned heterogeneous factors. ATLAS yields near-oracle performance for downstream latent factor regression, enables transferable prediction in new environments through the full latent signal when auxiliary labels are available, and reduces to robust invariant-factor-only prediction otherwise. We establish sharp non-asymptotic error bounds for recovering invariant and heterogeneous factors, identifying all the response-invariant factors, and estimating the invariant signal in $Y$.

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arXiv2026

Optimally taming biases in black-box models for efficient semiparametric estimation

Modern semiparametric estimation often relies on flexible black-box machine learning methods to estimate nuisance functions, raising a fundamental question: how do nuisance estimation errors propagate into inference for low-dimensional target parameters? The dominant paradigm, exemplified by double machine learning (DML), yields error bounds in which nuisance estimation errors enter multiplicatively. While widely adopted, it remains unclear whether this multiplicative-rate dependence is optimal for black-box models. In this paper, we start by revisiting the partial linear model $Y = \mu_0(X)+T\cdot\beta_0+\varepsilon$ under a structure-agnostic setting, where the nuisance function $\mu_0$ is estimated using a generic machine learning model, with approximation error $\delta^a_\mu$ and stochastic error $\delta_\mu^s$. We show that the standard DML rate is not optimal in the regime where the auxiliary function $\mathbb{E}[T|X=x]$ cannot be consistently estimated. We propose a new estimator for $\beta_0$ that achieves a sharper rate of $n^{-1/2}+\delta^a_\mu+(\delta_\mu^s)^2$ and establish a matching lower bound demonstrating its optimality. Our results reveal a new principle: the first-order stochastic error of nuisance estimation can be eliminated without imposing any additional assumptions. This also leads to a revised tuning strategy favoring under-smoothing, where $\delta^a_\mu\asymp(\delta_\mu^s)^2$, rather than the classical bias-variance trade-off $\delta^a_\mu \asymp \delta_\mu^s$. Under mild additional conditions, the estimator is asymptotically normal with minimal asymptotic variance. The proposed method extends to a broad class of semi-parametric linear functional estimation problems, including average treatment effect estimation. Our results imply that popular orthogonal score methods in semiparametric estimation with black-box nuisance learners can be substantially improved.

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arXiv2026

Neural Generative Distributional Regression

Any continuous conditional distribution of $Y$ given $X$ can be generated from a transform of a known noise distribution $U$ such as the uniform or normal distribution via $Y = g(X, U)$. This paper provides an estimator of such a generative transformation $g$ by minimizing the empirical energy distance between distributions of $Y$ and $g(X, U)$, and implements it via neural networks. The estimated distribution can then be readily applied to downstream tasks such as conditional moment estimation, predictive interval construction, and conditional density estimation. By leveraging the representation power of neural networks, the estimator can adaptively exploit low-dimensional structures in a purely algorithmic manner. Theoretically, we establish an oracle inequality attaining the adaptive optimal nonparametric rates. Numerical simulations and real data analysis further demonstrate the practical effectiveness of the proposed method.

stat.ME↗

arXiv2025

Near-Optimal Tensor PCA via Normalized Stochastic Gradient Ascent with Overparameterization

We study the Order-$k$ ($k \geq 4$) spiked tensor model for the tensor principal component analysis (PCA) problem: given $N$ i.i.d. observations of a $k$-th order tensor generated from the model $\mathbf{T} = \lambda \cdot v_*^{\otimes k} + \mathbf{E}$, where $\lambda > 0$ is the signal-to-noise ratio (SNR), $v_*$ is a unit vector, and $\mathbf{E}$ is a random noise tensor, the goal is to recover the planted vector $v_*$. We propose a normalized stochastic gradient ascent (NSGA) method with overparameterization for solving the tensor PCA problem. Without any global (or spectral) initialization step, the proposed algorithm successfully recovers the signal $v_*$ when $N\lambda^2 \geq \widetilde{\Omega}(d^{\lceil k/2 \rceil})$, thereby breaking the previous conjecture that (stochastic) gradient methods require at least $\Omega(d^{k-1})$ samples for recovery. For even $k$, the $\widetilde{\Omega}(d^{k/2})$ threshold coincides with the optimal threshold under computational constraints, attained by sum-of-squares relaxations and related algorithms. Theoretical analysis demonstrates that the overparameterized stochastic gradient method not only establishes a significant initial optimization advantage during the early learning phase but also achieves strong generalization guarantees. This work provides the first evidence that overparameterization improves statistical performance relative to exact parameterization that is solved via standard continuous optimization.

math.OC↗

arXiv2025

Optimal estimation of a factorizable density using diffusion models with ReLU neural networks

This paper investigates the score-based diffusion models for density estimation when the target density admits a factorizable low-dimensional nonparametric structure. To be specific, we show that when the log density admits a $d^*$-way interaction model with $\beta$-smooth components, the vanilla diffusion model, which uses a fully connected ReLU neural network for score matching, can attain optimal $n^{-\beta/(2\beta+d^*)}$ statistical rate of convergence in total variation distance. This is, to the best of our knowledge, the first in the literature showing that diffusion models with standard configurations can adapt to the low-dimensional factorizable structures. The main challenge is that the low-dimensional factorizable structure no longer holds for most of the diffused timesteps, and it is very challenging to show that these diffused score functions can be well approximated without a significant increase in the number of network parameters. Our key insight is to demonstrate that the diffused score functions can be decomposed into a composition of either super-smooth or low-dimensional components, leading to a new approximation error analysis of ReLU neural networks with respect to the diffused score function. The rate of convergence under the 1-Wasserstein distance is also derived with a slight modification of the method.

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arXiv2025

CINDES: Classification induced neural density estimator and simulator

Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints, and theoretical understanding remains limited. In particular, it is unclear whether such estimators can adaptively achieve faster convergence rates when the underlying density exhibits a low-dimensional structure. This paper addresses these gaps by proposing a structure-agnostic neural density estimator that is (i) straightforward to implement and (ii) provably adaptive, attaining faster rates when the true density admits a low-dimensional composition structure. Another key contribution of our work is to show that the proposed estimator integrates naturally into generative sampling pipelines, most notably score-based diffusion models, where it achieves provably faster convergence when the underlying density is structured. We validate its performance through extensive simulations and a real-data application.

stat.ML↗

arXiv2025

Fundamental Computational Limits in Pursuing Invariant Causal Prediction and Invariance-Guided Regularization

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as ICP [Peters et al., 2016] and EILLS [Fan et al., 2024] that can attain sample-efficient estimation are based on exponential time algorithms. In this paper, we show that such a problem is intrinsically hard in computation: the decision problem, testing whether a non-trivial prediction-invariant solution exists across two environments, is NP-hard even for the linear causal relationship. In the world where P$\neq$NP, our results imply that the estimation error rate can be arbitrarily slow using any computationally efficient algorithm. This suggests that pursuing causality is fundamentally harder than detecting associations when no prior assumption is pre-offered. Given there is almost no hope of computational improvement under the worst case, this paper proposes a method capable of attaining both computationally and statistically efficient estimation under additional conditions. Furthermore, our estimator is a distributionally robust estimator with an ellipse-shaped uncertain set where more uncertainty is placed on spurious directions than invariant directions, resulting in a smooth interpolation between the most predictive solution and the causal solution by varying the invariance hyper-parameter. Non-asymptotic results and empirical applications support the claim.

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arXiv2024

Causality Pursuit from Heterogeneous Environments via Neural Adversarial Invariance Learning

Pursuing causality from data is a fundamental problem in scientific discovery, treatment intervention, and transfer learning. This paper introduces a novel algorithmic method for addressing nonparametric invariance and causality learning in regression models across multiple environments, where the joint distribution of response variables and covariates varies, but the conditional expectations of outcome given an unknown set of quasi-causal variables are invariant. The challenge of finding such an unknown set of quasi-causal or invariant variables is compounded by the presence of endogenous variables that have heterogeneous effects across different environments. The proposed Focused Adversarial Invariant Regularization (FAIR) framework utilizes an innovative minimax optimization approach that drives regression models toward prediction-invariant solutions through adversarial testing. Leveraging the representation power of neural networks, FAIR neural networks (FAIR-NN) are introduced for causality pursuit. It is shown that FAIR-NN can find the invariant variables and quasi-causal variables under a minimal identification condition and that the resulting procedure is adaptive to low-dimensional composition structures in a non-asymptotic analysis. Under a structural causal model, variables identified by FAIR-NN represent pragmatic causality and provably align with exact causal mechanisms under conditions of sufficient heterogeneity. Computationally, FAIR-NN employs a novel Gumbel approximation with decreased temperature and a stochastic gradient descent ascent algorithm. The procedures are demonstrated using simulated and real-data examples.

math.ST↗

arXiv2024

The Implicit Bias of Heterogeneity towards Invariance: A Study of Multi-Environment Matrix Sensing

Models are expected to engage in invariance learning, which involves distinguishing the core relations that remain consistent across varying environments to ensure the predictions are safe, robust and fair. While existing works consider specific algorithms to realize invariance learning, we show that model has the potential to learn invariance through standard training procedures. In other words, this paper studies the implicit bias of Stochastic Gradient Descent (SGD) over heterogeneous data and shows that the implicit bias drives the model learning towards an invariant solution. We call the phenomenon the implicit invariance learning. Specifically, we theoretically investigate the multi-environment low-rank matrix sensing problem where in each environment, the signal comprises (i) a lower-rank invariant part shared across all environments; and (ii) a significantly varying environment-dependent spurious component. The key insight is, through simply employing the large step size large-batch SGD sequentially in each environment without any explicit regularization, the oscillation caused by heterogeneity can provably prevent model learning spurious signals. The model reaches the invariant solution after certain iterations. In contrast, model learned using pooled SGD over all data would simultaneously learn both the invariant and spurious signals. Overall, we unveil another implicit bias that is a result of the symbiosis between the heterogeneity of data and modern algorithms, which is, to the best of our knowledge, first in the literature.

cs.LG↗

arXiv2023

Factor Augmented Sparse Throughput Deep ReLU Neural Networks for High Dimensional Regression

This paper introduces a Factor Augmented Sparse Throughput (FAST) model that utilizes both latent factors and sparse idiosyncratic components for nonparametric regression. The FAST model bridges factor models on one end and sparse nonparametric models on the other end. It encompasses structured nonparametric models such as factor augmented additive models and sparse low-dimensional nonparametric interaction models and covers the cases where the covariates do not admit factor structures. Via diversified projections as estimation of latent factor space, we employ truncated deep ReLU networks to nonparametric factor regression without regularization and to a more general FAST model using nonconvex regularization, resulting in factor augmented regression using neural network (FAR-NN) and FAST-NN estimators respectively. We show that FAR-NN and FAST-NN estimators adapt to the unknown low-dimensional structure using hierarchical composition models in nonasymptotic minimax rates. We also study statistical learning for the factor augmented sparse additive model using a more specific neural network architecture. Our results are applicable to the weak dependent cases without factor structures. In proving the main technical result for FAST-NN, we establish a new deep ReLU network approximation result that contributes to the foundation of neural network theory. Our theory and methods are further supported by simulation studies and an application to macroeconomic data.

math.ST↗

arXiv2023

Environment Invariant Linear Least Squares

This paper considers a multi-environment linear regression model in which data from multiple experimental settings are collected. The joint distribution of the response variable and covariates may vary across different environments, yet the conditional expectations of $y$ given the unknown set of important variables are invariant. Such a statistical model is related to the problem of endogeneity, causal inference, and transfer learning. The motivation behind it is illustrated by how the goals of prediction and attribution are inherent in estimating the true parameter and the important variable set. We construct a novel environment invariant linear least squares (EILLS) objective function, a multi-environment version of linear least-squares regression that leverages the above conditional expectation invariance structure and heterogeneity among different environments to determine the true parameter. Our proposed method is applicable without any additional structural knowledge and can identify the true parameter under a near-minimal identification condition. We establish non-asymptotic $\ell_2$ error bounds on the estimation error for the EILLS estimator in the presence of spurious variables. Moreover, we further show that the $\ell_0$ penalized EILLS estimator can achieve variable selection consistency in high-dimensional regimes. These non-asymptotic results demonstrate the sample efficiency of the EILLS estimator and its capability to circumvent the curse of endogeneity in an algorithmic manner without any prior structural knowledge. To the best of our knowledge, this paper is the first to realize statistically efficient invariance learning in the general linear model.

math.ST↗

arXiv2022

How do noise tails impact on deep ReLU networks?

This paper investigates the stability of deep ReLU neural networks for nonparametric regression under the assumption that the noise has only a finite p-th moment. We unveil how the optimal rate of convergence depends on p, the degree of smoothness and the intrinsic dimension in a class of nonparametric regression functions with hierarchical composition structure when both the adaptive Huber loss and deep ReLU neural networks are used. This optimal rate of convergence cannot be obtained by the ordinary least squares but can be achieved by the Huber loss with a properly chosen parameter that adapts to the sample size, smoothness, and moment parameters. A concentration inequality for the adaptive Huber ReLU neural network estimators with allowable optimization errors is also derived. To establish a matching lower bound within the class of neural network estimators using the Huber loss, we employ a different strategy from the traditional route: constructing a deep ReLU network estimator that has a better empirical loss than the true function and the difference between these two functions furnishes a low bound. This step is related to the Huberization bias, yet more critically to the approximability of deep ReLU networks. As a result, we also contribute some new results on the approximation theory of deep ReLU neural networks.

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arXiv2020

Domain Adaptive Imitation Learning

We study the question of how to imitate tasks across domains with discrepancies such as embodiment, viewpoint, and dynamics mismatch. Many prior works require paired, aligned demonstrations and an additional RL step that requires environment interactions. However, paired, aligned demonstrations are seldom obtainable and RL procedures are expensive. We formalize the Domain Adaptive Imitation Learning (DAIL) problem, which is a unified framework for imitation learning in the presence of viewpoint, embodiment, and dynamics mismatch. Informally, DAIL is the process of learning how to perform a task optimally, given demonstrations of the task in a distinct domain. We propose a two step approach to DAIL: alignment followed by adaptation. In the alignment step we execute a novel unsupervised MDP alignment algorithm, Generative Adversarial MDP Alignment (GAMA), to learn state and action correspondences from \emph{unpaired, unaligned} demonstrations. In the adaptation step we leverage the correspondences to zero-shot imitate tasks across domains. To describe when DAIL is feasible via alignment and adaptation, we introduce a theory of MDP alignability. We experimentally evaluate GAMA against baselines in embodiment, viewpoint, and dynamics mismatch scenarios where aligned demonstrations don't exist and show the effectiveness of our approach.

cs.LG↗

arXiv2019

Convex Formulation of Overparameterized Deep Neural Networks

Analysis of over-parameterized neural networks has drawn significant attention in recentyears. It was shown that such systems behave like convex systems under various restrictedsettings, such as for two-level neural networks, and when learning is only restricted locally inthe so-called neural tangent kernel space around specialized initializations. However, there areno theoretical techniques that can analyze fully trained deep neural networks encountered inpractice. This paper solves this fundamental problem by investigating such overparameterizeddeep neural networks when fully trained. We generalize a new technique called neural feature repopulation, originally introduced in (Fang et al., 2019a) for two-level neural networks, to analyze deep neural networks. It is shown that under suitable representations, overparameterized deep neural networks are inherently convex, and when optimized, the system can learn effective features suitable for the underlying learning task under mild conditions. This new analysis is consistent with empirical observations that deep neural networks are capable of learning efficient feature representations. Therefore, the highly unexpected result of this paper can satisfactorily explain the practical success of deep neural networks. Empirical studies confirm that predictions of our theory are consistent with results observed in practice.

cs.LG↗

arXiv2018

Language Modeling with Sparse Product of Sememe Experts

Most language modeling methods rely on large-scale data to statistically learn the sequential patterns of words. In this paper, we argue that words are atomic language units but not necessarily atomic semantic units. Inspired by HowNet, we use sememes, the minimum semantic units in human languages, to represent the implicit semantics behind words for language modeling, named Sememe-Driven Language Model (SDLM). More specifically, to predict the next word, SDLM first estimates the sememe distribution gave textual context. Afterward, it regards each sememe as a distinct semantic expert, and these experts jointly identify the most probable senses and the corresponding word. In this way, SDLM enables language models to work beyond word-level manipulation to fine-grained sememe-level semantics and offers us more powerful tools to fine-tune language models and improve the interpretability as well as the robustness of language models. Experiments on language modeling and the downstream application of headline gener- ation demonstrate the significant effect of SDLM. Source code and data used in the experiments can be accessed at https:// github.com/thunlp/SDLM-pytorch.

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arXiv2017

ZhuSuan: A Library for Bayesian Deep Learning

In this paper we introduce ZhuSuan, a python probabilistic programming library for Bayesian deep learning, which conjoins the complimentary advantages of Bayesian methods and deep learning. ZhuSuan is built upon Tensorflow. Unlike existing deep learning libraries, which are mainly designed for deterministic neural networks and supervised tasks, ZhuSuan is featured for its deep root into Bayesian inference, thus supporting various kinds of probabilistic models, including both the traditional hierarchical Bayesian models and recent deep generative models. We use running examples to illustrate the probabilistic programming on ZhuSuan, including Bayesian logistic regression, variational auto-encoders, deep sigmoid belief networks and Bayesian recurrent neural networks.

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