arXiv subjects

Lingzhou Xue

Publications and source records attributed to Lingzhou Xue.

At least 19 recordsLinked to original sources

arXiv2026

New Empirical Process Tools and Their Applications to Robust Deep ReLU Networks and Phase Transitions for Nonparametric Regression

This paper introduces new empirical process tools for analyzing a broad class of statistical learning models under heavy-tailed noise and complex function classes. Our primary contribution is the derivation of two Dudley-type maximal inequalities for expected empirical processes that remove restrictive assumptions such as light tails and uniform boundedness of the function class. These inequalities enlarge the scope of empirical process theory available for statistical learning and nonparametric estimation. Exploiting the new bounds, we establish robustness guarantees for deep ReLU network estimators in Huber and quantile regression. In particular, we prove a unified non-asymptotic sub-Gaussian concentration bound that remains valid even under infinite-variance noise and provide a comprehensive analysis of non-asymptotic robustness for deep Huber estimators across all noise regimes. For deep quantile regression, we provide the first non-asymptotic sub-Gaussian bounds without requiring moment assumptions. As an additional application, our framework yields estimation error bounds for nonparametric least-squares estimators that simultaneously accommodate infinite-variance noise, non-Donsker function classes, and approximation error. Moreover, unlike prior approaches based on specialized multiplier processes, our framework extends to broader empirical risk minimization problems, including the nonparametric generalized linear models and the ``set-structured'' models.

math.ST↗

arXiv2026

Score-Preserving Continual Lasso under Task Shift

Continual learning (CL) aims to learn from sequential tasks while mitigating catastrophic forgetting when historical data are no longer accessible. We study continual learning for high-dimensional sparse linear regression, where $\ell_1$ regularization creates a difficulty absent from continual ridge regression: that recursively reusing an $\ell_1$-penalized estimator can propagate earlier shrinkage and accumulate regularization bias across tasks. We propose score-preserving continual Lasso (SP-CL), which separates sparse estimation from state transmission by preserving the historical squared-loss score. Under squared loss, its cumulative estimator exactly recovers a full-history Lasso minimizer. When task coefficients coincide, it inherits the full-history sparse rate. For related task-specific coefficients, SP-CL uses a regularized current-task correction that leaves the transmitted state unchanged and attains the offline source-assisted rate under an oracle related-task condition. We also derive Overall/BWT/FWT decompositions that distinguish historical information loss, task conflict, and current-task specialization, and validate the resulting regimes in simulation.

stat.ML↗

arXiv2026

Adaptive Algorithms for Robust Phase Retrieval

This paper considers robust phase retrieval, which can be cast as a nonsmooth and nonconvex optimization problem. We propose two first-order algorithms with adaptive step sizes: the subgradient algorithm (AdaSubGrad) and the inexact proximal linear algorithm (AdaIPL). Our contribution lies in a novel design of adaptive step sizes based on quantiles of the absolute residuals. We analyze local linear convergence of both algorithms across different hyperparameter regimes under i.i.d. centered sub-Gaussian measurements, a stability condition linking the measurement distribution and the corruption level, and an additional uniform small-ball condition. Numerical experiments on synthetic datasets and image recovery also demonstrate that our methods are competitive with existing methods in the literature that utilize predetermined (possibly impractical) step sizes, such as subgradient methods and the inexact proximal linear method.

math.OC↗

arXiv2026

MLToolBench: Learning Tool-Augmented Agents for Machine Learning Development

Machine learning engineering (MLE) agents have made substantial progress, but learning through ML experimentation remains costly in time and computation. Synthetic environments reduce these costs while introducing variations in data and experimental settings that require task-specific diagnosis. Access to diagnostic tools alone does not ensure that agents learn when to use them or how to act on their findings. We introduce ToolMLBench, a suite of executable tools for data inspection, code verification, and experiment diagnosis, together with an SFT and RL pipeline for learning their use. Diagnostic calls acquire evidence whose value depends on subsequent decisions, so final outcomes provide limited guidance on which calls to reinforce. We address this challenge with SPICE, which measures how privileged context changes the likelihood of a sampled tool action and uses this difference as a turn-level reward alongside the final outcome. We train on 80 synthetic tasks and evaluate on 25 in-domain and 10 out-of-domain tasks. Providing tool interfaces and descriptions alone yields inconsistent gains across unadapted models. With the same diagnostic interface, our training pipeline raises in-domain success from 24.8% to 52.4% for Qwen3-8B and from 35.6% to 69.2% for Qwen3.5-35B-A3B. The latter also improves from 31% to 48% out-of-domain, supporting learned diagnostic tool use on held-out sources and targets.

cs.AI↗

arXiv2026

Verify Less, Evolve More: Training Idea-Level Critics for Verification-Efficient ML Evolving Agents

As large language models become more powerful, self-evolving agents are able to tackle challenging tasks including AI for machine learning (AI4ML). In AI4ML, while empirical verification is available, it often requires computationally costly model training and evaluation, limiting the speed and scale of agent evolution. Yet verification efficiency remains under-explored, and frontier models provide only limited gains when used directly as idea selectors. We address this gap with specialized idea-level critic models that predict whether a proposed ML modification will improve upon the current solution, allowing agents to screen ideas and concentrate verification resources on the most promising candidates. We train the critic models through supervised fine-tuning on high-quality critiques synthesized by Gemini-3.1-Pro, followed by GRPO to further improve their predictive accuracy. Empirically, our critic models outperform Gemini-3.1-Pro in static idea evaluation, and these gains extend to agent inference, continual learning, and policy training. During inference-time evolution, they improve final solution quality under the same verification budget by selecting more promising ideas, with further gains from continual learning. During policy training, they serve as learned reward models, reserving empirical verification for uncertain cases and enabling substantially more policy updates with the same verification resources. Together, these results show that idea-level critic models help ML agents discover better solutions and learn stronger proposal policies under limited verification budgets.

cs.AI↗

arXiv2026

A New Inexact Manifold Proximal Linear Algorithm with Adaptive Stopping Criteria

This paper proposes a new inexact manifold proximal linear (IManPL) algorithm for solving nonsmooth, nonconvex composite optimization problems over an embedded submanifold. At each iteration, IManPL solves a convex subproblem inexactly, guided by two adaptive stopping criteria. Under the stated assumptions, we establish convergence guarantees and an $O(ε^{-3})$ first-order oracle complexity bound for APG subproblem solves, matching the best-known order for this class of problems. Numerical experiments on sparse spectral clustering and sparse principal component analysis demonstrate that our methods outperform existing approaches.

math.OC↗

arXiv2026

Understanding Gap-Dependent Regret for Optimism-Based Reinforcement Learning with Linear Function Approximation

We study gap-dependent regret for reinforcement learning with linear function approximation. While prior works have established gap-dependent guarantees in this setting, existing analyses do not apply to algorithms that achieve the nearly minimax-optimal worst-case regret bound $\tilde{O}(d\sqrt{H^3K})$, where $d$ is the feature dimension, $H$ is the horizon length, and $K$ is the number of episodes. We bridge this gap by establishing the first gap-dependent regret bound for the nearly minimax-optimal algorithm LSVI-UCB++ (He et al., 2023), with an expected regret bound $\tilde{O}(d^2H^3/Δ_{\min}+d^6H^5)$, improving the dependence on both $d$ and $H$ in the leading gap-dependent term compared with previous results. To understand the exploration cost induced by optimism, we establish a structural lower bound $Ω(d^2H^3/Δ_{\min})$ for a broad class of algorithms based on persistent ellipsoidal optimism. When specialized to LSVI-UCB++, this result shows that the leading dependence of our upper bound on $d$, $H$, and $Δ_{\min}$ is tight up to logarithmic factors. Beyond this algorithmic class, we establish a general gap-dependent lower bound $Ω(dH^3\log K/Δ_{\min})$ for arbitrary learning algorithms, showing that the logarithmic dependence on $K$ and the cubic dependence on $H$ are intrinsic to gap-dependent expected regret in linear MDPs. Together, our results substantially narrow the gap between upper and lower bounds and provide a sharper characterization of gap-dependent learning and optimism-based exploration with linear function approximation.

stat.ML↗

arXiv2026

Exact Fast Batch Simulation for Tabular Reinforcement Learning

Simulation is a fundamental computational primitive in reinforcement learning (RL), yet conventional simulation explicitly generates individual trajectories even when downstream procedures use only aggregate statistics. To address this, we develop an exact fast-simulation framework for finite-horizon tabular Markov decision processes. Our framework has two complementary modes. In direct batch simulation, a batch is represented by its aggregate Markov flow. With sufficient parallel simulation resources, this flow can be obtained by trajectory aggregation; when such simulation is unavailable or costly but the initial state and transition distributions are directly accessible, we instead generate an identically distributed flow through forward Markov-flow sampling without materializing individual trajectories. The latter reduces the simulator-side computational dependence on batch size $m$ from $O(m)$ to $O(1)$. In adaptive batch simulation, when batch length is determined by a data-dependent condition, exact multivariate-hypergeometric splitting recursively refines a candidate Markov flow while preserving the conditional law, reducing the cost dependence on $m$ from $O(m)$ to $O(\log m)$. Together, these modes accelerate simulation by keeping trajectories aggregated whenever possible and refining flows only when required to locate data-dependent boundaries. The framework applies broadly across simulator-based, offline, and online batch or stage-based RL, as illustrated with representative algorithms from each setting.

stat.ML↗

arXiv2026

Variance-Aware Fine-Grained Gap-Dependent Bounds for Online Reinforcement Learning

We study model-free online reinforcement learning (RL) for episodic tabular Markov decision processes, focusing on both gap-dependent regret and policy switching cost. While fine-grained gap-dependent analysis has been established for model-free RL algorithms using Hoeffding-type exploration bonuses, such results for model-free algorithms with variance-based exploration bonuses remain unknown, despite their superior worst-case and coarse-grained gap-dependent guarantees. In this paper, we resolve this open problem by establishing the first fine-grained gap-dependent regret upper bound for UCB-Bernstein+, a refined UCB-Bernstein algorithm, in variance-aware model-free online RL. Moreover, by integrating a stage-wise policy update design into our fine-grained framework and using refined variance-based bonuses, we achieve the best-known gap-dependent local switching cost to date. In addition, our analysis yields improved worst-case guarantees for both regret and local switching cost over the original UCB-Bernstein algorithm. Numerical experiments further demonstrate that UCB-Bernstein+ achieves favorable empirical performance in both regret and local switching cost.

stat.ML↗

arXiv2026

Asymptotic Theory for Combining Dependent $p$-Values for Global Hypothesis Testing

Combining $p$-values is a fundamental procedure in global hypothesis testing. In modern high-dimensional settings, however, component $p$-values often exhibit complex dependence and rely on asymptotic approximations rather than exact finite-sample uniform distributions. This paper establishes a unified asymptotic theory for weighted transformation statistics that decouples marginal finite-sample approximation error from the joint dependence structure. We also provide sufficient conditions based on conditional probability bounds to verify the joint-tail conditions. Utilizing this framework, we derive explicit dimension-growth and correlation rates for test statistics operating under asymptotic Gaussian and chi-square calibrations. For non-exact finite-sample statistics, we analyze standardized weighted sums, demonstrating how Cramér moderate deviations control relative tail error. Analytical examples demonstrate why both marginal and joint conditions are mathematically indispensable for valid global inference under dependence, and numerical experiments confirm that our asymptotic framework maintains accurate finite-sample size control at extreme significance levels.

math.ST↗

arXiv2026

Belted Engression: Sufficient Dimension Reduction for Generative Distributional Regression

Modern conditional generative models face significant challenges when learning complex covariate dependencies. While sufficient dimension reduction (SDR) provides a principled approach to compress these dependencies, traditional SDR frameworks were not formulated for conditional generation. To bridge this gap, we propose Belted Engression, a unified and architecturally parameter-efficient framework for generative distributional regression. Our approach establishes an end-to-end compress-then-generate paradigm driven by sufficient representation learning, embedding a structural bottleneck into the generative architecture. Theoretically, we prove that the standard SDR condition is equivalent to a law-preserving generative factorization, which is achieved at the global optimum of the population Belted Engression objective. Furthermore, by uncovering a localized Bernstein-type control for the energy-score loss, we establish finite-sample convergence rates that are sharper than those of existing results. We also prove that this belted architecture is strictly smaller, operating with an asymptotically vanishing parameter count relative to the unstructured baseline. Extensive simulations and real-world applications demonstrate that Belted Engression achieves superior distributional prediction and SDR recovery with fewer trainable parameters.

cs.LG↗

arXiv2026

Adaptive Regularization via Extreme Value Distributions for Gaussian Graphical Models

Edge selection in Gaussian graphical models is fundamentally a variable selection problem where pairwise relationships determine construct validity and variable importance in psychological networks. In psychology, network estimation relies predominantly on $\ell_1$ regularization where uniform shrinkage systematically underestimates edge and centrality parameters. Alternative penalties overcome this bias but rely on fixed hyperparameters that do not adapt to the signal in the data. We develop a family of data-adaptive regularization penalties grounded in extreme value theory. Across 290 empirical psychological datasets, we show that absolute partial correlations are well-described by the Weibull distribution. Using this empirical regularity, we derive Weibull, Gumbel, and Exponential penalties that approximate $\ell_0$ penalization and calibrate their hyperparameters to each dataset's noise floor. We formally prove the asymptotic properties of their static forms and conduct a large-scale simulation spanning two network topologies and various sample sizes ($N$ = 100--10,000), demonstrating that their adaptive forms maintain high specificity while accumulating sensitivity as sample size increases with low parameter bias and high rank-order centrality congruence relative to field standards. Empirically, method choice alone determined centrality rankings at sample sizes typical in psychology. Of the three adaptive penalties, Weibull is recommended given the interpretability of its parameters.

stat.ME↗

arXiv2026

Provably Efficient Federated Reinforcement Learning with Linear Function Approximation and Logarithmic Communication Cost

We study federated online reinforcement learning with linear function approximation. While recent multi-agent reinforcement learning algorithms achieve strong regret guarantees, they typically require sharing raw trajectories. This reliance incurs a communication cost that scales linearly with the number of episodes and violates the privacy constraints of federated settings. To address these limitations, we propose Fed-LSVI, the first provably efficient federated algorithm for online reinforcement learning with linear function approximation in episodic Markov decision processes. By integrating a determinant-based event-triggered synchronization with a stepwise backward update mechanism, Fed-LSVI enables agents to collaboratively learn an optimal policy by exchanging only compressed sufficient statistics. We prove that Fed-LSVI achieves a regret bound of $\widetilde{\mathcal O}(\sqrt{Md^3H^4T})$, where $d$ is the feature dimension, $H$ is the horizon length, $M$ is the number of agents, and $T$ is the number of episodes per agent, matching the best-known regret for multi-agent online reinforcement learning with linear function approximation. Moreover, by following the stringent communication and privacy constraints of the federated setting, Fed-LSVI reduces the communication cost to only logarithmic dependence on $T$, representing a significant improvement over prior methods.

stat.ML↗

arXiv2026

Preference-Based Self-Distillation: Beyond KL Matching via Reward Regularization

On-policy distillation is an efficient alternative to reinforcement learning, offering dense token-level training signals. However, its reliance on a stronger external teacher has driven recent work on on-policy self-distillation, where the same model serves as both teacher and student under different prompt contexts. Yet, existing self-distillation methods largely reduce learning to KL matching toward the context-augmented teacher model. This approach often suffers from training instability and can degrade reasoning performance over time. Moreover, self-distillation from the same model with prompt augmentation lacks the exploratory diversity provided by a genuine external teacher. To address these limitations, we move beyond fixed-teacher KL matching and propose \textbf{P}reference-\textbf{B}ased \textbf{S}elf-\textbf{D}istillation (\textbf{PBSD}), which revisits on-policy self-distillation through a reward-regularized perspective. Instead of directly matching the teacher distribution, we derive a reward-regularized objective whose analytic optimum is a reward-reweighted teacher distribution, yielding a target policy provably superior to the original teacher under this objective. Practically, PBSD optimizes preference gaps between teacher and student samples while maintaining on-policy student sampling. We support this framework with a statistical analysis of the induced preference-learning problem, formally establishing when on policy self-distillation is preferable to learning from an external teacher in our setting. Experiments on mathematical reasoning and tool-use benchmarks across multiple model scales demonstrate that PBSD consistently achieves the strongest average performance among comparable baselines, showing improved training stability over prior self-distillation baselines while preserving token efficiency.

cs.LG↗

arXiv2026

Difficulty-Aware Semantic-ID Optimization for Generative Recommendation

Semantic-ID-based generative recommendation casts retrieval and ranking as autoregressive generation over hierarchical item identifiers. A common recipe is SFT followed by GRPO, yet vanilla GRPO is poorly matched to this tree-structured task. Under the frozen SFT checkpoint, the exact target is absent from the first 16 candidates of the 50-beam constrained ranking for many prompts, and in harder cases none of these candidates enters the target SID branch. This prompt-level diagnostic motivates a training concern: when on-policy GRPO groups are similarly target-missing, item-level rewards may produce weak or degenerate reward variation even if some candidates follow part of the target path. We propose Difficulty-Aware Semantic-ID Optimization (DASO), a tree-aware post-training method that addresses this failure mode as an online rollout-allocation problem. Instead of using fixed difficulty buckets or uniformly injecting ground-truth completions, DASO profiles each current rollout group by prefix-match depth, locates the bottleneck SID levels where candidates leave the target path, and reallocates a bounded portion of the group to prefix-guided completions while retaining raw rollouts for contrast. A SID-prefix reward provides graded credit, while an auxiliary SFT anchor mitigates regression on examples already solved by the SFT checkpoint. On the public benchmarks, DASO improves over MiniOneRec-style GRPO on 11 of 12 metrics and achieves the best result on 9 of 12 metrics; it also improves most level-wise recall metrics on the internal recommendation task.

cs.AI↗

arXiv2026

Distance Profile Embedding for Independence and Conditional Independence Testing of Random Objects

Testing independence or conditional independence is fundamental to statistical inference, yet existing methods for non-Euclidean random objects often face a difficult trade-off between geometric flexibility and theoretical tractability. We introduce the Distance Profile Embedding (DPE), a novel representation that maps random objects from general metric spaces into a Hilbert space of square-integrable functions. We prove that this mapping is injective and preserves full distributional information without requiring isometric Hilbert embeddings or one-to-one correspondence conditions. Leveraging the DPE, we develop a unified framework for marginal and conditional independence testing of random objects that enjoys a rigorous asymptotic theory for both size and power. Notably, our framework is the first in the literature to accommodate object-valued conditioning variables when testing conditional independence, overcoming the Euclidean or Hilbertian constraints of existing methodologies. We facilitate the calculation of analytic $p$-values using closed-form asymptotic null distributions, which avoids the computational burden of permutation tests common in existing metric-based methods. The numerical properties of our methods are demonstrated through both simulations and two real-world applications involving gut microbiome compositions and global human mortality distributions, respectively.

stat.ME↗

arXiv2026

Train Large, Deploy Compact: Structured Compression for Compact Low-Rank Adaptation

Low-rank adaptation (LoRA) has become a widely used paradigm for parameter-efficient fine-tuning of large language models, yet its representational capacity often lags behind full fine-tuning. Within the context of LoRA, a key open question is how to obtain expressive low-rank adapters from over-parameterized spaces. We propose \textit{PrunedLoRA}, a new framework that leverages structured pruning to obtain highly representative low-rank adapters from an over-parameterized initialization. Unlike prior approaches that impose a fixed low-rank budget, PrunedLoRA dynamically prunes less important components during fine-tuning and prevents their reactivation, enabling flexible and adaptive rank allocation. For structured pruning, by minimizing the pruning error for overall loss, we provide fine-grained pruning and recovery updates in a gradient-based pruning strategy with grounded interpretation. We provide the first theoretical analysis of the robustness of structured pruning and provably show that under the impact of weight perturbation, gradient-based pruning is more robust than activation-based pruning with respect to overall loss. Empirically, PrunedLoRA consistently outperforms LoRA and its variants across supervised fine-tuning tasks in mathematical reasoning, code generation, and natural language understanding, and it also demonstrates advantages over existing structured pruning methods across diverse sparsity levels.

cs.LG↗

arXiv2026

A Test for Treatment Heterogeneity under a Distributional Difference-in-Difference Framework

We develop a novel distributional Difference-in-Differences (DiD) framework to capture treatment heterogeneity across outcome distributions. By leveraging optimal transport, we use the control group to estimate the untreated distributional drift from the pre- to post-treatment period and apply it to the treated group's pre-treatment baseline, constructing a counterfactual distribution under the assumption of no treatment effect. We frame the null hypothesis as a distributional equality between the transported counterfactual distribution and the observed treated post-treatment distribution, and test it using a maximum mean discrepancy statistic in a reproducing kernel Hilbert space (RKHS). The resulting nonparametric omnibus test is sensitive to changes in location, scale, shape, and tail behavior. Under the null, we derive the asymptotic Gaussian quadratic-form limit of the test statistic, while under local alternatives, we provide a unified characterization of power that establishes its Pitman local power and moderate-deviation consistency. Our theory reveals how detectability is shaped by the interaction between transport-induced drift and RKHS geometry. Simulations and an application to the Card--Krueger minimum-wage data demonstrate that the proposed method identifies key distributional treatment effects missed by classical mean-based DiD.

stat.ME↗