arXiv subjects

Shuheng Zhou

Publications and source records attributed to Shuheng Zhou.

At least 19 recordsLinked to original sources

arXiv2026

ArmorOCR: Grounded Adversarial Visual Perception via Observation-Transferred Self-Distillation

Large multimodal models (LMMs) have demonstrated strong OCR recognition capabilities, yet remain vulnerable to adversarial visual text that is readable to humans but challenging for models to localize and recognize. Existing OCR benchmarks mainly focus on natural or document-style text, while adversarial OCR evaluations remain limited in scale, task coverage, or region-aware evaluation. In this paper, we formulate adversarial OCR as a \textbf{grounded OCR perception} task and introduce \textbf{AdvSpot}, the first benchmark for grounded adversarial OCR evaluation. AdvSpot comprises 390 images with region-level annotations, spanning 5 primary categories and 13 fine-grained adversarial OCR types. To address this challenge, we propose \textbf{ArmorOCR}, a two-stage training framework for robust adversarial OCR perception. ArmorOCR first acquires missing adversarial OCR perception from privileged transformed observations through On-Policy Self-Distillation (OPSD), and then refines grounded OCR perception through Group Relative Policy Optimization (GRPO) with task-conditioned rewards for localization, recognition, full spotting, and visual question answering (VQA). Experiments on our AdvSpot, other adversarial OCR benchmarks, and general OCR benchmarks demonstrate that ArmorOCR consistently improves adversarial OCR perception while preserving competitive general OCR capability.

cs.CV↗

arXiv2026

Semidefinite programming relaxations and debiasing for MAXCUT-based clustering

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions in $\mathbb{R}^p$. We consider semidefinite programming relaxations of an integer quadratic program that is formulated essentially as finding the maximum cut on a graph, where edge weights in the cut represent dissimilarity scores between two nodes based on their $p$ features. We define the signal-to-noise ratio (SNR) as $s^2 := \min\{n p γ^2, Δ^2\}$, where $Δ^2 := p γ$ denotes the $\ell_2^2$ distance between the two cluster centers. Our contributions are twofold. First, we provide a unified framework for analyzing three computationally efficient algorithms: SDP1, BalancedSDP, and Spectral clustering, yielding universal polynomial-rate misclassification guarantees for all three algorithms. Moreover, our theory allows for partial recovery (success rate $< 100\%$) as long as $s^2$ is lower bounded by a constant. Second, we prove that the misclassification errors for SDP1 and BalancedSDP decay exponentially with respect to the SNR $s^2$ and the BalancedSDP requires no explicit debiasing when the two clusters have equal sizes. To our knowledge, this is the first time such results are obtained for semidefinite relaxations of MAX CUT in population clustering. We provide simulation evidence illuminating the theoretical predictions.

stat.ML↗

arXiv2026

LoMC: Localized Multidirectional Correction for Refusal Suppression in Routed Foundation Models

We study controlled post-training refusal suppression in routed MoE and hybrid-MoE foundation models, aiming to increase non-refusal target-response behavior while preserving general capability under a compact intervention footprint. Existing broad direction-based edits can perturb general-purpose computation, whereas support-only expert edits often lack sufficient capacity to correct heterogeneous refusal representations. To address this limitation, we introduce Localized Multidirectional Correction (LoMC), a support-gated intervention framework that follows a support-then-correction execution order: it first identifies a compact edit support, then aggregates prototype correction directions into layer-wise correction directions, and finally applies rank-one layer-wise correction only within the selected support. By using the edit support as a structural gating constraint, LoMC increases correction capacity without expanding the intervention scope. Experiments on text-only and multimodal safety benchmarks across four routed backbones show that LoMC substantially improves non-refusal target-response behavior while maintaining general capability under a compact intervention footprint.

stat.ML↗

arXiv2026

RoCo-ACE: Rollout-Conditioned Online Distillation for Retention-Aware Knowledge Injection

Knowledge injection updates pretrained MLLMs with new factual or domain-specific knowledge, but fitting full authoritative answers can cause drift in non-updated behavior. Online distillation mitigates this drift by training on model-generated rollouts, yet uniform reference-conditioned distillation provides coarse supervision: it can under-emphasize reference-supported rollout tokens and supervise omitted facts only indirectly. We introduce RoCo-ACE, a rollout-conditioned online distillation objective for knowledge injection. RoCo uses same-rollout reference-free/reference-conditioned likelihood contrast to reallocate additional distillation weight to reference-supported rollout tokens, while ACE adds sparse reference-side anchored correction for authoritative anchors omitted from the rollout without full-answer imitation. Across three knowledge-injection settings, six retention benchmarks, multiple baselines, and multiple base models, RoCo-ACE achieves the best injected-knowledge accuracy among compared methods while keeping evaluated retention close to the base model.

cs.AI↗

arXiv2025

Finite sample rates of convergence for the Bigraphical and Tensor graphical Lasso estimators

Many modern datasets exhibit dependencies among observations as well as variables. A decade ago, Kalaitzis et. al. (2013) proposed the Bigraphical Lasso, an estimator for precision matrices of matrix-normals based on the Cartesian product of graphs; they observed that the associativity of the Kronecker sum yields an approach to the modeling of datasets organized into 3 or higher-order tensors. Subsequently, Greenewald, Zhou and Hero (2019) explored this possibility to a great extent, by introducing the tensor graphical Lasso (TeraLasso) for estimating sparse $L$-way decomposable inverse covariance matrices for all $L \ge 2$, and showing the rates of convergence in the Frobenius and operator norms for estimating this class of inverse covariance matrices for sub-gaussian tensor-valued data. In this paper, we provide sharper rates of convergence for both Bigraphical and TeraLasso estimators for inverse covariance matrices. This improves upon the rates presented in GZH 2019. In particular, (a) we strengthen the bounds for the relative errors in the operator and Frobenius norm by a factor of approximately $\log p$; (b) Crucially, this improvement allows for finite sample estimation errors in both norms to be derived for the two-way Kronecker sum model. This closes the gap between the low single-sample error for the two-way model as observed in GZH 2019 and the lack of theoretical guarantee for this particular case. The two-way regime is important because it is the setting that is the most theoretically challenging, and simultaneously the most common in applications. In the current paper, we elaborate on the Kronecker Sum model, highlight the proof strategy and provide full proofs of all main theorems.

math.ST↗

arXiv2025

Thresholded Lasso for high dimensional variable selection

Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $β\in {\mathbb R}^p$ in a linear model $Y = X β+ ε$, where $X_{n \times p}$ is a design matrix normalized to have column $\ell_2$-norm $\sqrt{n}$, and $ε\sim N(0, σ^2 I_n)$. We show that under the restricted eigenvalue (RE) condition, it is possible to achieve the $\ell_2$ loss within a logarithmic factor of the ideal mean square error one would achieve with an $oracle$ while selecting a sufficiently sparse model -- hence achieving $sparse \ oracle \ inequalities$; the oracle would supply perfect information about which coordinates are non-zero and which are above the noise level. We also show for the Gauss-Dantzig selector (Candès-Tao 07), if $X$ obeys a uniform uncertainty principle, one will achieve the sparse oracle inequalities as above, while allowing at most $s_0$ irrelevant variables in the model in the worst case, where $s_0 \leq s$ is the smallest integer such that for $λ= \sqrt{2 \log p/n}$, $\sum_{i=1}^p \min(β_i^2, λ^2 σ^2) \leq s_0 λ^2 σ^2$. Our simulation results on the Thresholded Lasso match our theoretical analysis excellently.

math.ST↗

arXiv2025

NanoHTNet: Nano Human Topology Network for Efficient 3D Human Pose Estimation

The widespread application of 3D human pose estimation (HPE) is limited by resource-constrained edge devices, requiring more efficient models. A key approach to enhancing efficiency involves designing networks based on the structural characteristics of input data. However, effectively utilizing the structural priors in human skeletal inputs remains challenging. To address this, we leverage both explicit and implicit spatio-temporal priors of the human body through innovative model design and a pre-training proxy task. First, we propose a Nano Human Topology Network (NanoHTNet), a tiny 3D HPE network with stacked Hierarchical Mixers to capture explicit features. Specifically, the spatial Hierarchical Mixer efficiently learns the human physical topology across multiple semantic levels, while the temporal Hierarchical Mixer with discrete cosine transform and low-pass filtering captures local instantaneous movements and global action coherence. Moreover, Efficient Temporal-Spatial Tokenization (ETST) is introduced to enhance spatio-temporal interaction and reduce computational complexity significantly. Second, PoseCLR is proposed as a general pre-training method based on contrastive learning for 3D HPE, aimed at extracting implicit representations of human topology. By aligning 2D poses from diverse viewpoints in the proxy task, PoseCLR aids 3D HPE encoders like NanoHTNet in more effectively capturing the high-dimensional features of the human body, leading to further performance improvements. Extensive experiments verify that NanoHTNet with PoseCLR outperforms other state-of-the-art methods in efficiency, making it ideal for deployment on edge devices like the Jetson Nano. Code and models are available at https://github.com/vefalun/NanoHTNet.

cs.CV↗

arXiv2025

Kronecker sum covariance models for spatio-temporal data

In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ which consists of a signal matrix $X_0$ and a noise matrix $W$. More specifically, we study a subgaussian model using the Kronecker sum covariance as in Rudelson and Zhou (2017). Let $Z_1, Z_2$ be independent copies of a subgaussian random matrix $Z =(Z_{ij})$, where $Z_{ij}, \forall i, j$ are independent mean 0, unit variance, subgaussian random variables with bounded $ψ_2$ norm. We use $X \sim \mathcal{M}_{n,m}(0, A \oplus B)$ to denote the subgaussian random matrix $X_{n \times m}$ which is generated using: $$ X = Z_1 A^{1/2} + B^{1/2} Z_2. $$ In this covariance model, the first component $A \otimes I_n$ describes the covariance of the signal $X_0 = Z_1 A^{1/2}$, which is an ${n \times m}$ random design matrix with independent subgaussian row vectors, and the other component $I_m \otimes B$ describes the covariance for the noise matrix $W =B^{1/2} Z_2$, which contains independent subgaussian column vectors $w^1, \ldots, w^m$, independent of $X_0$. This leads to a non-separable class of models for the observation $X$, which we denote by $X \sim \mathcal{M}_{n,m}(0, A \oplus B)$ throughout this paper. Our method on inverse covariance estimation corresponds to the proposal in Yuan (2010) and Loh and Wainwright (2012), only now dropping the i.i.d. or Gaussian assumptions. We present the statistical rates of convergence.

math.ST↗

arXiv2023

Semidefinite programming on population clustering: a local analysis

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. In particular, we design and analyze two computational efficient algorithms to partition data into two groups approximately according to their population of origin given a small sample in a recent paper (Zhou 2023a). Our work is motivated by the application of clustering individuals according to their population of origin using markers, when the divergence between any two of the populations is small. Moreover, we are interested in the case that individual features are of low average quality $γ$, and we want to use as few of them as possible to correctly partition the sample. Here we use $p γ$ to denote the $\ell_2^2$ distance between two population centers (mean vectors), namely, $μ^{(1)}$, $μ^{(2)}$ $\in$ ${\mathbb R}^p$. We allow a full range of tradeoffs between $n, p, γ$ in the sense that partial recovery (success rate $< 100\%$) is feasible once the signal to noise ratio $s^2 := \min\{np γ^2, p γ\}$ is lower bounded by a constant. Our work builds upon the semidefinite relaxation of an integer quadratic program that is formulated essentially as finding the maximum cut on a graph, where edge weights in the cut represent dissimilarity scores between two nodes based on their $p$ features in Zhou (2023a). More importantly, we prove that the misclassification error decays exponentially with respect to the SNR $s^2$ in the present paper. The significance of such an exponentially decaying error bound is: when $s^2 =Ω(\log n)$, perfect recovery of the cluster structure is accomplished. This result was introduced in Zhou (2023a) without a proof. We therefore present the full proof in the present work.

math.ST↗

arXiv2023

Semidefinite programming on population clustering: a global analysis

In this paper, we consider the problem of partitioning a small data sample of size $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is motivated by the application of clustering individuals according to their population of origin using markers, when the divergence between the two populations is small. We are interested in the case that individual features are of low average quality $γ$, and we want to use as few of them as possible to correctly partition the sample. We consider semidefinite relaxation of an integer quadratic program which is formulated essentially as finding the maximum cut on a graph where edge weights in the cut represent dissimilarity scores between two nodes based on their features. A small simulation result in Blum, Coja-Oghlan, Frieze and Zhou (2007, 2009) shows that even when the sample size $n$ is small, by increasing $p$ so that $np= Ω(1/γ^2)$, one can classify a mixture of two product populations using the spectral method therein with success rate reaching an ``oracle'' curve. There the ``oracle'' was computed assuming that distributions were known, where success rate means the ratio between correctly classified individuals and the sample size $n$. In this work, we show the theoretical underpinning of this observed concentration of measure phenomenon in high dimensions, simultaneously for the semidefinite optimization goal and the spectral method, where the input is based on the gram matrix computed from centered data. We allow a full range of tradeoffs between the sample size and the number of features such that the product of these two is lower bounded by $1/{γ^2}$ so long as the number of features $p$ is lower bounded by $1/γ$.

math.ST↗

arXiv2022

Concentration of measure bounds for matrix-variate data with missing values

We consider the following data perturbation model, where the covariates incur multiplicative errors. For two $n \times m$ random matrices $U, X$, we denote by $U \circ X$ the Hadamard or Schur product, which is defined as $(U \circ X)_{ij} = (U_{ij}) \cdot (X_{ij})$. In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ through a random mask $U$: $$ {\mathcal X} = U \circ X \; \; \; \text{ where} \; \; \;X = B^{1/2} {\mathbb{Z}} A^{1/2}, $$ where ${\mathbb{Z}}$ is a random matrix with independent subgaussian entries, and $U$ is a mask matrix with either zero or positive entries, where ${\mathbb E} U_{ij} \in [0, 1]$ and all entries are mutually independent. Subsampling in rows, or columns, or random sampling of entries of $X$ are special cases of this model. Under the assumption of independence between $U$ and $X$, we introduce componentwise unbiased estimators for estimating covariance $A$ and $B$, and prove the concentration of measure bounds in the sense of guaranteeing the restricted eigenvalue($\textsf{RE}$) conditions to hold on the unbiased estimator for $B$, when columns of data matrix $X$ are sampled with different rates. We further develop multiple regression methods for estimating the inverse of $B$ and show statistical rate of convergence. Our results provide insight for sparse recovery for relationships among entities (samples, locations, items) when features (variables, time points, user ratings) are present in the observed data matrix ${\mathcal X}$ with heterogeneous rates. Our proof techniques can certainly be extended to other scenarios. We provide simulation evidence illuminating the theoretical predictions.

math.ST↗

arXiv2019

Tensor Graphical Lasso (TeraLasso)

This paper introduces a multi-way tensor generalization of the Bigraphical Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal model for the precision matrix to parsimoniously model conditional dependence relationships of matrix-variate data based on the Cartesian product of graphs. We call this generalization the {\bf Te}nsor g{\bf ra}phical Lasso (TeraLasso). We demonstrate using theory and examples that the TeraLasso model can be accurately and scalably estimated from very limited data samples of high dimensional variables with multiway coordinates such as space, time and replicates. Statistical consistency and statistical rates of convergence are established for both the BiGLasso and TeraLasso estimators of the precision matrix and estimators of its support (non-sparsity) set, respectively. We propose a scalable composite gradient descent algorithm and analyze the computational convergence rate, showing that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to the global minimizer of the TeraLasso objective function. Finally, we illustrate the TeraLasso using both simulation and experimental data from a meteorological dataset, showing that we can accurately estimate precision matrices and recover meaningful conditional dependency graphs from high dimensional complex datasets.

stat.ME↗

arXiv2019

Precision Matrix Estimation with Noisy and Missing Data

Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard tools for estimating graphical models under sparsity conditions. Extensions of these methods to more complex settings where data are contaminated with additive or multiplicative noise have been developed in recent years. In these settings, however, the relative performance of different methods is not well understood and algorithmic gaps still exist. In particular, in high-dimensional settings these methods require using non-positive semidefinite matrices as inputs, presenting novel optimization challenges. We develop an alternating direction method of multipliers (ADMM) algorithm for these problems, providing a feasible algorithm to estimate precision matrices with indefinite input and potentially nonconvex penalties. We compare this method with existing alternative solutions and empirically characterize the tradeoffs between them. Finally, we use this method to explore the networks among US senators estimated from voting records data.

stat.ML↗

arXiv2018

Tensor models for linguistics pitch curve data of native speakers of Afrikaans

We use tensor analysis techniques for high-dimensional data to gain insight into pitch curves, which play an important role in linguistics research. In particular, we propose that demeaned phonetics pitch curve data can be modeled as having a Kronecker product inverse covariance structure with sparse factors corresponding to words and time. Using data from a study of native Afrikaans speakers, we show that by targeting conditional independence through a graphical model, we reveal relationships associated with natural properties of words as studied by linguists. We find that words with long vowels cluster based on whether the vowel is pronounced at the front or back of the mouth, and words with short vowels have strong edges associated with the initial consonant.

stat.ME↗

arXiv2018

Joint mean and covariance estimation with unreplicated matrix-variate data

It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated high-dimensional data with unknown mean and dependence structures. Matrix-variate approaches that impose various forms of (inverse) covariance sparsity allow flexible dependence structures to be estimated, but cannot directly be applied when the mean and covariance matrices are estimated jointly. We present a practical method utilizing generalized least squares and penalized (inverse) covariance estimation to address this challenge. We establish consistency and obtain rates of convergence for estimating the mean parameters and covariance matrices. The advantages of our approaches are: (i) dependence graphs and covariance structures can be estimated in the presence of unknown mean structure, (ii) the mean structure becomes more efficiently estimated when accounting for the dependence structure among observations; and (iii) inferences about the mean parameters become correctly calibrated. We use simulation studies and analysis of genomic data from a twin study of ulcerative colitis to illustrate the statistical convergence and the performance of our methods in practical settings. Several lines of evidence show that the test statistics for differential gene expression produced by our methods are correctly calibrated and improve power over conventional methods.

stat.ML↗

arXiv2017

Time-dependent spatially varying graphical models, with application to brain fMRI data analysis

In this work, we present an additive model for space-time data that splits the data into a temporally correlated component and a spatially correlated component. We model the spatially correlated portion using a time-varying Gaussian graphical model. Under assumptions on the smoothness of changes in covariance matrices, we derive strong single sample convergence results, confirming our ability to estimate meaningful graphical structures as they evolve over time. We apply our methodology to the discovery of time-varying spatial structures in human brain fMRI signals.

stat.ME↗

arXiv2017

Non-separable covariance models for spatio-temporal data, with applications to neural encoding analysis

Neural encoding studies explore the relationships between measurements of neural activity and measurements of a behavior that is viewed as a response to that activity. The coupling between neural and behavioral measurements is typically imperfect and difficult to measure.To enhance our ability to understand neural encoding relationships, we propose that a behavioral measurement may be decomposable as a sum of two latent components, such that the direct neural influence and prediction is primarily localized to the component which encodes temporal dependence. For this purpose, we propose to use a non-separable Kronecker sum covariance model to characterize the behavioral data as the sum of terms with exclusively trial-wise, and exclusively temporal dependencies. We then utilize a corrected form of Lasso regression in combination with the nodewise regression approach for estimating the conditional independence relationships between and among variables for each component of the behavioral data, where normality is necessarily assumed. We provide the rate of convergence for estimating the precision matrices associated with the temporal as well as spatial components in the Kronecker sum model. We illustrate our methods and theory using simulated data, and data from a neural encoding study of hawkmoth flight; we demonstrate that the neural encoding signal for hawkmoth wing strokes is primarily localized to a latent component with temporal dependence, which is partially obscured by a second component with trial-wise dependencies.

stat.ME↗

arXiv2017

Errors-in-variables models with dependent measurements

Suppose that we observe $y \in \mathbb{R}^n$ and $X \in \mathbb{R}^{n \times m}$ in the following errors-in-variables model: \begin{eqnarray*} y & = & X_0 β^* +ε\\ X & = & X_0 + W, \end{eqnarray*} where $X_0$ is an $n \times m$ design matrix with independent subgaussian row vectors, $ε\in \mathbb{R}^n$ is a noise vector and $W$ is a mean zero $n \times m$ random noise matrix with independent subgaussian column vectors, independent of $X_0$ and $ε$. This model is significantly different from those analyzed in the literature in the sense that we allow the measurement error for each covariate to be a dependent vector across its $n$ observations. Such error structures appear in the science literature when modeling the trial-to-trial fluctuations in response strength shared across a set of neurons. Under sparsity and restrictive eigenvalue type of conditions, we show that one is able to recover a sparse vector $β^* \in \mathbb{R}^m$ from the model given a single observation matrix $X$ and the response vector $y$. We establish consistency in estimating $β^*$ and obtain the rates of convergence in the $\ell_q$ norm, where $q = 1, 2$. We show error bounds which approach that of the regular Lasso and the Dantzig selector in case the errors in $W$ are tending to 0. We analyze the convergence rates of the gradient descent methods for solving the nonconvex programs and show that the composite gradient descent algorithm is guaranteed to converge at a geometric rate to a neighborhood of the global minimizers: the size of the neighborhood is bounded by the statistical error in the $\ell_2$ norm. Our analysis reveals interesting connections between computational and statistical efficiency and the concentration of measure phenomenon in random matrix theory. We provide simulation evidence illuminating the theoretical predictions.

stat.ML↗