arXiv subjects

Xun Tang

Publications and source records attributed to Xun Tang.

At least 19 recordsLinked to original sources

arXiv2026

Estimation of Random-Coefficient Dynamic Panel Data Models with a Fixed T

We study dynamic linear panel data models in which the lagged outcomes and strictly exogenous covariates carry individual-specific coefficients and the time-varying errors have a flexible covariance structure. With a fixed number of time periods, we point-identify the joint distribution of the random coefficients and the structural errors under a distributional form of strict exogeneity, and propose a closed-form, multi-step estimator based on the inverse Radon transform. We establish a uniform convergence rate for the estimator of the random coefficient density, as well as uniform consistency of the estimator for the conditional density of the time-varying structural errors. Monte Carlo simulations demonstrate good finite-sample performance of the estimators.

econ.EM↗

arXiv2026

Vision Guided Target Conditioned Control for Autonomous Excavation

Autonomous excavation requires an intelligent control system that can convert spatial work intent into coordinated bucket motion under contact-rich soil interaction. This paper presents a target-conditioned intelligent control framework for autonomous excavation in a physics-based deformable-soil simulation workflow. An image-aligned target mask serves as a visual spatial command for the desired digging region, while a mask-conditioned Action Chunking Transformer maps multi-view RGB observations, proprioception, and the target mask to temporally extended joystick commands. To reduce target-ignoring behavior, demonstrations are organized with paired-condition supervision, where the same or closely matched scene is demonstrated with different target masks and corresponding action chunks. The framework is evaluated through both a diagnostic manipulation task and an excavation simulation benchmark with single-scoop and sequential pile-clearing protocols. In manipulation, target success is 4\% for no-condition ACT, 63\% for non-paired mask-conditioned ACT, and 96\% for paired-condition mask-conditioned ACT. In sequential pile clearing, paired-condition mask-conditioned ACT removes 76.8\% of the pile versus 27.4\% and 15.7\% for the two baselines, with 91.0\% human-normalized efficiency. The results show that visual target conditioning, paired demonstration structure, and action-chunk control form a practical cyber-physical simulation pipeline for excavator automation.

cs.RO↗

arXiv2026

Variational inference and density estimation with non-negative tensor of hierarchical tucker format

In this work, we present an efficient method to compress a high-dimensional discrete probability function, i.e., a probability tensor, into a non-negative hierarchical Tucker format. The methodology is a two-stage procedure. In the first stage, we take an existing interpolation method to compress the target tensor into a hierarchical Tucker (HT) in a manner similar to the CUR decomposition for low-rank matrix reconstruction. In the second stage, we fit the first-stage output against a non-negative hierarchical Tucker ansatz using a second-order method tailored specifically for this setting. When the tensor is of order $d$, both stages admit an $\mathcal{O}(d)$ computational complexity, and therefore the proposed methodology readily extends into high-dimensional settings. Numerical experiments show success in compressing various high-dimensional probability tensors.

math.NA↗

arXiv2026

Numerically stable variants of overrelaxation for operator Sinkhorn iteration

We consider accelerated versions of the operator Sinkhorn iteration (OSI) for solving scaling problems for completely positive maps. Based on the interpretation of OSI as alternating fixed point iteration, it has been recently proposed to achieve acceleration by means of nonlinear successive overrelaxation (SOR), e.g.~with respect to geodesics in Hilbert metric. The direct implementation of the proposed SOR algorithms, however, can be numerically unstable for ill-conditioned instances, limiting the achievable accuracy. Here we derive equivalent versions of OSI with SOR where, similar to the original OSI formulation, scalings are applied on the fly in order to take advantage of preconditioning effects. Numerical experiments confirm that this modification allows for numerically stable SOR-acceleration of OSI even in ill-conditioned cases.

math.OC↗

arXiv2025

Machine Learning-based Optimal Control for Colloidal Self-Assembly

Achieving precise control of colloidal self-assembly into specific patterns remains a longstanding challenge due to the complex process dynamics. Recently, machine learning-based state representation and reinforcement learning-based control strategies have started to accumulate popularity in the field, showing great potential in achieving an automatable and generalizable approach to producing patterned colloidal assembly. In this work, we adopted a machine learning-based optimal control framework, combining unsupervised learning and graph convolutional neural work for state observation with deep reinforcement learning-based optimal control policy calculation, to provide a data-driven control approach that can potentially be generalized to other many-body self-assembly systems. With Brownian dynamics simulations, we demonstrated its superior performance as compared to traditional order parameter-based state description, and its efficacy in obtaining ordered 2-dimensional spherical colloidal self-assembly in an electric field-mediated system with an actual success rate of 97%.

cond-mat.soft↗

arXiv2025

Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State

We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure applies to the case where the ground truth quantum state is a matrix product state (MPS). The density matrix of the ground truth state admits a tensor train ansatz as a result of the MPS assumption, and we estimate the tensor components of the ansatz through a series of observable estimations, thus outputting an approximation of the density matrix. The procedure is provably convergent with a sample complexity that scales quadratically in the system size. We conduct extensive numerical experiments to show that the procedure outputs an accurate approximation to the quantum state. For observable estimation tasks involving moderately large subsystems, we show that our procedure gives rise to a more accurate estimation than the classical shadow protocol. We also show that sketch tomography is more accurate in observable estimation than quantum states trained from the maximum likelihood estimation formulation.

quant-ph↗

arXiv2025

Estimating Social Network Models with Link Misclassification

We propose an adjusted 2SLS estimator for social network models when reported binary network links are misclassified (some zeros reported as ones and vice versa) due, e.g., to survey respondents' recall errors, or lapses in data input. We show misclassification adds new sources of correlation between the regressors and errors, which makes all covariates endogenous and invalidates conventional estimators. We resolve these issues by constructing a novel estimator of misclassification rates and using those estimates to both adjust endogenous peer outcomes and construct new instruments for 2SLS estimation. A distinctive feature of our method is that it does not require structural modeling of link formation. Simulation results confirm our adjusted 2SLS estimator corrects the bias from a naive, unadjusted 2SLS estimator which ignores misclassification and uses conventional instruments. We apply our method to study peer effects in household decisions to participate in a microfinance program in Indian villages.

econ.EM↗

arXiv2025

An efficient algorithm for entropic optimal transport under martingale-type constraints

This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete martingale optimal transport (MOT) problem. Moreover, as the (super-)martingale conditions are equivalent to row-wise (in-)equality constraints on the coupling matrix, our work applies to a prevalent class of OT problems with structural constraints. Inspired by the recent empirical success of Sinkhorn-type algorithms, we propose an entropic formulation for the MOT problem and introduce Sinkhorn-type algorithms with sparse Newton iterations that utilize the (approximate) sparsity of the Hessian matrix of the dual objective. As exact martingale conditions are typically infeasible, we adopt entropic regularization to find an approximate constraint-satisfied solution. We show that, in practice, the proposed algorithms enjoy both super-exponential convergence and robustness with controllable thresholds for total constraint violations.

math.OC↗

arXiv2025

Variational inference and density estimation with non-negative tensor train

This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings we consider are variational inference and density estimation, whereby one has access to either the unnormalized analytic formula of the distribution or the samples generated from the distribution. In particular, the compression is done through a two-stage approach. In the first stage, we use existing subroutines to encode the distribution function in a tensor train format. In the second stage, we use an NTT ansatz to fit the obtained tensor train. For the NTT fitting procedure, we use a log barrier term to ensure the positivity of each tensor component, and then utilize a second-order alternating minimization scheme to accelerate convergence. In practice, we observe that the proposed NTT fitting procedure exhibits drastically faster convergence than an alternative multiplicative update method that has been previously proposed. Through challenging numerical experiments, we show that our approach can accurately compress target distribution functions.

math.NA↗

arXiv2025

On a spherically lifted spin model at finite temperature

We investigate an $n$-vector model over $k$ sites with generic pairwise interactions and spherical constraints. The model is a lifting of the Ising model whereby the support of the spin is lifted to a hypersphere. We show that the $n$-vector model converges to a limiting distribution at a rate of $n^{-1/2 + o(1)}$. We show that the limiting distribution for $n \to \infty$ is determined by the solution of an equality-constrained maximization task over positive definite matrices. We prove that the obtained maximal value and maximizer, respectively, give rise to the free energy and correlation function of the limiting distribution. In the finite temperature regime, the maximization task is a log-determinant regularization of the semidefinite program (SDP) in the Goemans-Williamson algorithm. Moreover, the inverse temperature determines the regularization strength, with the zero temperature limit converging to the SDP in Goemans-Williamson. Our derivation draws a curious connection between the semidefinite relaxation of integer programming and the spherical lifting of sampling on a hypercube. To the authors' best knowledge, this work is the first to solve the setting of fixed $k$ and infinite $n$ under unstructured pairwise interactions.

math.PR↗

arXiv2025

Initialization and training of matrix product state probabilistic models

Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a common failure mode in training randomly initialized matrix product states (MPS) using gradient descent. The results show that the trained MPS models do not accurately predict the strong interactions between boundary sites in periodic spin chain models. In the case of the Born machine algorithm, we further identify a causality trap, where the trained MPS models resemble causal models that ignore the non-local correlations in the true distribution. We propose two complementary strategies to overcome the training failure -- one through optimization and one through initialization. First, we develop a natural gradient descent (NGD) method, which approximately simulates the gradient flow on tensor manifolds and significantly enhances training efficiency. Numerical experiments show that NGD avoids local minima in both Born machines and in general MPS tomography. Remarkably, we show that NGD with line search can converge to the global minimum in only a few iterations. Second, for the BM algorithm, we introduce a warm-start initialization based on the TTNS-Sketch algorithm. We show that gradient descent under a warm initialization does not encounter the causality trap and admits rapid convergence to the ground truth.

math.NA↗

arXiv2025

Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor

We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model describes density fluctuations of interacting particle systems, and it is a highly singular stochastic partial differential equation. By performing a finite-volume discretization of the Dean-Kawasaki model, we derive a stochastic differential equation (SDE). To fully characterize the discretized Dean-Kawasaki model, we solve the associated Fokker-Planck equation of the SDE dynamics. In particular, we use a particle-based approach whereby the solution to the Fokker-Planck equation is obtained by performing a series of density estimation tasks from the simulated trajectories, and we use a functional hierarchical tensor model to represent the density. To address the challenge that the sample trajectories are supported on a simplex, we apply a coordinate transformation from the simplex to a Euclidean space by logarithmic parameterization, after which we apply a sketching-based density estimation procedure on the transformed variables. Our approach is general and can be applied to general density estimation tasks over a simplex. We apply the proposed method successfully to the 1D and 2D Dean-Kawasaki models. Moreover, we show that the proposed approach is highly accurate in the presence of external potential and particle interaction.

math.NA↗

arXiv2025

Wavelet-based density sketching with functional hierarchical tensor

We introduce the functional hierarchical tensor under a wavelet basis (FHT-W) ansatz for high-dimensional density estimation in lattice models. Recently, the functional tensor network has emerged as a suitable candidate for density estimation due to its ability to calculate the normalization constant exactly, a defining feature not enjoyed by neural network alternatives such as energy-based models or diffusion models. While current functional tensor network models show good performance for lattice models with weak or moderate couplings, we show that they face significant model capacity constraints when applied to lattice models with strong coupling. To address this issue, this work proposes to perform density estimation on the lattice model under a wavelet transformation. Motivated by the literature on scale separation, we perform iterative wavelet coarsening to separate the lattice model into different scales. Based on this multiscale structure, we design a new functional hierarchical tensor ansatz using a hierarchical tree topology, whereby information on the finer scale is further away from the root node of the tree. Our experiments show that the numerical rank of typical lattice models is significantly lower under appropriate wavelet transformation. Furthermore, we show that our proposed model allows one to model challenging Gaussian field models and Ginzburg-Landau models.

math.NA↗

arXiv2025

Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors

The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant calculations. This work addresses this challenge by performing a particle-based high-dimensional parametric density estimation subroutine, and the input to the subroutine is Gibbs samples generated by leveraging advanced sampling techniques. Specifically, to generate Gibbs samples, we employ ensemble-based annealed importance sampling, a population-based approach for sampling multimodal distributions. These samples are then processed using functional hierarchical tensor sketching, a tensor-network-based density estimation method for high-dimensional distributions, to obtain the numerical representation of the Gibbs distribution. We successfully apply the proposed approach to complex Ginzburg-Landau models with hundreds of variables. In particular, we show that the approach proposed is successful at addressing the metastability issue under difficult numerical cases.

math.NA↗

arXiv2024

Heterogeneous Treatment Effects via Linear Dynamic Panel Data Models

We study the identification of heterogeneous, intertemporal treatment effects (TE) when potential outcomes depend on past treatments. First, applying a dynamic panel data model to observed outcomes, we show that an instrumental variable (IV) version of the estimand in Arellano and Bond (1991) recovers a non-convex (negatively weighted) aggregate of TE plus non-vanishing trends. We then provide conditions on sequential exchangeability (SE) of treatment and on TE heterogeneity that reduce such an IV estimand to a convex (positively weighted) aggregate of TE. Second, even when SE is generically violated, such estimands identify causal parameters when potential outcomes are generated by dynamic panel data models with some homogeneity or mild selection assumptions. Finally, we motivate SE and compare it with parallel trends (PT) in various settings with experimental data (when treatments are sequentially randomized) and observational data (when treatments are dynamic, rational choices under learning).

econ.EM↗

arXiv2024

MOLA: Enhancing Industrial Process Monitoring Using Multi-Block Orthogonal Long Short-Term Memory Autoencoder

In this work, we introduce MOLA: a Multi-block Orthogonal Long short-term memory Autoencoder paradigm, to conduct accurate, reliable fault detection of industrial processes. To achieve this, MOLA effectively extracts dynamic orthogonal features by introducing an orthogonality-based loss function to constrain the latent space output. This helps eliminate the redundancy in the features identified, thereby improving the overall monitoring performance. On top of this, a multi-block monitoring structure is proposed, which categorizes the process variables into multiple blocks by leveraging expert process knowledge about their associations with the overall process. Each block is associated with its specific Orthogonal Long short-term memory Autoencoder model, whose extracted dynamic orthogonal features are monitored by distance-based Hotelling's $T^2$ statistics and quantile-based cumulative sum (CUSUM) designed for multivariate data streams that are nonparametric, heterogeneous in nature. Compared to having a single model accounting for all process variables, such a multi-block structure improves the overall process monitoring performance significantly, especially for large-scale industrial processes. Finally, we propose an adaptive weight-based Bayesian fusion (W-BF) framework to aggregate all block-wise monitoring statistics into a global statistic that we monitor for faults, with the goal of improving fault detection speed by assigning weights to blocks based on the sequential order where alarms are raised. We demonstrate the efficiency and effectiveness of our MOLA framework by applying it to the Tennessee Eastman Process and comparing the performance with various benchmark methods.

cs.LG↗

arXiv2024

Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor

This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a particle under Brownian motion. In particular, the existence of diffusion presents a new challenge to conventional tensor network methods for deterministic optimal control. To overcome the difficulty, we use a general regression-based formulation where the loss term is the Bellman consistency error combined with a Sobolev-type penalization term. We propose two novel sketching-based subroutines for obtaining the tensor-network approximation to the action-value functions and the value functions, which greatly accelerate the convergence for the subsequent regression phase. We apply the proposed approach successfully to two challenging control problems with Ginzburg-Landau potential in 1D and 2D with 64 variables.

math.NA↗

arXiv2024

Solving high-dimensional Kolmogorov backward equations with functional hierarchical tensor operators

Solving high-dimensional partial differential equations necessitates methods free of exponential scaling in the dimension of the problem. This work introduces a tensor network approach for the Kolmogorov backward equation via approximating directly the Markov operator. We show that the high-dimensional Markov operator can be obtained under a functional hierarchical tensor (FHT) ansatz with a hierarchical sketching algorithm. When the terminal condition admits an FHT ansatz, the proposed operator outputs an FHT ansatz for the PDE solution through an efficient functional tensor network contraction procedure. In addition, the proposed operator-based approach also provides an efficient way to solve the Kolmogorov forward equation when the initial distribution is in an FHT ansatz. We apply the proposed approach successfully to two challenging time-dependent Ginzburg-Landau models with hundreds of variables.

math.NA↗