Meixia Lin

Meixia Lin, Mingkai Liu, Shuxue Peng et al.

We present a hybrid cross-device localization pipeline developed for the CroCoDL 2025 Challenge. Our approach integrates a shared retrieval encoder and two complementary localization branches: a classical geometric branch using feature fusion and PnP, and a neural feed-forward branch (MapAnything) for metric localization conditioned on geometric inputs. A neural-guided candidate pruning strategy further filters unreliable map frames based on translation consistency, while depth-conditioned localization refines metric scale and translation precision on Spot scenes. These components jointly lead to significant improvements in recall and accuracy across both HYDRO and SUCCU benchmarks. Our method achieved a final score of 92.62 (R@0.5m, 5°) during the challenge.

Chengjing Wang, Peipei Tang, Wenling He et al.

Graphical models have exhibited their performance in numerous tasks ranging from biological analysis to recommender systems. However, graphical models with hub nodes are computationally difficult to fit, particularly when the dimension of the data is large. To efficiently estimate the hub graphical models, we introduce a two-phase algorithm. The proposed algorithm first generates a good initial point via a dual alternating direction method of multipliers (ADMM), and then warm starts a semismooth Newton (SSN) based augmented Lagrangian method (ALM) to compute a solution that is accurate enough for practical tasks. We fully excavate the sparsity structure of the generalized Jacobian arising from the hubs in the graphical models, which ensures that the algorithm can obtain a nice solution very efficiently. Comprehensive experiments on both synthetic data and real data show that it obviously outperforms the existing state-of-the-art algorithms. In particular, in some high dimensional tasks, it can save more than 70\% of the execution time, meanwhile still achieves a high-quality estimation.

Meixia Lin, Yangjing Zhang

We consider the problem of jointly learning row-wise and column-wise dependencies of matrix-variate observations, which are modelled separately by two precision matrices. Due to the complicated structure of Kronecker-product precision matrices in the commonly used matrix-variate Gaussian graphical models, a sparser Kronecker-sum structure was proposed recently based on the Cartesian product of graphs. However, existing methods for estimating Kronecker-sum structured precision matrices do not scale well to large scale datasets. In this paper, we introduce DNNLasso, a diagonally non-negative graphical lasso model for estimating the Kronecker-sum structured precision matrix, which outperforms the state-of-the-art methods by a large margin in both accuracy and computational time. Our code is available at https://github.com/YangjingZhang/DNNLasso.

Mingkai Liu, Dikai Fan, Haohua Que et al.

Efficient localization and high-quality rendering in large-scale scenes remain a significant challenge due to the computational cost involved. While Scene Coordinate Regression (SCR) methods perform well in small-scale localization, they are limited by the capacity of a single network when extended to large-scale scenes. To address these challenges, we propose the Mixed Expert-based Accelerated Coordinate Encoding method (MACE), which enables efficient localization and high-quality rendering in large-scale scenes. Inspired by the remarkable capabilities of MOE in large model domains, we introduce a gating network to implicitly classify and select sub-networks, ensuring that only a single sub-network is activated during each inference. Furtheremore, we present Auxiliary-Loss-Free Load Balancing(ALF-LB) strategy to enhance the localization accuracy on large-scale scene. Our framework provides a significant reduction in costs while maintaining higher precision, offering an efficient solution for large-scale scene applications. Additional experiments on the Cambridge test set demonstrate that our method achieves high-quality rendering results with merely 10 minutes of training.

Meixia Lin, Meijiao Shi, Yunhai Xiao et al.

High-dimensional regression often suffers from heavy-tailed noise and outliers, which can severely undermine the reliability of least-squares based methods. To improve robustness, we adopt a non-smooth Wilcoxon score based rank objective and incorporate structured group sparsity regularization, a natural generalization of the lasso, yielding a group lasso regularized rank regression method. By extending the tuning-free parameter selection scheme originally developed for the lasso, we introduce a data-driven, simulation-based tuning rule and further establish a finite-sample error bound for the resulting estimator. On the computational side, we develop a proximal augmented Lagrangian method for solving the associated optimization problem, which eliminates the singularity issues encountered in existing methods, thereby enabling efficient semismooth Newton updates for the subproblems. Extensive numerical experiments demonstrate the robustness and effectiveness of our proposed estimator against alternatives, and showcase the scalability of the algorithm across both simulated and real-data settings.

Remi Bardenet, Subhro Ghosh, Meixia Lin

Stochastic gradient descent (SGD) is a cornerstone of machine learning. When the number N of data items is large, SGD relies on constructing an unbiased estimator of the gradient of the empirical risk using a small subset of the original dataset, called a minibatch. Default minibatch construction involves uniformly sampling a subset of the desired size, but alternatives have been explored for variance reduction. In particular, experimental evidence suggests drawing minibatches from determinantal point processes (DPPs), distributions over minibatches that favour diversity among selected items. However, like in recent work on DPPs for coresets, providing a systematic and principled understanding of how and why DPPs help has been difficult. In this work, we contribute an orthogonal polynomial-based DPP paradigm for minibatch sampling in SGD. Our approach leverages the specific data distribution at hand, which endows it with greater sensitivity and power over existing data-agnostic methods. We substantiate our method via a detailed theoretical analysis of its convergence properties, interweaving between the discrete data set and the underlying continuous domain. In particular, we show how specific DPPs and a string of controlled approximations can lead to gradient estimators with a variance that decays faster with the batchsize than under uniform sampling. Coupled with existing finite-time guarantees for SGD on convex objectives, this entails that, DPP minibatches lead to a smaller bound on the mean square approximation error than uniform minibatches. Moreover, our estimators are amenable to a recent algorithm that directly samples linear statistics of DPPs (i.e., the gradient estimator) without sampling the underlying DPP (i.e., the minibatch), thereby reducing computational overhead. We provide detailed synthetic as well as real data experiments to substantiate our theoretical claims.

Subhroshekhar Ghosh, Meixia Lin, Dongfang Sun

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima. This is complemented by a recent interest in their zeros or minima, following seminal work by Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, the zero sets (or extrema) of GAFs have a complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from the analysis of spatial data, whose distributional properties for spectrograms are mostly understood only at an empirical level. In this work, we investigate spectrogram analysis via an examination of the stochastic geometric properties of their level sets. We obtain rigorous theorems demonstrating the efficacy of a spectrogram level sets based approach to the detection and estimation of signals, framed in a concrete inferential set-up. Exploiting these ideas as theoretical underpinnings, we propose a level sets based algorithm for signal analysis that is intrinsic to given spectrogram data, and substantiate its effectiveness via extensive empirical studies. Our results also have theoretical implications for spectrogram zero based approaches to signal analysis. To our knowledge, these results are arguably among the first to provide a rigorous statistical understanding of signal detection and reconstruction in this set up, complemented with provable guarantees on detection thresholds and rates of convergence.

Meixia Lin, Defeng Sun, Kim-Chuan Toh et al.

Estimation of Gaussian graphical models is important in natural science when modeling the statistical relationships between variables in the form of a graph. The sparsity and clustering structure of the concentration matrix is enforced to reduce model complexity and describe inherent regularities. We propose a model to estimate the sparse Gaussian graphical models with hidden clustering structure, which also allows additional linear constraints to be imposed on the concentration matrix. We design an efficient two-phase algorithm for solving the proposed model. We develop a symmetric Gauss-Seidel based alternating direction method of the multipliers (sGS-ADMM) to generate an initial point to warm-start the second phase algorithm, which is a proximal augmented Lagrangian method (pALM), to get a solution with high accuracy. Numerical experiments on both synthetic data and real data demonstrate the good performance of our model, as well as the efficiency and robustness of our proposed algorithm.

Meixia Lin, Defeng Sun, Kim-Chuan Toh

Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a comprehensive mechanism for computing the least squares estimator of a multivariate shape-constrained convex regression function in $\mathbb{R}^d$. We prove that the least squares estimator is computable via solving a constrained convex quadratic programming (QP) problem with $(n+1)d$ variables and at least $n(n-1)$ linear inequality constraints, where $n$ is the number of data points. For solving the generally very large-scale convex QP, we design two efficient algorithms, one is the symmetric Gauss-Seidel based alternating direction method of multipliers ({\tt sGS-ADMM}), and the other is the proximal augmented Lagrangian method ({\tt pALM}) with the subproblems solved by the semismooth Newton method ({\tt SSN}). Comprehensive numerical experiments, including those in the pricing of basket options and estimation of production functions in economics, demonstrate that both of our proposed algorithms outperform the state-of-the-art algorithm. The {\tt pALM} is more efficient than the {\tt sGS-ADMM} but the latter has the advantage of being simpler to implement.

Meixia Lin, Defeng Sun, Kim-Chuan Toh et al.

The exclusive lasso (also known as elitist lasso) regularization has become popular recently due to its superior performance on group sparsity. Compared to the group lasso regularization which enforces the competition on variables among different groups, the exclusive lasso regularization also enforces the competition within each group. In this paper, we propose a highly efficient dual Newton based preconditioned proximal point algorithm (PPDNA) to solve machine learning models involving the exclusive lasso regularizer. As an important ingredient, we provide a rigorous proof for deriving the closed-form solution to the proximal mapping of the weighted exclusive lasso regularizer. In addition, we derive the corresponding HS-Jacobian to the proximal mapping and analyze its structure --- which plays an essential role in the efficient computation of the PPA subproblem via applying a semismooth Newton method on its dual. Various numerical experiments in this paper demonstrate the superior performance of the proposed PPDNA against other state-of-the-art numerical algorithms.

Meixia Lin, Yong-Jin Liu, Defeng Sun et al.

We focus on solving the clustered lasso problem, which is a least squares problem with the $\ell_1$-type penalties imposed on both the coefficients and their pairwise differences to learn the group structure of the regression parameters. Here we first reformulate the clustered lasso regularizer as a weighted ordered-lasso regularizer, which is essential in reducing the computational cost from $O(n^2)$ to $O(n\log (n))$. We then propose an inexact semismooth Newton augmented Lagrangian ({\sc Ssnal}) algorithm to solve the clustered lasso problem or its dual via this equivalent formulation, depending on whether the sample size is larger than the dimension of the features. An essential component of the {\sc Ssnal} algorithm is the computation of the generalized Jacobian of the proximal mapping of the clustered lasso regularizer. Based on the new formulation, we derive an efficient procedure for its computation. Comprehensive results on the global convergence and local linear convergence of the {\sc Ssnal} algorithm are established. For the purpose of exposition and comparison, we also summarize/design several first-order methods that can be used to solve the problem under consideration, but with the key improvement from the new formulation of the clustered lasso regularizer. As a demonstration of the applicability of our algorithms, numerical experiments on the clustered lasso problem are performed. The experiments show that the {\sc Ssnal} algorithm substantially outperforms the best alternative algorithm for the clustered lasso problem.