Contributions to Robust and Efficient Methods for Analysis of High Dimensional Data

• URL: http://arxiv.org/abs/2509.08155v1
• Date: Tue, 09 Sep 2025 21:30:01 GMT
• Title: Contributions to Robust and Efficient Methods for Analysis of High Dimensional Data
• Authors: Kai Yang,
• Abstract summary: This thesis develops robust and computationally efficient methods to analyze high-dimensional data.<n>I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power sparse-law entropy.<n>I develop a novel conjugate algorithm that accelerates a nonlinear convergence while maintaining numerical stability.
• Score: 3.8590360275860767
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A ubiquitous feature of data of our era is their extra-large sizes and dimensions. Analyzing such high-dimensional data poses significant challenges, since the feature dimension is often much larger than the sample size. This thesis introduces robust and computationally efficient methods to address several common challenges associated with high-dimensional data. In my first manuscript, I propose a coherent approach to variable screening that accommodates nonlinear associations. I develop a novel variable screening method that transcends traditional linear assumptions by leveraging mutual information, with an intended application in neuroimaging data. This approach allows for accurate identification of important variables by capturing nonlinear as well as linear relationships between the outcome and covariates. Building on this foundation, I develop new optimization methods for sparse estimation using nonconvex penalties in my second manuscript. These methods address notable challenges in current statistical computing practices, facilitating computationally efficient and robust analyses of complex datasets. The proposed method can be applied to a general class of optimization problems. In my third manuscript, I contribute to robust modeling of high-dimensional correlated observations by developing a mixed-effects model based on Tsallis power-law entropy maximization and discussed the theoretical properties of such distribution. This model surpasses the constraints of conventional Gaussian models by accommodating a broader class of distributions with enhanced robustness to outliers. Additionally, I develop a proximal nonlinear conjugate gradient algorithm that accelerates convergence while maintaining numerical stability, along with rigorous statistical properties for the proposed framework.

Related papers

• Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computation [51.65236537605077]
  We propose a new type of network compression optimization technique, fully randomized tensor network compression (FCTN)<n>FCTN has significant advantages in correlation characterization and transpositional in algebra, and has notable achievements in multi-dimensional data processing and analysis.<n>We derive efficient algorithms with guarantees to solve the formulated models.
  arXiv  Detail & Related papers  (2026-02-13T14:56:37Z)
• Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update [60.414548453838506]
  We study the generalized linear bandit (GLB) problem, a contextual multi-armed bandit framework that extends the classical linear model by incorporating a non-linear link function.<n>GLBs are widely applicable to real-world scenarios, but their non-linear nature introduces significant challenges in achieving both computational and statistical efficiency.<n>We propose a jointly efficient algorithm that attains a nearly optimal regret bound with $mathcalO(1)$ time and space complexities per round.
  arXiv  Detail & Related papers  (2025-07-16T02:24:21Z)
• Latent mixed-effect models for high-dimensional longitudinal data [6.103940626659986]
  We propose LMM-VAE, a scalable, interpretable and identifiable model for longitudinal data. We highlight theoretical connections between it and GP-based techniques, providing a unified framework for this class of methods.
  arXiv  Detail & Related papers  (2024-09-17T09:16:38Z)
• Adaptive debiased SGD in high-dimensional GLMs with streaming data [4.704144189806667]
  This paper introduces a novel approach to online inference in high-dimensional generalized linear models.<n>Our method operates in a single-pass mode, making it different from existing methods that require full dataset access or large-dimensional summary statistics storage.<n>The core of our methodological innovation lies in an adaptive descent algorithm tailored for dynamic objective functions, coupled with a novel online debiasing procedure.
  arXiv  Detail & Related papers  (2024-05-28T15:36:48Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Improved Distribution Matching for Dataset Condensation [91.55972945798531]
  We propose a novel dataset condensation method based on distribution matching. Our simple yet effective method outperforms most previous optimization-oriented methods with much fewer computational resources.
  arXiv  Detail & Related papers  (2023-07-19T04:07:33Z)
• ProjB: An Improved Bilinear Biased ProjE model for Knowledge Graph Completion [1.5576879053213302]
  This work improves on ProjE KGE due to low computational complexity and high potential for model improvement. Experimental results on benchmark Knowledge Graphs (KGs) such as FB15K and WN18 show that the proposed approach outperforms the state-of-the-art models in entity prediction task.
  arXiv  Detail & Related papers  (2022-08-15T18:18:05Z)
• Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
  The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
  arXiv  Detail & Related papers  (2022-02-23T11:23:59Z)
• Low-rank statistical finite elements for scalable model-data synthesis [0.8602553195689513]
  statFEM acknowledges a priori model misspecification, by embedding forcing within the governing equations. The method reconstructs the observed data-generating processes with minimal loss of information. This article overcomes this hurdle by embedding a low-rank approximation of the underlying dense covariance matrix.
  arXiv  Detail & Related papers  (2021-09-10T09:51:43Z)
• SODEN: A Scalable Continuous-Time Survival Model through Ordinary Differential Equation Networks [14.564168076456822]
  We propose a flexible model for survival analysis using neural networks along with scalable optimization algorithms. We demonstrate the effectiveness of the proposed method in comparison to existing state-of-the-art deep learning survival analysis models.
  arXiv  Detail & Related papers  (2020-08-19T19:11:25Z)
• Slice Sampling for General Completely Random Measures [74.24975039689893]
  We present a novel Markov chain Monte Carlo algorithm for posterior inference that adaptively sets the truncation level using auxiliary slice variables. The efficacy of the proposed algorithm is evaluated on several popular nonparametric models.
  arXiv  Detail & Related papers  (2020-06-24T17:53:53Z)
• Predicting Multidimensional Data via Tensor Learning [0.0]
  We develop a model that retains the intrinsic multidimensional structure of the dataset. To estimate the model parameters, an Alternating Least Squares algorithm is developed. The proposed model is able to outperform benchmark models present in the forecasting literature.
  arXiv  Detail & Related papers  (2020-02-11T11:57:07Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.