The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.
arXiv:2507.02248v2 Announce Type: replace-cross Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank t...
This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments. The joint distribution of the covariates may vary across environments, whereas the latent structure is decomposed into invariant factors with shared loadings and heterogeneous factors with environment-specific loadings.
arXiv:2607. 18209v1 Announce Type: cross Abstract: This paper considers a multi-environment factor model in which high-dimensional covariates are collected from heterogeneous environments, with auxiliary labels available in a subset of these environments.
arXiv:2610.07284v1 Announce Type: cross Abstract: Spectral methods are central to high-dimensional statistics and machine learning, underlying procedures for covariance estimation, matrix denoising,...
The paper challenges the common assumption that the successor measure in reinforcement learning is approximately low-rank, showing instead that a low-rank structure emerges in a shifted successor measure that ignores initial transitions. It provides finite-sample guarantees for estimating this low-rank approximation, introduces Type II Poincaré inequalities to bound spectral recoverability, and links the necessary shift to the decay of high-order singular values and local mixing properties. Experiments confirm that shifting the successor measure improves goal-conditioned RL performance.
arXiv:2610. 23337v1 Announce Type: new Abstract: Pretrained models are often reused across downstream tasks, motivating the question of whether this transfer learning procedure can provide a substantial performance improvement, namely, in terms of the scaling law.
arXiv:2610.15571v2 Announce Type: replace Abstract: In this work, we propose a transfer learning algorithm for covariate shift, integrating sample reweighting with representation learning. A key feat...
arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.
The paper introduces an adaptive multi‑resolution Gaussian process framework that achieves scalable, exact inference by constructing a naturally data‑sparse covariance matrix using basis functions anchored directly to samples. By shrinking the support domains of these basis functions, the resulting matrix has limited block sizes, ensuring sparsity and enabling efficient computation of its inverse via a sparse Cholesky algorithm. The authors demonstrate that this approach yields exact inference with training cost ≠≠ O(n log^2 n) and prediction cost ≠≠ O(log^d n), while also improving predictive uncertainties through an augmented basis function.
arXiv:2608. 13922v1 Announce Type: new Abstract: Detecting distributional changes in high dimension is difficult when neither the pre-change nor post-change density is parametrically specified.
The paper introduces LoDA, a LoRA-based continual learning method that decomposes update spaces into task‑shared and truly task‑specific subspaces using energy‑based objectives. By fixing down‑projections and learning up‑projections with Gradient‑Aligned Optimization, LoDA recalibrates general updates in closed form after each task, aiming to improve knowledge sharing and isolation. Experiments show that LoDA outperforms existing CL methods.
arXiv:2606. 08691v1 Announce Type: new Abstract: Modern data-driven applications increasingly involve learning from multiple heterogeneous sources, where a target dataset is limited but related information is available across domains.