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Yuetian Luo

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4 papers

2 author rows

ICML Conference 2023 Conference Paper

Iterative Approximate Cross-Validation

Yuetian Luo
Zhimei Ren
Rina Barber

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk minimization (ERM) framework, a line of works proposed efficient methods to approximate CV based on the solution of the ERM problem trained on the full dataset. However, in large-scale problems, it can be hard to obtain the exact solution of the ERM problem, either due to limited computational resources or due to early stopping as a way of preventing overfitting. In this paper, we propose a new paradigm to efficiently approximate CV when the ERM problem is solved via an iterative first-order algorithm, without running until convergence. Our new method extends existing guarantees for CV approximation to hold along the whole trajectory of the algorithm, including at convergence, thus generalizing existing CV approximation methods. Finally, we illustrate the accuracy and computational efficiency of our method through a range of empirical studies.

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JMLR Journal 2023 Journal Article

Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence

Yuetian Luo
Anru R. Zhang

In this paper, we consider the estimation of a low Tucker rank tensor from a number of noisy linear measurements. The general problem covers many specific examples arising from applications, including tensor regression, tensor completion, and tensor PCA/SVD. We consider an efficient Riemannian Gauss-Newton (RGN) method for low Tucker rank tensor estimation. Different from the generic (super)linear convergence guarantee of RGN in the literature, we prove the first local quadratic convergence guarantee of RGN for lowrank tensor estimation in the noisy setting under some regularity conditions and provide the corresponding estimation error upper bounds. A deterministic estimation error lower bound, which matches the upper bound, is provided that demonstrates the statistical optimality of RGN. The merit of RGN is illustrated through two machine learning applications: tensor regression and tensor SVD. Finally, we provide the simulation results to corroborate our theoretical findings. [abs] [ pdf ][ bib ] [ code ] &copy JMLR 2023. ( edit, beta )

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JMLR Journal 2021 Journal Article

A Sharp Blockwise Tensor Perturbation Bound for Orthogonal Iteration

Yuetian Luo
Garvesh Raskutti
Ming Yuan
Anru R. Zhang

In this paper, we develop novel perturbation bounds for the higher-order orthogonal iteration (HOOI). Under mild regularity conditions, we establish blockwise tensor perturbation bounds for HOOI with guarantees for both tensor reconstruction in Hilbert-Schmidt norm $\|\widehat{\mathcal{T}} - \mathcal{T} \|_{\rm HS}$ and mode-$k$ singular subspace estimation in Schatten-$q$ norm $\| \sin \Theta (\widehat{U}_k, U_k) \|_q$ for any $q \geq 1$. We show the upper bounds of mode-$k$ singular subspace estimation are unilateral and converge linearly to a quantity characterized by blockwise errors of the perturbation and signal strength. For the tensor reconstruction error bound, we express the bound through a simple quantity $\xi$, which depends only on perturbation and the multilinear rank of the underlying signal. Rate matching deterministic lower bound for tensor reconstruction, which demonstrates the optimality of HOOI, is also provided. Furthermore, we prove that one-step HOOI (i.e., HOOI with only a single iteration) is also optimal in terms of tensor reconstruction and can be used to lower the computational cost. The perturbation results are also extended to the case that only partial modes of $\mathcal{T}$ have low-rank structure. We support our theoretical results by extensive numerical studies. Finally, we apply the novel perturbation bounds of HOOI on two applications, tensor denoising and tensor co-clustering, from machine learning and statistics, which demonstrates the superiority of the new perturbation results. [abs] [ pdf ][ bib ] &copy JMLR 2021. ( edit, beta )

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AAAI Conference 2018 Conference Paper

Diagnosing University Student Subject Proficiency and Predicting Degree Completion in Vector Space

Yuetian Luo
Zachary Pardos

We investigate the issues of undergraduate on-time graduation with respect to subject proficiencies through the lens of representation learning, training a student vector embeddings from a dataset of 8 years of course enrollments. We compare the per-semester student representations of a cohort of undergraduate Integrative Biology majors to those of graduated students in subject areas involved in their degree requirements. The result is an embedding rich in information about the relationships between majors and pathways taken by students which encoded enough information to improve prediction accuracy of on-time graduation to 95%, up from a baseline of 87. 3%. Challenges to preparation of the data for student vectorization and sourcing of validation sets for optimization are discussed.

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