A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the partially observed matrix is of low-rank. We propose a new matrix approximation model w…
We provide new approximation guarantees for greedy low rank matrix estimation under standard assumptions of restricted strong convexity and smoothness. Our novel analysis also uncovers previously unknown connections between the low rank estimation and combinatorial optimization, so much so that our bounds are reminisce…
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the …
Many applications require recovering a ground truth low-rank matrix from noisy observations of the entries, which in practice is typically formulated as a weighted low-rank approximation problem and solved by non-convex optimization heuristics such as alternating minimization. In this paper, we provide provable recover…
The paper tackles matrix estimation from noisy data, focusing on low-rank matrices.
problem Estimating a low-rank matrix from noisy observations.
method The paper analyzes several estimators, including constrained nuclear-norm minimization, nuclear-norm regularized least squares, and a nonconvex constrained low-rank optimization problem.
result The estimators provide upper error bounds that depend on matrix rank, observed fraction, and matrix sums, and are minimax optimal.
Paper connects tensor regression and Gaussian processes for multi-way data analysis.
problem Learning high-order correlations from multi-way data.
method Demonstrates connections between low-rank tensor regression and Gaussian processes, proving oracle inequality and learning curve.
result Low-rank tensor regression is equivalent to constrained Bayesian inference in Gaussian processes, with learning dependent on eigenvalues and variable correlations.
The paper improves multi-task learning by selecting variables and grouping tasks.
problem Improving generalization performance in multi-task learning.
method Factorizes a coefficient matrix into two matrices with sparsity for variable selection and overlapping group structure among tasks. Minimized using alternating optimization methods.
result Validated the effectiveness of the method on both synthetic and real-world datasets.
Unified approach tackles high-dimensional tensor bandits with convex optimization and weakly decomposable regularizers.
problem Challenges in high-dimensional generalized tensor bandits where existing algorithms fail.
method Proposes a generalized linear tensor bandits algorithm with a unified analytical framework using convex optimization and weakly decomposable regularizers.
result Unified analytical framework provides better bounds and broader applicability compared to existing methods.
DM2L tackles missing labels in multi-label learning by modeling local and global rank structures.
problem Missing labels in multi-label learning.
method DM2L imposes local low-rank structures and global high-rank structures on predictions of instances from the same and different labels, respectively.
result DM2L outperforms state-of-the-art methods in multi-label learning with missing labels.
The Nystrom method is an efficient technique used to speed up large-scale learning applications by generating low-rank approximations. Crucial to the performance of this technique is the assumption that a matrix can be well approximated by working exclusively with a subset of its columns. In this work we relate this as…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More s…
Flat minima lead to better generalization in low-rank matrix recovery models.
problem Understanding why flat minima generalize well in overparameterized models.
method Analysis of overparameterized matrix and bilinear sensing, robust PCA, covariance matrix estimation, and neural networks with quadratic activation functions.
result Flat minima, measured by the trace of the Hessian, exactly recover the ground truth in low-rank matrix recovery models under standard statistical assumptions.
The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard, Candès and Recht showed that it can be exactly relaxed if the number of observed entrie…
The effectiveness of supervised learning techniques has made them ubiquitous in research and practice. In high-dimensional settings, supervised learning commonly relies on dimensionality reduction to improve performance and identify the most important factors in predicting outcomes. However, the economic importance of …