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arXiv research

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.

168,694 papers · 148 categories

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4 results for “Eigen-subspace”

Risk Bounds of Accelerated SGD for Overparameterized Linear Regressioncs.LG

ASGD outperforms SGD in overparameterized linear regression, especially in subspaces of small eigenvalues.

problem Generalization of ASGD for overparameterized linear regression.

method Established instance-dependent excess risk bound for ASGD in each eigen-subspace of the data covariance matrix.

result ASGD outperforms SGD in subspaces of small eigenvalues, exhibiting faster decay of bias error.

Accelerated SGD Overparameterized Linear Regression Generalization Excess Risk Bound Eigen-subspace

2023-11-23abs ↗pdf ↗

Understanding SGD with Exponential Moving Average: A Case Study in Linear Regressioncs.LG

Paper analyzes how EMA improves SGD in linear regression.

problem Understanding the effectiveness of EMA in training deep learning models.

method Established risk bound for online SGD with EMA in linear regression.

result SGD with EMA has smaller variance error and exponentially decaying bias error.

SGD EMA Linear Regression Risk Bound Bias Error

2025-02-19abs ↗pdf ↗

Sparse PCA through Low-rank Approximationsstat.ML

We introduce a novel algorithm that computes the $k$ -sparse principal component of a positive semidefinite matrix $A$ . Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional eigen-subspace of $A$ . We obtain provable approximation guarantees that depend on t…

2013-03-03abs ↗pdf ↗

σ

-PCA: a building block for neural learning of identifiable linear transformationscs.LG

Proposes $σ$ -PCA to learn identifiable linear transformations without whitening.

problem Cannot identify axes with equal variances in PCA.

method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.

result Eliminates subspace rotational indeterminacy in PCA.

PCA linear transformations rotational indeterminacy statistical independence whitening

2023-11-22abs ↗pdf ↗