arXiv:2603. 28257v2 Announce Type: replace-cross Abstract: KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder.
arXiv:2606. 14533v1 Announce Type: new Abstract: Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events.
arXiv:2603. 11308v3 Announce Type: replace Abstract: Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.
arXiv:2402. 06635v3 Announce Type: replace-cross Abstract: We show that a deep neural network (DNN) trained to construct a stochastic discount factor (SDF) admits an additive decomposition separating nonlinear characteristic discovery from the pricing rule that aggregates them.
arXiv:2602. 10680v2 Announce Type: replace-cross Abstract: Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features.
arXiv:2604. 21174v3 Announce Type: replace-cross Abstract: Kolmogorov-Arnold Networks (KANs) replace fixed activations with learnable univariate edge functions whose behavior depends strongly on the chosen basis.
arXiv:2601. 07687v3 Announce Type: replace-cross Abstract: Recent advances in nonlinear shrinkage yield asymptotically optimal cleaners for large covariance matrices and have been extended to empirical cross-covariances via singular-value shrinkage.
arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).
arXiv:2601. 10199v2 Announce Type: replace Abstract: Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise.
arXiv:2510. 04758v3 Announce Type: replace Abstract: In this work, we establish the sufficient conditions under which nonlinear Canonical Correlation Analysis (CCA) recovers ground-truth latent factors up to an affine transformation.
arXiv:2607. 27507v1 Announce Type: new Abstract: Matrix factorisation is a fundamental tool for exploiting low-dimensional structure in high-dimensional data, with applications such as data compression, denoising, structure discovery, interpretable representation learning, and dimensionality reduction.
arXiv:2606. 03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data.
arXiv:2608. 06618v1 Announce Type: cross Abstract: Current portfolio construction methods are either agnostic to the effects of idiosyncratic shocks (standard factor models) or to the latent data structure driving systematic returns (recent graph-based approaches).