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.
The paper studies streaming principal component analysis under a robust setting where the covariance matrix can vary within a temporal uncertainty set, rather than being fixed. It establishes fundamental convergence limits for any algorithm that recovers principal components and analyzes the noisy power method and Oja's algorithm, showing that the noisy power method achieves rate‑optimal convergence in this setting. Numerical experiments on synthetic and real‑world data confirm the theoretical findings.
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:2606.08560v2 Announce Type: replace-cross Abstract: We adopt the canonical polyadic (CP) decomposition to model high-dimensional tensor time series. Our primary goal is to identify and estimate...
arXiv:2601. 19179v2 Announce Type: replace Abstract: Autoencoders have long been considered a nonlinear extension of Principal Component Analysis (PCA).
The paper introduces Temporal Kolmogorov‑Arnold Networks (T‑KAN) for forecasting high‑frequency limit order book data, replacing fixed linear weights in LSTMs with learnable B‑spline activation functions. This approach captures the shape of market signals, yielding a 19.1% relative improvement in F1‑score at a 100‑step horizon and a 132.48% return versus a -82.76% drawdown for DeepLOB under 1.0 bps transaction costs. T‑KAN also offers interpretability through visible dead‑zones in the splines and is optimized for low‑latency FPGA deployment via High‑Level Synthesis.
arXiv:2601. 10199v2 Announce Type: replace Abstract: Multivariate data often exhibit complex dependencies that violate the assumption of isotropic residual noise.
The paper introduces an online framework for functional principal component analysis (FPCA) tailored to multidimensional functional data streams. It models functional principal components with tensor product splines, enforcing smoothness and orthonormality via a penalized approach on a Stiefel manifold. The authors present efficient Riemannian stochastic gradient descent and AdaGrad algorithms, along with a dynamic smoothing parameter tuning strategy based on rolling block validation, and provide asymptotic normality results and confidence intervals for the estimators.