arXiv subjects

Luxuan Yang

Publications and source records attributed to Luxuan Yang.

3 recordsLinked to original sources

arXiv2025

Learning L\'evy density via adaptive RKHS regression with bi-level optimization

We propose a nonparametric method to learn the L\'evy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the kernel in a nonlocal integral operator from discrete data, which leads to an ill-posed inverse problem. To regularize it, we construct an adaptive reproducing kernel Hilbert space (RKHS) whose kernel is built directly from the data. Under standard source and spectral decay conditions, we show that the reconstruction error decays in the mesh size at a near optimal rate. Importantly, we develop a generalized singular value decomposition (GSVD)-based bilevel optimization algorithm to choose the regularization parameter, leading to efficient and robust computation of the regularized estimator. Numerical experiments for several L\'evy densities, drift fields and data types (PDE-based densities and sample ensemble-based KDE reconstructions) demonstrate that our bilevel RKHS method outperforms classical L-curve and generalized cross-validation strategies and that the adaptive RKHS norm is more accurate and robust than $L^2_\rho$- and $\ell^2$-based regularization.

math.NA↗

arXiv2024

Multi-task Meta Label Correction for Time Series Prediction

Time series classification faces two unavoidable problems. One is partial feature information and the other is poor label quality, which may affect model performance. To address the above issues, we create a label correction method to time series data with meta-learning under a multi-task framework. There are three main contributions. First, we train the label correction model with a two-branch neural network in the outer loop. While in the model-agnostic inner loop, we use pre-existing classification models in a multi-task way and jointly update the meta-knowledge so as to help us achieve adaptive labeling on complex time series. Second, we devise new data visualization methods for both image patterns of the historical data and data in the prediction horizon. Finally, we test our method with various financial datasets, including XOM, S\&P500, and SZ50. Results show that our method is more effective and accurate than some existing label correction techniques.

cs.LG↗

arXiv2022

Neural network stochastic differential equation models with applications to financial data forecasting

In this article, we employ a collection of stochastic differential equations with drift and diffusion coefficients approximated by neural networks to predict the trend of chaotic time series which has big jump properties. Our contributions are, first, we propose a model called Lévy induced stochastic differential equation network, which explores compounded stochastic differential equations with $α$-stable Lévy motion to model complex time series data and solve the problem through neural network approximation. Second, we theoretically prove that the numerical solution through our algorithm converges in probability to the solution of corresponding stochastic differential equation, without curse of dimensionality. Finally, we illustrate our method by applying it to real financial time series data and find the accuracy increases through the use of non-Gaussian Lévy processes. We also present detailed comparisons in terms of data patterns, various models, different shapes of Lévy motion and the prediction lengths.

cs.LG↗