Department of Data Science and Analytics

arxiv.org

Warped Gaussian processes (GPs) handle non-Gaussian observations by mapping them into a latent standard GP via a parametric transformation called warping. Existing online variants either optimize the warping parameters periodically rather than sequentially, or sacrifice analytical tractability and computational efficiency for higher model expressivity. In this paper, we avoid these compromises. To achieve this, we first show that the gradient of the instantaneous negative log-likelihood of a warped GP admits an exact recursive computation. Based on this result, we propose a novel online method for warped GPs that jointly updates the latent GP moments and optimizes the warping parameters. Finally, we validate our method on an existing benchmark adapted to an online formulation.

Structural Equation Modeling p. 10-10 Doi: https://doi.org/10.1080/10705511.2026.2714956

Journal of applied econometrics Doi: https://doi.org/10.1002/jae.70074

arXiv Doi: https://doi.org/10.48550/ARXIV.2606.22964

McKean-Vlasov-type stochastic differential equations (SDEs) are characterized by coefficients depending on both the state and the law of the solution. In this work, we focus on a class of such equations where the coefficients depend on a linear combination of the expected signature of the geometric p-rough path lift of its solution, with $p\in(2,3)$. After establishing the strong existence and uniqueness of a solution, we prove how such an equation can approximate a general class of path-dependent McKean-Vlasov SDEs. Finally, we consider the associated particle system and propagation of chaos is established.

International Conference on Machine Learning (ICML)