Machine learning Vasicek model calibration with Gaussian processes

In this article, we calibrate the Vasicek interest rate model under the risk neutral measure by learning the model parameters using Gaussian processes for machine learning regression. The calibration is done by maximizing the likelihood of zero coupon bond log prices, using mean and covariance functions computed analytically, as well as likelihood derivatives with respect to the parameters. The maximization method used is the conjugate gradients. The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained in the arbitrage free risk neutral measure.

Brownian bridge and other path-dependent Gaussian processes vectorial simulation

The iterative simulation of the Brownian bridge is well known. In this article, we present a vectorial simulation alternative based on Gaussian processes for machine learning regression that is suitable for interpreted programming languages implementations. We extend the vectorial simulation of path-dependent trajectories to other Gaussian processes, namely, sequences of Brownian bridges, geometric Brownian motion, fractional Brownian motion, and Ornstein-Ulenbeck mean reversion process.

Lévy area for Gaussian processes: A double Wiener--Itô integral approach

"Vegeu el resum a l'inici del document del fitxer adjunt."

Gaussian processes autoencoder for dimensionality reduction

Learning low dimensional manifold from highly nonlinear data of high dimensionality has become increasingly important for discovering intrinsic representation that can be utilized for data visualization and preprocessing. The autoencoder is a powerful dimensionality reduction technique based on minimizing reconstruction error, and it has regained popularity because it has been efficiently used for greedy pretraining of deep neural networks. Compared to Neural Network (NN), the superiority of Gaussian Process (GP) has been shown in model inference, optimization and performance. GP has been successfully applied in nonlinear Dimensionality Reduction (DR) algorithms, such as Gaussian Process Latent Variable Model (GPLVM). In this paper we propose the Gaussian Processes Autoencoder Model (GPAM) for dimensionality reduction by extending the classic NN based autoencoder to GP based autoencoder. More interestingly, the novel model can also be viewed as back constrained GPLVM (BC-GPLVM) where the back constraint smooth function is represented by a GP. Experiments verify the performance of the newly proposed model.

Linear latent force models using Gaussian Processes

Purely data-driven approaches for machine learning present difficulties when data are scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic approaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the issue of how to parameterize the system. In this paper, we present a hybrid approach using Gaussian processes and differential equations to combine data-driven modeling with a physical model of the system. We show how different, physically inspired, kernel functions can be developed through sensible, simple, mechanistic assumptions about the underlying system. The versatility of our approach is illustrated with three case studies from motion capture, computational biology, and geostatistics.