Gaussian Processes is a powerful framework for several machine learning tasks such as regression, classification and inference. Given a finite set of input output training data that is generated out of a fixed (but possibly unknown) function, the framework models the unknown function as a stochastic process such that the training outputs are a finite number of jointly Gaussian random variables, whose properties can then be used to infer the statistics (the mean and variance) of the function at test values of input.
However, these estimates are of a Bayesian nature, whereas for some important applications, like learning-based control with safety guarantees, frequentist uncertainty bounds are required.
These properties enable us to embed the numerical GP state space model into the recursive Kalman filter algorithm.
The model is analyzed in connection to the quadratic hedging problem and some related analytical results are developed.
Gaussian processes (GPs) are non-linear probabilistic models popular in many applications.
We propose a parameter efficient Bayesian layer for hierarchical convolutional Gaussian Processes that incorporates Gaussian Processes operating in Wasserstein-2 space to reliably propagate uncertainty.
Using this representation, we show that the Sinkhorn divergence between two centered Gaussian processes can be consistently and efficiently estimated from the divergence between their corresponding normalized finite-dimensional covariance matrices, or alternatively, their sample covariance operators.
Bayesian optimization (BO) with Gaussian processes is a powerful methodology to optimize an expensive black-box function with as few function evaluations as possible.
Specifically, we propose a data-driven approach that utilizes Gaussian processes for the offline simulation model and use the associated posterior uncertainty prediction to account for joint chance constraints and plant-model mismatch.
Instead, we propose performing BO on complex, structured problems by using Bayesian Neural Networks (BNNs), a class of scalable surrogate models that have the representation power and flexibility to handle structured data and exploit auxiliary information.
Moreover, we find that capturing correlated dynamics can have implications for understanding changes in consumers preferences over time, and developing targeted marketing strategies based on those dynamics.