Laila Melkas

Laila Melkas, Rafael Savvides, Suyog Chandramouli et al.

Causal structure discovery (CSD) models are making inroads into several domains, including Earth system sciences. Their widespread adaptation is however hampered by the fact that the resulting models often do not take into account the domain knowledge of the experts and that it is often necessary to modify the resulting models iteratively. We present a workflow that is required to take this knowledge into account and to apply CSD algorithms in Earth system sciences. At the same time, we describe open research questions that still need to be addressed. We present a way to interactively modify the outputs of the CSD algorithms and argue that the user interaction can be modelled as a greedy finding of the local maximum-a-posteriori solution of the likelihood function, which is composed of the likelihood of the causal model and the prior distribution representing the knowledge of the expert user. We use a real-world data set for examples constructed in collaboration with our co-authors, who are the domain area experts. We show that finding maximally usable causal models in the Earth system sciences or other similar domains is a difficult task which contains many interesting open research questions. We argue that taking the domain knowledge into account has a substantial effect on the final causal models discovered.

Antti Honkela, Laila Melkas

Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the privacy of the prediction targets (model outputs) but not inputs. We break this limitation by introducing GPs with DP protection for both model inputs and outputs. We achieve this by using sparse GP methodology and publishing a private variational approximation on known inducing points. The approximation covariance is adjusted to approximately account for the added uncertainty from DP noise. The approximation can be used to compute arbitrary predictions using standard sparse GP techniques. We propose a method for hyperparameter learning using a private selection protocol applied to validation set log-likelihood. Our experiments demonstrate that given sufficient amount of data, the method can produce accurate models under strong privacy protection.