# Semi-described and semi-supervised learning with Gaussian processes

arXiv: https://arxiv.org/abs/1509.01168 · HTML: https://mlsanity.com/paper/1509.01168/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2015.

## Built on by (most cited first, 1 of 1)

- [Deep Gaussian Processes for Biogeophysical Parameter Retrieval and Model Inversion](https://mlsanity.com/paper/2104.10638/) (2021)

## Abstract (arXiv)

Propagating input uncertainty through non-linear Gaussian process (GP) mappings is intractable. This hinders the task of training GPs using uncertain and partially observed inputs. In this paper we refer to this task as "semi-described learning". We then introduce a GP framework that solves both, the semi-described and the semi-supervised learning problems (where missing values occur in the outputs). Auto-regressive state space simulation is also recognised as a special case of semi-described learning. To achieve our goal we develop variational methods for handling semi-described inputs in GPs, and couple them with algorithms that allow for imputing the missing values while treating the uncertainty in a principled, Bayesian manner. Extensive experiments on simulated and real-world data study the problems of iterative forecasting and regression/classification with missing values. The results suggest that the principled propagation of uncertainty stemming from our framework can significantly improve performance in these tasks.