Fréchet regression has emerged as a promising approach for regression analysis involving non-Euclidean response variables.

The ocean is a crucial component of the Earth's system.

We present a multi-temporal, multi-modal remote-sensing dataset for predicting how active wildfires will spread at a resolution of 24 hours. The dataset consists of 13 607 images across 607 fire events in the United States from January 2018 to October 2021. For each fire event, the dataset contains a full time series of daily observations, containing detected active fires and variables related to fuel, topography and weather conditions. The dataset is challenging due to: a) its inputs being multi-temporal, b) the high number of 23 multi-modal input channels, c) highly imbalanced labels and d) noisy labels, due to smoke, clouds, and inaccuracies in the active fire detection.

Rather than specifying a model, the GP framework revolves around selecting an appropriate kernel, transforming the problem into one of parameter estimation.

In such cases, re-training the model from scratch could be time-consuming.

The chain structure is also convenient to handle streaming data as we will explain later. We first give a brief introduction to the EP and CEP framework. Step 2. We construct a tilted distribution to combine the true likelihood, Step 3. We project the tilted distribution back to the exponential family, q KL( null p nullq) where q belongs to the exponential family. Step 4. We update the approximation term by's in parallel, and uses damping to avoid divergence. The above computation are very conveniently to implement.