Feature Representation

Whirlwind Tour¶

Parametric Model¶

For the parametric model, we assume that we can immediate describe the

Data Representation. We assume that all data points are IID.

where $N=N_s N_t$ is the product of all spatiotemporal coordinates.

Data Likelihood. We assume that the extreme observations, $\boldsymbol{y}$, can be immediately explained by a parametric distribution, $p(\boldsymbol{y}|\boldsymbol{\theta})$.

This distribution could be the GEVD or the GPD depending upon how the maximum values are selected from the dataset.

Posterior. In this case, our posterior is the best parameters given the observations, $\boldsymbol{y}$.

Extensions I: Conditional Models¶

We can extend this to include other (possibly multivariate) covariate vectors. For example, we can include some additional information such as

Modern Architectures¶

Examples

Spatial Considerations:

• Convolutions
• Spectral Convolutions
• Transformers

Temporal Considerations:

• Recurrent Neural Networks (RNN), Gated Recurrent Units (GRU), Long-Short-Term-Memory (LSTM)
• Autoregressive Methods