Tackling Spatio-Temporal Challenges

Identifying the unique challenges in rare event prediction not only sharpens our modeling approach but also directly impacts the effectiveness of our solutions in real-world scenarios.

The step after formulating a problem is to identify the modeling challenges. Challenges, if identified, enable a better modeling direction. It tells a practitioner the issues to address during the modeling.

A few acute challenges posed by a rare event problem are:

• High-dimensional multivariate time series process
• Early prediction
• Imbalanced data

Since this is a lot, it is broken down into its elements for clarity. Earlier, in the previous lesson, it was mentioned that a rare event process is a multivariate time series. A multivariate approach has multiple features (variables). Rare event problems typically have 10s to 100s of features, categorizing them as a high-dimensional process.

A high-dimensional process poses modeling challenges due to spatial relationships between the features. This is also known as cross-correlations in space. The term “space” is used because the features mentioned here are spread in space.

While this space is in a mathematical context, for an intuitive understanding, think of the sensors placed at different locations in space on a paper manufacturing machine and how they correlate with each other.

Spatio-temporal relationships

The above illustration visually demonstrates the spatial correlations and dependencies of features with the response. Since every feature can be related to each other, the possible spatial relationships increase exponentially with the number of features, $p$.

The issue with excess spatial relationships with large $p$ is that they can induce spurious dependencies in the model. For example, in the illustration above, $x_1$ and $x_2$ ...