With sequential data

Trajectory prediction

Problem

Consider sequential data: observations $S$ consisting of labels $L_1..L_n$ observed at different positions $X_1..X_n$ (perhaps times). We want to predict $L_{n+1}$ corresponding to $X_{n+1}$.

The underlying process is such that the distribution of $L_{n+1}$ depends on both $S$ and $X_{n+1}$.

Simplifications

Even predicting a lower bound or upper bound (whp) of $L_{n+1}$ may be useful.

Applications

Predicting trajectory of a missile, market price of a security tomorrow.