[szvsw]

I mean, if you like state space models, then you should read the paper on Mamba if you haven’t already! Because it quite literally uses state spaces… and you will probably think it’s a really cool application of state spaces!

Apologies if you know the following already, but maybe others reading your comment feeling similarly will not be familiar and might be interested.

At least intuitively, I like to motivate it this way- pick your favorite simple state space problem. Say a coupled spring system of two masses, maybe with some driving forces. Set it up. Perturb it. Make a bunch of observations at various points in time. Now use your observations to figure out the state space matrices.

There’s fundamentally not really anything different (in my opinion) with using Mamba (or another state space model) as a function approximation of whatever phenomenon you are interested in. Okay Mamba has more moving parts, but the core idea is the same: you are saying that on some level, a state space is an appropriate prior for approximation of the dynamics of the quantities of interest. It turns out being pretty remarkable the number of things this can work out quite well for. For instance, I use it to model the 15-min interval data for heating, cooling, and electricity usage of a whole building given 15 min weather data, occupancy schedules, and descriptions of the building characteristics (eg building envelope construction, equipment types, number of occupants, etc).