The gamma probability distribution may not be best for every problem. I think keep that as the default, but allow the selection of other kernels such as:
probability distributions like Log normal distribution or Bimodal.
Impulse responses of LTI systems like a parameterized underdamped oscillator (sin wave plus exponential decay)
The LTI system kernels would be especially nice since we'll want to represent the entire system (with latent states) as an LTI system for many applications (eg control).
This way users can select the most appropriate convolution for their data type. If the response is obviously oscillatory, it would be nice to have a cheap way to cleanly fit that with an appropriate kernel rather than using multiple gamma transformations of the same input.
Moving toward the generic idea of: put a convolution kernel in front of your equation discovery to capture delayed causation. As opposed to holding up gamma as the special kernel (though are good theoretical reasons to keep it as the default - eg max entropy) .
there should also be a "try-all" option which will do a cheap fit with all the kernels we've got to narrow down the best options. we could also do "run-all", which would run an expensive fit with all kernel options
The gamma probability distribution may not be best for every problem. I think keep that as the default, but allow the selection of other kernels such as:
probability distributions like Log normal distribution or Bimodal.
Impulse responses of LTI systems like a parameterized underdamped oscillator (sin wave plus exponential decay)
The LTI system kernels would be especially nice since we'll want to represent the entire system (with latent states) as an LTI system for many applications (eg control).
This way users can select the most appropriate convolution for their data type. If the response is obviously oscillatory, it would be nice to have a cheap way to cleanly fit that with an appropriate kernel rather than using multiple gamma transformations of the same input.
Moving toward the generic idea of: put a convolution kernel in front of your equation discovery to capture delayed causation. As opposed to holding up gamma as the special kernel (though are good theoretical reasons to keep it as the default - eg max entropy) .
there should also be a "try-all" option which will do a cheap fit with all the kernels we've got to narrow down the best options. we could also do "run-all", which would run an expensive fit with all kernel options