HSTP

[ferrine]

Description

After some research, seems like if you replace Normal distribution with StudentT distribution and get HSTP

Here is a related paper as well
https://proceedings.mlr.press/v202/sellier23a.html

pymc/pymc/gp/hsgp_approx.py

Lines 322 to 331 in bc4b51d

	if self._parameterization == "noncentered":
	self._beta = pm.Normal(
	f"{name}_hsgp_coeffs_", size=self._m_star - int(self._drop_first)
	)
	self._sqrt_psd = sqrt_psd
	f = self.mean_func(X) + phi @ (self._beta * self._sqrt_psd)
	elif self._parameterization == "centered":
	self._beta = pm.Normal(f"{name}_hsgp_coeffs_", sigma=sqrt_psd)
	f = self.mean_func(X) + phi @ self._beta

Turning into

        if self._parameterization == "noncentered":
            self._beta = pm.StudentT(
                f"{name}_hsgp_coeffs_", self.nu, size=self._m_star - int(self._drop_first)
            )
            self._sqrt_psd = sqrt_psd
            f = self.mean_func(X) + phi @ (self._beta * self._sqrt_psd)


        elif self._parameterization == "centered":
            self._beta = pm.StudentT(f"{name}_hsgp_coeffs_", self.nu, sigma=sqrt_psd)
            f = self.mean_func(X) + phi @ self._beta

Alternatively, you can use Fisher transfrom or any other inverse normalizing transformations to "pull out" nu

https://www.jstor.org/stable/2334301

[bwengals]

That's really cool, this should definitely be added. Probably could just put an additional kwarg nu=None on the HSGP class and fix the code like you did.

I don't follow the second paper though, about transforming a t distributed RV to a normal. What do you mean to pull out nu?

[ferrine]

What do you mean to pull out nu?
It specifies non-centered parameterization (non-exact) for Student T by transforming normal distribution to StudentT

[bwengals]

ah I see now. I'm not sure which would work better. It's an approximation right? The first way you did it, pm.Normal -> pm.StudentT is exact and looks simpler to me

[ferrine]

Yes, I tried exact one and it works like charm

[ferrine]

Should it come with HSGP name or HSTP subclass? GP is Gaussian process, while T Process is different

[bwengals]

True... definitely less code to have nu be an optional kwarg that makes it a TP. But you're right, the code would say "GP" when it's really a t-process.

I kinda prefer the kwarg option? Though there already is a TP class

[ferrine]

I prefer the explicit way to create a subclass

[bwengals]

From the user perspective I agree. For implementing it'd make for a lot of code dup, unless I'm missing something clever. Maybe have kwargs for HSGP, and also an HSTP class that calls it?

[fonnesbeck]

If we want to generalize, we could rename the class HSP or HSSP (stochastic process), and then specify the type of process as a keyword arg.