rs-distributions

---

Table of Contents

• Installation
• Distributions
• Modules
• License

rs-distributions provides statistical tools which are helpful for structural biologists who wish to model their data using variational inference.

Installation

pip install rs-distributions

Distributions

rs_distributions.distributions provides learnable distributions that are important in structural biology. These distributions follow the conventions in torch.dist. Here's a small example of distribution matching between a learnable distribution, q, and a target distribion, p. The example works by minimizing the Kullback-Leibler divergence between q and p using gradients calculated by the implicit reparameterization method.

import torch
from rs_distributions import distributions as rsd

target_loc = 4.
target_scale = 2.

loc_initial_guess = 10.
scale_initial_guess  = 3.

loc = torch.tensor(loc_initial_guess, requires_grad=True)

scale_transform = torch.distributions.transform_to(
    rsd.FoldedNormal.arg_constraints['scale']
)
scale_initial_guess = scale_transform.inv(
    torch.tensor(scale_initial_guess)
)
unconstrained_scale = torch.tensor(
    torch.tensor(scale_initial_guess),
    requires_grad=True
)

p = rsd.FoldedNormal(
    target_loc,
    target_scale,
)

opt = torch.optim.Adam([loc, unconstrained_scale])

steps = 10_000
num_samples = 100
for i in range(steps):
    opt.zero_grad()
    scale = scale_transform(unconstrained_scale)
    q = rsd.FoldedNormal(loc, scale)
    z = q.sample((num_samples,))
    kl_div = q.log_prob(z) - p.log_prob(z)
    kl_div = kl_div.mean()
    kl_div.backward()
    opt.step()

This example uses the folded normal distribution which is important in X-ray crystallography.

Modules

Working with PyTorch distributions can be a little verbose. So in addition to the torch.distributions style implementation, we provide DistributionModule classes which enable learnable distributions with automatic bijections in less code. These DistributionModule classes are subclasses of torch.nn.Module. They automatically instantiate problem parameters as TransformedParameter modules following the constraints in the distribution definition. In the following example, a FoldedNormal DistributionModule is instantiated with an initial location and scale and trained to match a target distribution.

from rs_distributions import modules as rsm
import torch

loc_init = 10.
scale_init = 5.

q = rsm.FoldedNormal(loc_init, scale_init)
p = torch.distributions.HalfNormal(1.)

opt = torch.optim.Adam(q.parameters())

steps = 10_000
num_samples = 256
for i in range(steps):
    opt.zero_grad()
    z = q.rsample((num_samples,))
    kl = (q.log_prob(z) - p.log_prob(z)).mean()
    kl.backward()
    opt.step()

License

rs-distributions is distributed under the terms of the MIT license.