Custom probability models

When to use CPT vs custom models

TBNPy represents a Bayesian network as:

1. Variables (Variable) that define names and domains

2. Probability objects that define conditional relationships for each node

For discrete, tractable variables (small state spaces), you can use Cpt to define probability tables.

For continuous variables, non-tabular conditionals, or deterministic relationships, you should implement a custom probability model.

A probability object is any Python class that exposes a small interface used by tbnpy.inference and tbnpy.adaptiveMH.

Minimal interface

A custom probability model class should define:

Required attributes

Attribute	Meaning
childs	List of child variables (each a Variable)
parents	List of parent variables (each a Variable)
device	Torch device ("cpu" or "cuda"), or torch.device

Required methods

prob.sample(Cs_pars: torch.Tensor) → tuple[torch.Tensor, torch.Tensor]

Generate samples of the child variable(s) conditional on parent samples.

Parameters

Cs_pars

Parent realisations as a tensor of shape (n_samples, n_parents).

• For discrete parents, entries are typically integer state indices.

• For continuous parents, entries are floats.

Returns

(Cs_child, logp)

Cs_child is a tensor of shape (n_samples, n_childs) containing generated child samples.

logp is a tensor of shape (n_samples,) containing the log-probability of the generated samples under the model.

Notes

The return value logp is strongly recommended because it enables downstream inference routines to track likelihood contributions efficiently.

prob.log_prob(Cs: torch.Tensor) → torch.Tensor

Evaluate log-probability for provided samples.

Parameters

Cs

Tensor of shape (n_samples, n_childs + n_parents) storing realisations of:

• child variables first, then

• parent variables (in the same order as parents)

Returns

torch.Tensor

Log-probabilities of shape (n_samples,).

Device and performance notes

• Implement methods using PyTorch tensor operations so computations can run on CPU or GPU.

• Keep shapes consistent: TBNPy relies heavily on batched tensor operations.

• Deterministic relationships can be represented by returning: - child samples computed by a function of parent samples, and - a log-probability tensor (often zeros if treated as deterministic in your factorisation).

Examples in the ABCDE tutorial

The ABCDE example demonstrates three common cases:

• C | A, B : continuous conditional (Gaussian with parameters depending on discrete parents)

• OC | C : noisy observation model

• E | C, D : deterministic relationship

See the ABCDE example page for working code snippets.