pylimid

Mixed-type limited-memory influence diagrams, on NumPyro.

pylimid is a Python library for decision models that mix discrete and continuous variables. You describe chance, decision, and utility nodes; it validates the diagram, infers posteriors, and returns the optimal policy.

Exact tabular solvers like pyAgrum are the right tool for fully discrete influence diagrams, but they cannot express a continuous variable or a payoff that is not a table. pylimid takes the other trade. Distributions, decisions, and utilities are ordinary NumPyro callables evaluated with JAX, and every answer is a Monte-Carlo estimate from a solver with a stated guarantee. That makes reachable models that tabular solvers cannot express: arbitrary continuous distributions, mixed diagrams, and payoffs like jnp.log(wealth).

Early development. pylimid is pre-1.0; the public API may change between releases. Pin a version if you build on it.

Capabilities

• Mixed-type by construction. Chance nodes can be discrete, continuous, or mixed, using any NumPyro distribution.
• Callables, not tables. A distribution or utility is a Python function of its parents, so a payoff can be any JAX-traceable expression.
• Explicit information sets. A decision observes exactly the parents you draw — there is no implicit no-forgetting. Anything an agent should remember is a memory arc you add, and a classical influence diagram is the special case where all of them are drawn.
• Two verbs. infer computes posterior draws — exact enumeration for discrete sites, NUTS for continuous ones — and solve returns an optimal policy with its expected utility.
• Monte-Carlo with stated guarantees. Backward induction on solvable diagrams, an exhaustive scan otherwise; the result records which solver ran.
• A mutable workspace. Build incrementally, wire and rewire edges, and gate inference behind an explicit validate() / snapshot() checkpoint.

Decision problem example

A newsvendor stocks newspapers before the day's demand is known. Each paper costs $1 and sells for $10; leftovers are worthless. Demand is a right-skewed Gamma — quiet days average 40, busy days average 120 — and the profit is an arbitrary function of what is stocked and demanded.

import jax.numpy as jnp
import numpyro.distributions as dist

from pylimid import ChanceNode, DecisionNode, InfluenceDiagram, UtilityNode, solve

orders = jnp.arange(0, 261, 20)  # discrete stock levels
rates = jnp.array([0.1, 1 / 30])  # Gamma rate: quiet mean 40, busy mean 120

diagram = InfluenceDiagram()
diagram.add_node(
    ChanceNode(
        name="day",
        states=("quiet", "busy"),
        dist=lambda: dist.Categorical(probs=jnp.array([0.7, 0.3])),
    )
)
diagram.add_node(
    ChanceNode(
        name="demand",
        parents=("day",),
        dist=lambda day: dist.Gamma(concentration=4.0, rate=rates[day]),
    )
)
diagram.add_node(
    DecisionNode(name="order", parents=("day",), states=tuple(str(n) for n in orders))
)
diagram.add_node(
    UtilityNode(
        name="profit",
        parents=("order", "demand"),
        values=lambda order, demand: (
            10.0 * jnp.minimum(orders[order], demand) - 1.0 * orders[order]
        ),
    )
)

solution = solve(diagram)
solution.policy  # stock 60 on a quiet day, 200 on a busy day

The solver stocks well above the average demand — 60 on a quiet day (mean 40), 200 on a busy day (mean 120) — because a missed sale forfeits the $9 margin while an unsold paper costs only $1, so the optimum tracks the 90th percentile. The newsvendor tutorial walks through the full derivation.

Installation

Requires Python 3.12.

pip install pylimid

The default install runs on the CPU. For an NVIDIA GPU, install the CUDA extra — it pulls the matching CUDA-enabled JAX plugin:

pip install "pylimid[cuda12]"   # or "pylimid[cuda13]" for newer drivers

For a development checkout, see CONTRIBUTING.md.

Documentation

• Quickstart
• User guide
• Tutorials

Contributing

Contributions are welcome. See CONTRIBUTING.md for the development setup, the checks, and the conventions.

License

Apache 2.0 — see LICENSE.md.