Add FMPE (#25)

examples/bivariate_gaussian_fmpe.py

@@ -0,0 +1,77 @@
+"""
+Example using flow matching posterior estimation on a bivariate Gaussian
+"""
+
+import distrax
+import haiku as hk
+import matplotlib.pyplot as plt
+import optax
+import seaborn as sns
+from jax import numpy as jnp
+from jax import random as jr
+
+from sbijax import FMPE
+from sbijax.nn import CCNF
+
+
+def prior_model_fns():
+    p = distrax.Independent(distrax.Normal(jnp.zeros(2), jnp.ones(2)), 1)
+    return p.sample, p.log_prob
+
+
+def simulator_fn(seed, theta):
+    p = distrax.Normal(jnp.zeros_like(theta), 1.0)
+    y = theta + p.sample(seed=seed)
+    return y
+
+
+def make_model(dim):
+    @hk.transform
+    def _mlp(method, **kwargs):
+        def _nn(theta, time, context, **kwargs):
+            ins = jnp.concatenate([theta, time, context], axis=-1)
+            outs = hk.nets.MLP([64, 64, dim])(ins)
+            return outs
+
+        ccnf = CCNF(dim, _nn)
+        return ccnf(method, **kwargs)
+
+    return _mlp
+
+
+def run():
+    y_observed = jnp.array([2.0, -2.0])
+
+    prior_simulator_fn, prior_logdensity_fn = prior_model_fns()
+    fns = (prior_simulator_fn, prior_logdensity_fn), simulator_fn
+
+    estim = FMPE(fns, make_model(2))
+    optimizer = optax.adam(1e-3)
+
+    data, params = None, {}
+    for i in range(2):
+        data, _ = estim.simulate_data_and_possibly_append(
+            jr.fold_in(jr.PRNGKey(1), i),
+            params=params,
+            observable=y_observed,
+            data=data,
+        )
+        params, info = estim.fit(
+            jr.fold_in(jr.PRNGKey(2), i),
+            data=data,
+            optimizer=optimizer,
+        )
+
+    rng_key = jr.PRNGKey(23)
+    post_samples, _ = estim.sample_posterior(rng_key, params, y_observed)
+    fig, axes = plt.subplots(2)
+    for i, ax in enumerate(axes):
+        sns.histplot(post_samples[:, i], color="darkblue", ax=ax)
+        ax.set_xlim([-3.0, 3.0])
+    sns.despine()
+    plt.tight_layout()
+    plt.show()
+
+
+if __name__ == "__main__":
+    run()

sbijax/__init__.py

@@ -6,6 +6,7 @@
 
 
 from sbijax._src.abc.smc_abc import SMCABC
+from sbijax._src.fmpe import FMPE
 from sbijax._src.snass import SNASS
 from sbijax._src.snasss import SNASSS
 from sbijax._src.snl import SNL

sbijax/_src/fmpe.py

@@ -0,0 +1,272 @@
+from functools import partial
+
+import jax
+import numpy as np
+import optax
+from absl import logging
+from jax import numpy as jnp
+from jax import random as jr
+from tqdm import tqdm
+
+from sbijax._src._sne_base import SNE
+from sbijax._src.nn.continuous_normalizing_flow import CCNF
+from sbijax._src.util.early_stopping import EarlyStopping
+
+
+def _sample_theta_t(rng_key, times, theta, sigma_min):
+    mus = times * theta
+    sigmata = 1.0 - (1.0 - sigma_min) * times
+    sigmata = sigmata.reshape(times.shape[0], 1)
+
+    noise = jr.normal(rng_key, shape=(*theta.shape,))
+    theta_t = noise * sigmata + mus
+    return theta_t
+
+
+def _ut(theta_t, theta, times, sigma_min):
+    num = theta - (1.0 - sigma_min) * theta_t
+    denom = 1.0 - (1.0 - sigma_min) * times
+    return num / denom
+
+
+# pylint: disable=too-many-locals
+def _cfm_loss(
+    params, rng_key, apply_fn, sigma_min=0.001, is_training=True, **batch
+):
+    theta = batch["theta"]
+    n, _ = theta.shape
+
+    t_key, rng_key = jr.split(rng_key)
+    times = jr.uniform(t_key, shape=(n, 1))
+
+    theta_key, rng_key = jr.split(rng_key)
+    theta_t = _sample_theta_t(theta_key, times, theta, sigma_min)
+
+    train_rng, rng_key = jr.split(rng_key)
+    vs = apply_fn(
+        params,
+        train_rng,
+        method="vector_field",
+        theta=theta_t,
+        time=times,
+        context=batch["y"],
+        is_training=is_training,
+    )
+    uts = _ut(theta_t, theta, times, sigma_min)
+
+    loss = jnp.mean(jnp.square(vs - uts))
+    return loss
+
+
+# pylint: disable=too-many-arguments,unused-argument,useless-parent-delegation
+class FMPE(SNE):
+    """Flow matching posterior estimation.
+
+    Args:
+        model_fns: a tuple of tuples. The first element is a tuple that
+                consists of functions to sample and evaluate the
+                log-probability of a data point. The second element is a
+                simulator function.
+        density_estimator: a continuous normalizing flow model
+
+    Examples:
+        >>> import distrax
+        >>> from sbijax import SNP
+        >>> from sbijax.nn import make_affine_maf
+        >>>
+        >>> prior = distrax.Normal(0.0, 1.0)
+        >>> s = lambda seed, theta: distrax.Normal(theta, 1.0).sample(seed=seed)
+        >>> fns = (prior.sample, prior.log_prob), s
+        >>> flow = make_affine_maf()
+        >>>
+        >>> snr = SNP(fns, flow)
+
+    References:
+        .. [1] Wildberger, Jonas, et al. "Flow Matching for Scalable
+           Simulation-Based Inference." Advances in Neural Information
+           Processing Systems, 2024.
+    """
+
+    def __init__(self, model_fns, density_estimator: CCNF):
+        """Construct a FMPE object.
+
+        Args:
+            model_fns: a tuple of tuples. The first element is a tuple that
+                    consists of functions to sample and evaluate the
+                    log-probability of a data point. The second element is a
+                    simulator function.
+            density_estimator: a (neural) conditional density estimator
+                to model the posterior distribution
+        """
+        super().__init__(model_fns, density_estimator)
+
+    # pylint: disable=arguments-differ,too-many-locals
+    def fit(
+        self,
+        rng_key,
+        data,
+        *,
+        optimizer=optax.adam(0.0003),
+        n_iter=1000,
+        batch_size=100,
+        percentage_data_as_validation_set=0.1,
+        n_early_stopping_patience=10,
+        **kwargs,
+    ):
+        """Fit the model.
+
+        Args:
+            rng_key: a jax random key
+            data: data set obtained from calling
+                `simulate_data_and_possibly_append`
+            optimizer: an optax optimizer object
+            n_iter: maximal number of training iterations per round
+            batch_size:  batch size used for training the model
+            percentage_data_as_validation_set: percentage of the simulated
+                data that is used for validation and early stopping
+            n_early_stopping_patience: number of iterations of no improvement
+                of training the flow before stopping optimisation\
+
+        Returns:
+            a tuple of parameters and a tuple of the training information
+        """
+        itr_key, rng_key = jr.split(rng_key)
+        train_iter, val_iter = self.as_iterators(
+            itr_key, data, batch_size, percentage_data_as_validation_set
+        )
+        params, losses = self._fit_model_single_round(
+            seed=rng_key,
+            train_iter=train_iter,
+            val_iter=val_iter,
+            optimizer=optimizer,
+            n_iter=n_iter,
+            n_early_stopping_patience=n_early_stopping_patience,
+        )
+
+        return params, losses
+
+    # pylint: disable=undefined-loop-variable
+    def _fit_model_single_round(
+        self,
+        seed,
+        train_iter,
+        val_iter,
+        optimizer,
+        n_iter,
+        n_early_stopping_patience,
+    ):
+        init_key, seed = jr.split(seed)
+        params = self._init_params(init_key, **next(iter(train_iter)))
+        state = optimizer.init(params)
+
+        loss_fn = jax.jit(
+            partial(_cfm_loss, apply_fn=self.model.apply, is_training=True)
+        )
+
+        @jax.jit
+        def step(params, rng, state, **batch):
+            loss, grads = jax.value_and_grad(loss_fn)(params, rng, **batch)
+            updates, new_state = optimizer.update(grads, state, params)
+            new_params = optax.apply_updates(params, updates)
+            return loss, new_params, new_state
+
+        losses = np.zeros([n_iter, 2])
+        early_stop = EarlyStopping(1e-3, n_early_stopping_patience)
+        best_params, best_loss = None, np.inf
+        logging.info("training model")
+        for i in tqdm(range(n_iter)):
+            train_loss = 0.0
+            rng_key = jr.fold_in(seed, i)
+            for batch in train_iter:
+                train_key, rng_key = jr.split(rng_key)
+                batch_loss, params, state = step(
+                    params, train_key, state, **batch
+                )
+                train_loss += batch_loss * (
+                    batch["y"].shape[0] / train_iter.num_samples
+                )
+            val_key, rng_key = jr.split(rng_key)
+            validation_loss = self._validation_loss(val_key, params, val_iter)
+            losses[i] = jnp.array([train_loss, validation_loss])
+
+            _, early_stop = early_stop.update(validation_loss)
+            if early_stop.should_stop:
+                logging.info("early stopping criterion found")
+                break
+            if validation_loss < best_loss:
+                best_loss = validation_loss
+                best_params = params.copy()
+
+        losses = jnp.vstack(losses)[: (i + 1), :]
+        return best_params, losses
+
+    def _init_params(self, rng_key, **init_data):
+        times = jr.uniform(jr.PRNGKey(0), shape=(init_data["y"].shape[0], 1))
+        params = self.model.init(
+            rng_key,
+            method="vector_field",
+            theta=init_data["theta"],
+            time=times,
+            context=init_data["y"],
+            is_training=False,
+        )
+        return params
+
+    def _validation_loss(self, rng_key, params, val_iter):
+        loss_fn = jax.jit(
+            partial(_cfm_loss, apply_fn=self.model.apply, is_training=False)
+        )
+
+        def body_fn(batch_key, **batch):
+            loss = loss_fn(params, batch_key, **batch)
+            return loss * (batch["y"].shape[0] / val_iter.num_samples)
+
+        loss = 0.0
+        for batch in val_iter:
+            val_key, rng_key = jr.split(rng_key)
+            loss += body_fn(val_key, **batch)
+        return loss
+
+    def sample_posterior(
+        self, rng_key, params, observable, *, n_samples=4_000, **kwargs
+    ):
+        r"""Sample from the approximate posterior.
+
+        Args:
+            rng_key: a jax random key
+            params: a pytree of neural network parameters
+            observable: observation to condition on
+            n_samples: number of samples to draw
+
+        Returns:
+            returns an array of samples from the posterior distribution of
+            dimension (n_samples \times p)
+        """
+        observable = jnp.atleast_2d(observable)
+
+        thetas = None
+        n_curr = n_samples
+        n_total_simulations_round = 0
+        while n_curr > 0:
+            n_sim = jnp.minimum(200, jnp.maximum(200, n_curr))
+            n_total_simulations_round += n_sim
+            sample_key, rng_key = jr.split(rng_key)
+            proposal = self.model.apply(
+                params,
+                sample_key,
+                method="sample",
+                context=jnp.tile(observable, [n_sim, 1]),
+            )
+            proposal_probs = self.prior_log_density_fn(proposal)
+            proposal_accepted = proposal[jnp.isfinite(proposal_probs)]
+            if thetas is None:
+                thetas = proposal_accepted
+            else:
+                thetas = jnp.vstack([thetas, proposal_accepted])
+            n_curr -= proposal_accepted.shape[0]
+
+        self.n_total_simulations += n_total_simulations_round
+        return (
+            thetas[:n_samples],
+            thetas.shape[0] / n_total_simulations_round,
+        )