# Effect Handlers¶

This provides a small set of effect handlers in NumPyro that are modeled after Pyro’s poutine module. For a tutorial on effect handlers more generally, readers are encouraged to read Poutine: A Guide to Programming with Effect Handlers in Pyro. These simple effect handlers can be composed together or new ones added to enable implementation of custom inference utilities and algorithms.

Example

As an example, we are using `seed`, `trace` and `substitute` handlers to define the log_likelihood function below. We first create a logistic regression model and sample from the posterior distribution over the regression parameters using `MCMC()`. The log_likelihood function uses effect handlers to run the model by substituting sample sites with values from the posterior distribution and computes the log density for a single data point. The log_predictive_density function computes the log likelihood for each draw from the joint posterior and aggregates the results for all the data points, but does so by using JAX’s auto-vectorize transform called vmap so that we do not need to loop over all the data points.

```>>> import jax.numpy as jnp
>>> from jax import random, vmap
>>> from jax.scipy.special import logsumexp
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro import handlers
>>> from numpyro.infer import MCMC, NUTS

>>> N, D = 3000, 3
>>> def logistic_regression(data, labels):
...     coefs = numpyro.sample('coefs', dist.Normal(jnp.zeros(D), jnp.ones(D)))
...     intercept = numpyro.sample('intercept', dist.Normal(0., 10.))
...     logits = jnp.sum(coefs * data + intercept, axis=-1)
...     return numpyro.sample('obs', dist.Bernoulli(logits=logits), obs=labels)

>>> data = random.normal(random.PRNGKey(0), (N, D))
>>> true_coefs = jnp.arange(1., D + 1.)
>>> logits = jnp.sum(true_coefs * data, axis=-1)
>>> labels = dist.Bernoulli(logits=logits).sample(random.PRNGKey(1))

>>> num_warmup, num_samples = 1000, 1000
>>> mcmc = MCMC(NUTS(model=logistic_regression), num_warmup=num_warmup, num_samples=num_samples)
>>> mcmc.run(random.PRNGKey(2), data, labels)
sample: 100%|██████████| 1000/1000 [00:00<00:00, 1252.39it/s, 1 steps of size 5.83e-01. acc. prob=0.85]
>>> mcmc.print_summary()

mean         sd       5.5%      94.5%      n_eff       Rhat
coefs       0.96       0.07       0.85       1.07     455.35       1.01
coefs       2.05       0.09       1.91       2.20     332.00       1.01
coefs       3.18       0.13       2.96       3.37     320.27       1.00
intercept      -0.03       0.02      -0.06       0.00     402.53       1.00

>>> def log_likelihood(rng_key, params, model, *args, **kwargs):
...     model = handlers.substitute(handlers.seed(model, rng_key), params)
...     model_trace = handlers.trace(model).get_trace(*args, **kwargs)
...     obs_node = model_trace['obs']
...     return obs_node['fn'].log_prob(obs_node['value'])

>>> def log_predictive_density(rng_key, params, model, *args, **kwargs):
...     n = list(params.values()).shape
...     log_lk_fn = vmap(lambda rng_key, params: log_likelihood(rng_key, params, model, *args, **kwargs))
...     log_lk_vals = log_lk_fn(random.split(rng_key, n), params)
...     return jnp.sum(logsumexp(log_lk_vals, 0) - jnp.log(n))

>>> print(log_predictive_density(random.PRNGKey(2), mcmc.get_samples(),
...       logistic_regression, data, labels))
-874.89813
```

## block¶

class block(fn=None, hide_fn=None, hide=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a callable fn, return another callable that selectively hides primitive sites where hide_fn returns True from other effect handlers on the stack.

Parameters
• fn (callable) – Python callable with NumPyro primitives.

• hide_fn (callable) – function which when given a dictionary containing site-level metadata returns whether it should be blocked.

• hide (list) – list of site names to hide.

Example:

```>>> from jax import random
>>> import numpyro
>>> from numpyro.handlers import block, seed, trace
>>> import numpyro.distributions as dist

>>> def model():
...     a = numpyro.sample('a', dist.Normal(0., 1.))
...     return numpyro.sample('b', dist.Normal(a, 1.))

>>> model = seed(model, random.PRNGKey(0))
>>> block_all = block(model)
>>> block_a = block(model, lambda site: site['name'] == 'a')
>>> trace_block_all = trace(block_all).get_trace()
>>> assert not {'a', 'b'}.intersection(trace_block_all.keys())
>>> trace_block_a =  trace(block_a).get_trace()
>>> assert 'a' not in trace_block_a
>>> assert 'b' in trace_block_a
```
process_message(msg)[source]

## collapse¶

class collapse(*args, **kwargs)[source]

EXPERIMENTAL Collapses all sites in the context by lazily sampling and attempting to use conjugacy relations. If no conjugacy is known this will fail. Code using the results of sample sites must be written to accept Funsors rather than Tensors. This requires `funsor` to be installed.

process_message(msg)[source]

## condition¶

class condition(fn=None, data=None, condition_fn=None)[source]

Bases: `numpyro.primitives.Messenger`

Conditions unobserved sample sites to values from data or condition_fn. Similar to `substitute` except that it only affects sample sites and changes the is_observed property to True.

Parameters
• fn – Python callable with NumPyro primitives.

• data (dict) – dictionary of numpy.ndarray values keyed by site names.

• condition_fn – callable that takes in a site dict and returns a numpy array or None (in which case the handler has no side effect).

Example:

```>>> from jax import random
>>> import numpyro
>>> from numpyro.handlers import condition, seed, substitute, trace
>>> import numpyro.distributions as dist

>>> def model():
...     numpyro.sample('a', dist.Normal(0., 1.))

>>> model = seed(model, random.PRNGKey(0))
>>> exec_trace = trace(condition(model, {'a': -1})).get_trace()
>>> assert exec_trace['a']['value'] == -1
>>> assert exec_trace['a']['is_observed']
```
process_message(msg)[source]

## do¶

class do(fn=None, data=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a stochastic function with some sample statements and a dictionary of values at names, set the return values of those sites equal to the values as if they were hard-coded to those values and introduce fresh sample sites with the same names whose values do not propagate.

Composes freely with `condition()` to represent counterfactual distributions over potential outcomes. See Single World Intervention Graphs  for additional details and theory.

This is equivalent to replacing z = numpyro.sample(“z”, …) with z = 1. and introducing a fresh sample site numpyro.sample(“z”, …) whose value is not used elsewhere.

References:

1. Single World Intervention Graphs: A Primer, Thomas Richardson, James Robins

Parameters
• fn – a stochastic function (callable containing Pyro primitive calls)

• data – a `dict` mapping sample site names to interventions

Example:

```>>> import jax.numpy as jnp
>>> import numpyro
>>> from numpyro.handlers import do, trace, seed
>>> import numpyro.distributions as dist
>>> def model(x):
...     s = numpyro.sample("s", dist.LogNormal())
...     z = numpyro.sample("z", dist.Normal(x, s))
...     return z ** 2
>>> intervened_model = handlers.do(model, data={"z": 1.})
>>> with trace() as exec_trace:
...     z_square = seed(intervened_model, 0)(1)
>>> assert exec_trace['z']['value'] != 1.
>>> assert not exec_trace['z']['is_observed']
>>> assert not exec_trace['z'].get('stop', None)
>>> assert z_square == 1
```
process_message(msg)[source]

## infer_config¶

class infer_config(fn=None, config_fn=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a callable fn that contains NumPyro primitive calls and a callable config_fn taking a trace site and returning a dictionary, updates the value of the infer kwarg at a sample site to config_fn(site).

Parameters
• fn – a stochastic function (callable containing NumPyro primitive calls)

• config_fn – a callable taking a site and returning an infer dict

process_message(msg)[source]

## lift¶

class lift(fn=None, prior=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a stochastic function with `param` calls and a prior distribution, create a stochastic function where all param calls are replaced by sampling from prior. Prior should be a distribution or a dict of names to distributions.

Consider the following NumPyro program:

```>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.handlers import lift
>>>
>>> def model(x):
...     s = numpyro.param("s", 0.5)
...     z = numpyro.sample("z", dist.Normal(x, s))
...     return z ** 2
>>> lifted_model = lift(model, prior={"s": dist.Exponential(0.3)})
```

`lift` makes `param` statements behave like `sample` statements using the distributions in `prior`. In this example, site s will now behave as if it was replaced with `s = numpyro.sample("s", dist.Exponential(0.3))`.

Parameters
• fn – function whose parameters will be lifted to random values

• prior – prior function in the form of a Distribution or a dict of Distributions

process_message(msg)[source]

Bases: `numpyro.primitives.Messenger`

This messenger masks out some of the sample statements elementwise.

Parameters

mask – a boolean or a boolean-valued array for masking elementwise log probability of sample sites (True includes a site, False excludes a site).

process_message(msg)[source]

## reparam¶

class reparam(fn=None, config=None)[source]

Bases: `numpyro.primitives.Messenger`

Reparametrizes each affected sample site into one or more auxiliary sample sites followed by a deterministic transformation .

To specify reparameterizers, pass a `config` dict or callable to the constructor. See the `numpyro.infer.reparam` module for available reparameterizers.

Note some reparameterizers can examine the `*args,**kwargs` inputs of functions they affect; these reparameterizers require using `handlers.reparam` as a decorator rather than as a context manager.

 Maria I. Gorinova, Dave Moore, Matthew D. Hoffman (2019)

“Automatic Reparameterisation of Probabilistic Programs” https://arxiv.org/pdf/1906.03028.pdf

Parameters

config (dict or callable) – Configuration, either a dict mapping site name to `Reparam` , or a function mapping site to `Reparam` or None.

process_message(msg)[source]

## replay¶

class replay(fn=None, trace=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a callable fn and an execution trace trace, return a callable which substitutes sample calls in fn with values from the corresponding site names in trace.

Parameters
• fn – Python callable with NumPyro primitives.

• trace – an OrderedDict containing execution metadata.

Example:

```>>> from jax import random
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.handlers import replay, seed, trace

>>> def model():
...     numpyro.sample('a', dist.Normal(0., 1.))

>>> exec_trace = trace(seed(model, random.PRNGKey(0))).get_trace()
>>> print(exec_trace['a']['value'])
-0.20584235
>>> replayed_trace = trace(replay(model, exec_trace)).get_trace()
>>> print(exec_trace['a']['value'])
-0.20584235
>>> assert replayed_trace['a']['value'] == exec_trace['a']['value']
```
process_message(msg)[source]

## scale¶

class scale(fn=None, scale=1.0)[source]

Bases: `numpyro.primitives.Messenger`

This messenger rescales the log probability score.

This is typically used for data subsampling or for stratified sampling of data (e.g. in fraud detection where negatives vastly outnumber positives).

Parameters

scale (float or numpy.ndarray) – a positive scaling factor that is broadcastable to the shape of log probability.

process_message(msg)[source]

## scope¶

class scope(fn=None, prefix='', divider='/', *, hide_types=None)[source]

Bases: `numpyro.primitives.Messenger`

This handler prepend a prefix followed by a divider to the name of sample sites.

Example:

```>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.handlers import scope, seed, trace

>>> def model():
...     with scope(prefix="a"):
...         with scope(prefix="b", divider="."):
...             return numpyro.sample("x", dist.Bernoulli(0.5))
...
>>> assert "a/b.x" in trace(seed(model, 0)).get_trace()
```
Parameters
• fn – Python callable with NumPyro primitives.

• prefix (str) – a string to prepend to sample names

• divider (str) – a string to join the prefix and sample name; default to ‘/’

• hide_types (list) – an optional list of side types to skip renaming.

process_message(msg)[source]

## seed¶

class seed(fn=None, rng_seed=None)[source]

Bases: `numpyro.primitives.Messenger`

JAX uses a functional pseudo random number generator that requires passing in a seed `PRNGKey()` to every stochastic function. The seed handler allows us to initially seed a stochastic function with a `PRNGKey()`. Every call to the `sample()` primitive inside the function results in a splitting of this initial seed so that we use a fresh seed for each subsequent call without having to explicitly pass in a PRNGKey to each sample call.

Parameters
• fn – Python callable with NumPyro primitives.

• rng_seed (int, jnp.ndarray scalar, or jax.random.PRNGKey) – a random number generator seed.

Note

Unlike in Pyro, numpyro.sample primitive cannot be used without wrapping it in seed handler since there is no global random state. As such, users need to use seed as a contextmanager to generate samples from distributions or as a decorator for their model callable (See below).

Example:

```>>> from jax import random
>>> import numpyro
>>> import numpyro.handlers
>>> import numpyro.distributions as dist

>>> # as context manager
>>> with handlers.seed(rng_seed=1):
...     x = numpyro.sample('x', dist.Normal(0., 1.))

>>> def model():
...     return numpyro.sample('y', dist.Normal(0., 1.))

>>> # as function decorator (/modifier)
>>> y = handlers.seed(model, rng_seed=1)()
>>> assert x == y
```
process_message(msg)[source]

## substitute¶

class substitute(fn=None, data=None, substitute_fn=None)[source]

Bases: `numpyro.primitives.Messenger`

Given a callable fn and a dict data keyed by site names (alternatively, a callable substitute_fn), return a callable which substitutes all primitive calls in fn with values from data whose key matches the site name. If the site name is not present in data, there is no side effect.

If a substitute_fn is provided, then the value at the site is replaced by the value returned from the call to substitute_fn for the given site.

Note

This handler is mainly used for internal algorithms. For conditioning a generative model on observed data, please using the `condition` handler.

Parameters
• fn – Python callable with NumPyro primitives.

• data (dict) – dictionary of numpy.ndarray values keyed by site names.

• substitute_fn – callable that takes in a site dict and returns a numpy array or None (in which case the handler has no side effect).

Example:

```>>> from jax import random
>>> import numpyro
>>> from numpyro.handlers import seed, substitute, trace
>>> import numpyro.distributions as dist

>>> def model():
...     numpyro.sample('a', dist.Normal(0., 1.))

>>> model = seed(model, random.PRNGKey(0))
>>> exec_trace = trace(substitute(model, {'a': -1})).get_trace()
>>> assert exec_trace['a']['value'] == -1
```
process_message(msg)[source]

## trace¶

class trace(fn=None)[source]

Bases: `numpyro.primitives.Messenger`

Returns a handler that records the inputs and outputs at primitive calls inside fn.

Example:

```>>> from jax import random
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.handlers import seed, trace
>>> import pprint as pp

>>> def model():
...     numpyro.sample('a', dist.Normal(0., 1.))

>>> exec_trace = trace(seed(model, random.PRNGKey(0))).get_trace()
>>> pp.pprint(exec_trace)
OrderedDict([('a',
{'args': (),
'fn': <numpyro.distributions.continuous.Normal object at 0x7f9e689b1eb8>,
'is_observed': False,
'kwargs': {'rng_key': DeviceArray([0, 0], dtype=uint32)},
'name': 'a',
'type': 'sample',
'value': DeviceArray(-0.20584235, dtype=float32)})])
```
postprocess_message(msg)[source]
get_trace(*args, **kwargs)[source]

Run the wrapped callable and return the recorded trace.

Parameters
• *args – arguments to the callable.

• **kwargs – keyword arguments to the callable.

Returns

OrderedDict containing the execution trace.