# Copyright Contributors to the Pyro project. # SPDX-License-Identifier: Apache-2.0 from collections import OrderedDict, namedtuple from functools import partial import math import os from jax import device_put, lax, random, vmap from jax.flatten_util import ravel_pytree import jax.numpy as jnp from numpyro.infer.hmc_util import ( IntegratorState, build_tree, euclidean_kinetic_energy, find_reasonable_step_size, velocity_verlet, warmup_adapter, ) from numpyro.infer.mcmc import MCMCKernel from numpyro.infer.util import ParamInfo, init_to_uniform, initialize_model from numpyro.util import cond, fori_loop, identity HMCState = namedtuple( "HMCState", [ "i", "z", "z_grad", "potential_energy", "energy", "r", "trajectory_length", "num_steps", "accept_prob", "mean_accept_prob", "diverging", "adapt_state", "rng_key", ], ) """ A :func:`~collections.namedtuple` consisting of the following fields: - **i** - iteration. This is reset to 0 after warmup. - **z** - Python collection representing values (unconstrained samples from the posterior) at latent sites. - **z_grad** - Gradient of potential energy w.r.t. latent sample sites. - **potential_energy** - Potential energy computed at the given value of ``z``. - **energy** - Sum of potential energy and kinetic energy of the current state. - **r** - The current momentum variable. If this is None, a new momentum variable will be drawn at the beginning of each sampling step. - **trajectory_length** - The amount of time to run HMC dynamics in each sampling step. This field is not used in NUTS. - **num_steps** - Number of steps in the Hamiltonian trajectory (for diagnostics). In NUTS sampler, the tree depth of a trajectory can be computed from this field with `tree_depth = np.log2(num_steps).astype(int) + 1`. - **accept_prob** - Acceptance probability of the proposal. Note that ``z`` does not correspond to the proposal if it is rejected. - **mean_accept_prob** - Mean acceptance probability until current iteration during warmup adaptation or sampling (for diagnostics). - **diverging** - A boolean value to indicate whether the current trajectory is diverging. - **adapt_state** - A ``HMCAdaptState`` namedtuple which contains adaptation information during warmup: + **step_size** - Step size to be used by the integrator in the next iteration. + **inverse_mass_matrix** - The inverse mass matrix to be used for the next iteration. + **mass_matrix_sqrt** - The square root of mass matrix to be used for the next iteration. In case of dense mass, this is the Cholesky factorization of the mass matrix. - **rng_key** - random number generator seed used for the iteration. """ def _get_num_steps(step_size, trajectory_length): num_steps = jnp.ceil(trajectory_length / step_size) # NB: casting to jnp.int64 does not take effect (returns jnp.int32 instead) # if jax_enable_x64 is False return num_steps.astype(jnp.result_type(int)) def momentum_generator(prototype_r, mass_matrix_sqrt, rng_key): if isinstance(mass_matrix_sqrt, dict): rng_keys = random.split(rng_key, len(mass_matrix_sqrt)) r = {} for (site_names, mm_sqrt), rng_key in zip(mass_matrix_sqrt.items(), rng_keys): r_block = OrderedDict([(k, prototype_r[k]) for k in site_names]) r.update(momentum_generator(r_block, mm_sqrt, rng_key)) return r _, unpack_fn = ravel_pytree(prototype_r) eps = random.normal(rng_key, jnp.shape(mass_matrix_sqrt)[:1]) if mass_matrix_sqrt.ndim == 1: r = jnp.multiply(mass_matrix_sqrt, eps) return unpack_fn(r) elif mass_matrix_sqrt.ndim == 2: r = jnp.dot(mass_matrix_sqrt, eps) return unpack_fn(r) else: raise ValueError("Mass matrix has incorrect number of dims.") def hmc(potential_fn=None, potential_fn_gen=None, kinetic_fn=None, algo="NUTS"): r""" Hamiltonian Monte Carlo inference, using either fixed number of steps or the No U-Turn Sampler (NUTS) with adaptive path length. **References:** 1. *MCMC Using Hamiltonian Dynamics*, Radford M. Neal 2. *The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo*, Matthew D. Hoffman, and Andrew Gelman. 3. *A Conceptual Introduction to Hamiltonian Monte Carlo`*, Michael Betancourt :param potential_fn: Python callable that computes the potential energy given input parameters. The input parameters to `potential_fn` can be any python collection type, provided that `init_params` argument to `init_kernel` has the same type. :param potential_fn_gen: Python callable that when provided with model arguments / keyword arguments returns `potential_fn`. This may be provided to do inference on the same model with changing data. If the data shape remains the same, we can compile `sample_kernel` once, and use the same for multiple inference runs. :param kinetic_fn: Python callable that returns the kinetic energy given inverse mass matrix and momentum. If not provided, the default is euclidean kinetic energy. :param str algo: Whether to run ``HMC`` with fixed number of steps or ``NUTS`` with adaptive path length. Default is ``NUTS``. :return: a tuple of callables (`init_kernel`, `sample_kernel`), the first one to initialize the sampler, and the second one to generate samples given an existing one. .. warning:: Instead of using this interface directly, we would highly recommend you to use the higher level :class:`~numpyro.infer.mcmc.MCMC` API instead. **Example** .. doctest:: >>> import jax >>> from jax import random >>> import jax.numpy as jnp >>> import numpyro >>> import numpyro.distributions as dist >>> from numpyro.infer.hmc import hmc >>> from numpyro.infer.util import initialize_model >>> from numpyro.util import fori_collect >>> true_coefs = jnp.array([1., 2., 3.]) >>> data = random.normal(random.PRNGKey(2), (2000, 3)) >>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample(random.PRNGKey(3)) >>> >>> def model(data, labels): ... coefs = numpyro.sample('coefs', dist.Normal(jnp.zeros(3), jnp.ones(3))) ... intercept = numpyro.sample('intercept', dist.Normal(0., 10.)) ... return numpyro.sample('y', dist.Bernoulli(logits=(coefs * data + intercept).sum(-1)), obs=labels) >>> >>> model_info = initialize_model(random.PRNGKey(0), model, model_args=(data, labels,)) >>> init_kernel, sample_kernel = hmc(model_info.potential_fn, algo='NUTS') >>> hmc_state = init_kernel(model_info.param_info, ... trajectory_length=10, ... num_warmup=300) >>> samples = fori_collect(0, 500, sample_kernel, hmc_state, ... transform=lambda state: model_info.postprocess_fn(state.z)) >>> print(jnp.mean(samples['coefs'], axis=0)) # doctest: +SKIP [0.9153987 2.0754058 2.9621222] """ if kinetic_fn is None: kinetic_fn = euclidean_kinetic_energy vv_update = None max_treedepth = None wa_update = None wa_steps = None forward_mode_ad = False max_delta_energy = 1000.0 fixed_num_steps = None if algo not in {"HMC", "NUTS"}: raise ValueError("`algo` must be one of `HMC` or `NUTS`.") def init_kernel( init_params, num_warmup, step_size=1.0, inverse_mass_matrix=None, adapt_step_size=True, adapt_mass_matrix=True, dense_mass=False, target_accept_prob=0.8, *, num_steps=None, trajectory_length=2 * math.pi, max_tree_depth=10, find_heuristic_step_size=False, forward_mode_differentiation=False, regularize_mass_matrix=True, model_args=(), model_kwargs=None, rng_key=None, ): """ Initializes the HMC sampler. :param init_params: Initial parameters to begin sampling. The type must be consistent with the input type to `potential_fn`. :param int num_warmup: Number of warmup steps; samples generated during warmup are discarded. :param float step_size: Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1. :param inverse_mass_matrix: Initial value for inverse mass matrix. This may be adapted during warmup if adapt_mass_matrix = True. If no value is specified, then it is initialized to the identity matrix. For a potential_fn with general JAX pytree parameters, the order of entries of the mass matrix is the order of the flattened version of pytree parameters obtained with `jax.tree_flatten`, which is a bit ambiguous (see more at https://jax.readthedocs.io/en/latest/pytrees.html). If `model` is not None, here we can specify a structured block mass matrix as a dictionary, where keys are tuple of site names and values are the corresponding block of the mass matrix. For more information about structured mass matrix, see `dense_mass` argument. :type inverse_mass_matrix: numpy.ndarray or dict :param bool adapt_step_size: A flag to decide if we want to adapt step_size during warm-up phase using Dual Averaging scheme. :param bool adapt_mass_matrix: A flag to decide if we want to adapt mass matrix during warm-up phase using Welford scheme. :param dense_mass: This flag controls whether mass matrix is dense (i.e. full-rank) or diagonal (defaults to ``dense_mass=False``). To specify a structured mass matrix, users can provide a list of tuples of site names. Each tuple represents a block in the joint mass matrix. For example, assuming that the model has latent variables "x", "y", "z" (where each variable can be multi-dimensional), possible specifications and corresponding mass matrix structures are as follows: + dense_mass=[("x", "y")]: use a dense mass matrix for the joint (x, y) and a diagonal mass matrix for z + dense_mass=[] (equivalent to dense_mass=False): use a diagonal mass matrix for the joint (x, y, z) + dense_mass=[("x", "y", "z")] (equivalent to full_mass=True): use a dense mass matrix for the joint (x, y, z) + dense_mass=[("x",), ("y",), ("z")]: use dense mass matrices for each of x, y, and z (i.e. block-diagonal with 3 blocks) :type dense_mass: bool or list :param float target_accept_prob: Target acceptance probability for step size adaptation using Dual Averaging. Increasing this value will lead to a smaller step size, hence the sampling will be slower but more robust. Defaults to 0.8. :param int num_steps: if different than None, fix the number of steps allowed for each iteration. :param float trajectory_length: Length of a MCMC trajectory for HMC. Default value is :math:`2\\pi`. :param int max_tree_depth: Max depth of the binary tree created during the doubling scheme of NUTS sampler. Defaults to 10. This argument also accepts a tuple of integers `(d1, d2)`, where `d1` is the max tree depth during warmup phase and `d2` is the max tree depth during post warmup phase. :param bool find_heuristic_step_size: whether to a heuristic function to adjust the step size at the beginning of each adaptation window. Defaults to False. :param bool regularize_mass_matrix: whether or not to regularize the estimated mass matrix for numerical stability during warmup phase. Defaults to True. This flag does not take effect if ``adapt_mass_matrix == False``. :param tuple model_args: Model arguments if `potential_fn_gen` is specified. :param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified. :param jax.random.PRNGKey rng_key: random key to be used as the source of randomness. """ rng_key = random.PRNGKey(0) if rng_key is None else rng_key step_size = lax.convert_element_type(step_size, jnp.result_type(float)) if trajectory_length is not None: trajectory_length = lax.convert_element_type( trajectory_length, jnp.result_type(float) ) nonlocal wa_update, max_treedepth, vv_update, wa_steps, forward_mode_ad, fixed_num_steps forward_mode_ad = forward_mode_differentiation wa_steps = num_warmup max_treedepth = ( max_tree_depth if isinstance(max_tree_depth, tuple) else (max_tree_depth, max_tree_depth) ) fixed_num_steps = num_steps if isinstance(init_params, ParamInfo): z, pe, z_grad = init_params else: z, pe, z_grad = init_params, None, None pe_fn = potential_fn if potential_fn_gen: if pe_fn is not None: raise ValueError( "Only one of `potential_fn` or `potential_fn_gen` must be provided." ) else: kwargs = {} if model_kwargs is None else model_kwargs pe_fn = potential_fn_gen(*model_args, **kwargs) find_reasonable_ss = None if find_heuristic_step_size: find_reasonable_ss = partial( find_reasonable_step_size, pe_fn, kinetic_fn, momentum_generator ) wa_init, wa_update = warmup_adapter( num_warmup, adapt_step_size=adapt_step_size, adapt_mass_matrix=adapt_mass_matrix, dense_mass=dense_mass, target_accept_prob=target_accept_prob, find_reasonable_step_size=find_reasonable_ss, regularize_mass_matrix=regularize_mass_matrix, ) rng_key_hmc, rng_key_wa, rng_key_momentum = random.split(rng_key, 3) z_info = IntegratorState(z=z, potential_energy=pe, z_grad=z_grad) wa_state = wa_init( z_info, rng_key_wa, step_size, inverse_mass_matrix=inverse_mass_matrix ) r = momentum_generator(z, wa_state.mass_matrix_sqrt, rng_key_momentum) vv_init, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad) vv_state = vv_init(z, r, potential_energy=pe, z_grad=z_grad) energy = vv_state.potential_energy + kinetic_fn( wa_state.inverse_mass_matrix, vv_state.r ) zero_int = jnp.array(0, dtype=jnp.result_type(int)) hmc_state = HMCState( zero_int, vv_state.z, vv_state.z_grad, vv_state.potential_energy, energy, None, trajectory_length, zero_int, jnp.zeros(()), jnp.zeros(()), jnp.array(False), wa_state, rng_key_hmc, ) return device_put(hmc_state) def _hmc_next( step_size, inverse_mass_matrix, vv_state, model_args, model_kwargs, rng_key, trajectory_length, ): if potential_fn_gen: nonlocal vv_update, forward_mode_ad pe_fn = potential_fn_gen(*model_args, **model_kwargs) _, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad) if fixed_num_steps is not None: num_steps = fixed_num_steps # no need to spend too many steps if the state z has 0 size (i.e. z is empty) elif len(inverse_mass_matrix) == 0: num_steps = 1 else: num_steps = _get_num_steps(step_size, trajectory_length) # makes sure trajectory length is constant, rather than step_size * num_steps step_size = trajectory_length / num_steps vv_state_new = fori_loop( 0, num_steps, lambda i, val: vv_update(step_size, inverse_mass_matrix, val), vv_state, ) energy_old = vv_state.potential_energy + kinetic_fn( inverse_mass_matrix, vv_state.r ) energy_new = vv_state_new.potential_energy + kinetic_fn( inverse_mass_matrix, vv_state_new.r ) delta_energy = energy_new - energy_old delta_energy = jnp.where(jnp.isnan(delta_energy), jnp.inf, delta_energy) accept_prob = jnp.clip(jnp.exp(-delta_energy), a_max=1.0) diverging = delta_energy > max_delta_energy transition = random.bernoulli(rng_key, accept_prob) vv_state, energy = cond( transition, (vv_state_new, energy_new), identity, (vv_state, energy_old), identity, ) return vv_state, energy, num_steps, accept_prob, diverging def _nuts_next( step_size, inverse_mass_matrix, vv_state, model_args, model_kwargs, rng_key, max_treedepth_current, ): if potential_fn_gen: nonlocal vv_update, forward_mode_ad pe_fn = potential_fn_gen(*model_args, **model_kwargs) _, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad) binary_tree = build_tree( vv_update, kinetic_fn, vv_state, inverse_mass_matrix, step_size, rng_key, max_delta_energy=max_delta_energy, max_tree_depth=(max_treedepth_current, max(max_treedepth)), ) accept_prob = binary_tree.sum_accept_probs / binary_tree.num_proposals num_steps = binary_tree.num_proposals vv_state = IntegratorState( z=binary_tree.z_proposal, r=vv_state.r, potential_energy=binary_tree.z_proposal_pe, z_grad=binary_tree.z_proposal_grad, ) return ( vv_state, binary_tree.z_proposal_energy, num_steps, accept_prob, binary_tree.diverging, ) _next = _nuts_next if algo == "NUTS" else _hmc_next def sample_kernel(hmc_state, model_args=(), model_kwargs=None): """ Given an existing :data:`~numpyro.infer.mcmc.HMCState`, run HMC with fixed (possibly adapted) step size and return a new :data:`~numpyro.infer.mcmc.HMCState`. :param hmc_state: Current sample (and associated state). :param tuple model_args: Model arguments if `potential_fn_gen` is specified. :param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified. :return: new proposed :data:`~numpyro.infer.mcmc.HMCState` from simulating Hamiltonian dynamics given existing state. """ model_kwargs = {} if model_kwargs is None else model_kwargs rng_key, rng_key_momentum, rng_key_transition = random.split( hmc_state.rng_key, 3 ) r = ( momentum_generator( hmc_state.z, hmc_state.adapt_state.mass_matrix_sqrt, rng_key_momentum ) if hmc_state.r is None else hmc_state.r ) vv_state = IntegratorState( hmc_state.z, r, hmc_state.potential_energy, hmc_state.z_grad ) if algo == "HMC": hmc_length_args = (hmc_state.trajectory_length,) else: hmc_length_args = ( jnp.where(hmc_state.i < wa_steps, max_treedepth[0], max_treedepth[1]), ) vv_state, energy, num_steps, accept_prob, diverging = _next( hmc_state.adapt_state.step_size, hmc_state.adapt_state.inverse_mass_matrix, vv_state, model_args, model_kwargs, rng_key_transition, *hmc_length_args, ) # not update adapt_state after warmup phase adapt_state = cond( hmc_state.i < wa_steps, (hmc_state.i, accept_prob, vv_state, hmc_state.adapt_state), lambda args: wa_update(*args), hmc_state.adapt_state, identity, ) itr = hmc_state.i + 1 n = jnp.where(hmc_state.i < wa_steps, itr, itr - wa_steps) mean_accept_prob = ( hmc_state.mean_accept_prob + (accept_prob - hmc_state.mean_accept_prob) / n ) r = vv_state.r if hmc_state.r is not None else None return HMCState( itr, vv_state.z, vv_state.z_grad, vv_state.potential_energy, energy, r, hmc_state.trajectory_length, num_steps, accept_prob, mean_accept_prob, diverging, adapt_state, rng_key, ) # Make `init_kernel` and `sample_kernel` visible from the global scope once # `hmc` is called for sphinx doc generation. if "SPHINX_BUILD" in os.environ: hmc.init_kernel = init_kernel hmc.sample_kernel = sample_kernel return init_kernel, sample_kernel class HMC(MCMCKernel): """ Hamiltonian Monte Carlo inference, using fixed trajectory length, with provision for step size and mass matrix adaptation. .. note:: Until the kernel is used in an MCMC run, `postprocess_fn` will return the identity function. .. note:: The default init strategy ``init_to_uniform`` might not be a good strategy for some models. You might want to try other init strategies like ``init_to_median``. **References:** 1. *MCMC Using Hamiltonian Dynamics*, Radford M. Neal :param model: Python callable containing Pyro :mod:`~numpyro.primitives`. If model is provided, `potential_fn` will be inferred using the model. :param potential_fn: Python callable that computes the potential energy given input parameters. The input parameters to `potential_fn` can be any python collection type, provided that `init_params` argument to :meth:`init` has the same type. :param kinetic_fn: Python callable that returns the kinetic energy given inverse mass matrix and momentum. If not provided, the default is euclidean kinetic energy. :param float step_size: Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1. :param inverse_mass_matrix: Initial value for inverse mass matrix. This may be adapted during warmup if adapt_mass_matrix = True. If no value is specified, then it is initialized to the identity matrix. For a potential_fn with general JAX pytree parameters, the order of entries of the mass matrix is the order of the flattened version of pytree parameters obtained with `jax.tree_flatten`, which is a bit ambiguous (see more at https://jax.readthedocs.io/en/latest/pytrees.html). If `model` is not None, here we can specify a structured block mass matrix as a dictionary, where keys are tuple of site names and values are the corresponding block of the mass matrix. For more information about structured mass matrix, see `dense_mass` argument. :type inverse_mass_matrix: numpy.ndarray or dict :param bool adapt_step_size: A flag to decide if we want to adapt step_size during warm-up phase using Dual Averaging scheme. :param bool adapt_mass_matrix: A flag to decide if we want to adapt mass matrix during warm-up phase using Welford scheme. :param dense_mass: This flag controls whether mass matrix is dense (i.e. full-rank) or diagonal (defaults to ``dense_mass=False``). To specify a structured mass matrix, users can provide a list of tuples of site names. Each tuple represents a block in the joint mass matrix. For example, assuming that the model has latent variables "x", "y", "z" (where each variable can be multi-dimensional), possible specifications and corresponding mass matrix structures are as follows: + dense_mass=[("x", "y")]: use a dense mass matrix for the joint (x, y) and a diagonal mass matrix for z + dense_mass=[] (equivalent to dense_mass=False): use a diagonal mass matrix for the joint (x, y, z) + dense_mass=[("x", "y", "z")] (equivalent to full_mass=True): use a dense mass matrix for the joint (x, y, z) + dense_mass=[("x",), ("y",), ("z")]: use dense mass matrices for each of x, y, and z (i.e. block-diagonal with 3 blocks) :type dense_mass: bool or list :param float target_accept_prob: Target acceptance probability for step size adaptation using Dual Averaging. Increasing this value will lead to a smaller step size, hence the sampling will be slower but more robust. Defaults to 0.8. :param int num_steps: if different than None, fix the number of steps allowed for each iteration. :param float trajectory_length: Length of a MCMC trajectory for HMC. Default value is :math:`2\\pi`. :param callable init_strategy: a per-site initialization function. See :ref:`init_strategy` section for available functions. :param bool find_heuristic_step_size: whether or not to use a heuristic function to adjust the step size at the beginning of each adaptation window. Defaults to False. :param bool forward_mode_differentiation: whether to use forward-mode differentiation or reverse-mode differentiation. By default, we use reverse mode but the forward mode can be useful in some cases to improve the performance. In addition, some control flow utility on JAX such as `jax.lax.while_loop` or `jax.lax.fori_loop` only supports forward-mode differentiation. See `JAX's The Autodiff Cookbook `_ for more information. :param bool regularize_mass_matrix: whether or not to regularize the estimated mass matrix for numerical stability during warmup phase. Defaults to True. This flag does not take effect if ``adapt_mass_matrix == False``. """ def __init__( self, model=None, potential_fn=None, kinetic_fn=None, step_size=1.0, inverse_mass_matrix=None, adapt_step_size=True, adapt_mass_matrix=True, dense_mass=False, target_accept_prob=0.8, num_steps=None, trajectory_length=2 * math.pi, init_strategy=init_to_uniform, find_heuristic_step_size=False, forward_mode_differentiation=False, regularize_mass_matrix=True, ): if not (model is None) ^ (potential_fn is None): raise ValueError("Only one of `model` or `potential_fn` must be specified.") self._model = model self._potential_fn = potential_fn self._kinetic_fn = ( kinetic_fn if kinetic_fn is not None else euclidean_kinetic_energy ) self._num_steps = num_steps self._step_size = float(step_size) if isinstance(step_size, int) else step_size self._inverse_mass_matrix = inverse_mass_matrix self._adapt_step_size = adapt_step_size self._adapt_mass_matrix = adapt_mass_matrix self._dense_mass = dense_mass self._target_accept_prob = target_accept_prob self._trajectory_length = ( float(trajectory_length) if isinstance(trajectory_length, int) else trajectory_length ) self._algo = "HMC" self._max_tree_depth = 10 self._init_strategy = init_strategy self._find_heuristic_step_size = find_heuristic_step_size self._forward_mode_differentiation = forward_mode_differentiation self._regularize_mass_matrix = regularize_mass_matrix # Set on first call to init self._init_fn = None self._potential_fn_gen = None self._postprocess_fn = None self._sample_fn = None def _init_state(self, rng_key, model_args, model_kwargs, init_params): if self._model is not None: init_params, potential_fn, postprocess_fn, model_trace = initialize_model( rng_key, self._model, dynamic_args=True, init_strategy=self._init_strategy, model_args=model_args, model_kwargs=model_kwargs, forward_mode_differentiation=self._forward_mode_differentiation, ) if self._init_fn is None: self._init_fn, self._sample_fn = hmc( potential_fn_gen=potential_fn, kinetic_fn=self._kinetic_fn, algo=self._algo, ) self._potential_fn_gen = potential_fn self._postprocess_fn = postprocess_fn elif self._init_fn is None: self._init_fn, self._sample_fn = hmc( potential_fn=self._potential_fn, kinetic_fn=self._kinetic_fn, algo=self._algo, ) return init_params @property def model(self): return self._model @property def sample_field(self): return "z" @property def default_fields(self): return ("z", "diverging") def get_diagnostics_str(self, state): return "{} steps of size {:.2e}. acc. prob={:.2f}".format( state.num_steps, state.adapt_state.step_size, state.mean_accept_prob ) def init( self, rng_key, num_warmup, init_params=None, model_args=(), model_kwargs={} ): # non-vectorized if rng_key.ndim == 1: rng_key, rng_key_init_model = random.split(rng_key) # vectorized else: rng_key, rng_key_init_model = jnp.swapaxes( vmap(random.split)(rng_key), 0, 1 ) init_params = self._init_state( rng_key_init_model, model_args, model_kwargs, init_params ) if self._potential_fn and init_params is None: raise ValueError( "Valid value of `init_params` must be provided with" " `potential_fn`." ) # change dense_mass to a structural form dense_mass = self._dense_mass inverse_mass_matrix = self._inverse_mass_matrix if self._model is not None: z = init_params[0] if isinstance(init_params, ParamInfo) else init_params if isinstance(dense_mass, bool): # XXX: by default, the order variables are sorted by their names, # this is to be compatible with older numpyro versions # and to match autoguide scale parameter and jax flatten utils dense_mass = [tuple(sorted(z))] if dense_mass else [] assert isinstance(dense_mass, list) hmc_init_fn = lambda init_params, rng_key: self._init_fn( # noqa: E731 init_params, num_warmup=num_warmup, step_size=self._step_size, num_steps=self._num_steps, inverse_mass_matrix=inverse_mass_matrix, adapt_step_size=self._adapt_step_size, adapt_mass_matrix=self._adapt_mass_matrix, dense_mass=dense_mass, target_accept_prob=self._target_accept_prob, trajectory_length=self._trajectory_length, max_tree_depth=self._max_tree_depth, find_heuristic_step_size=self._find_heuristic_step_size, forward_mode_differentiation=self._forward_mode_differentiation, regularize_mass_matrix=self._regularize_mass_matrix, model_args=model_args, model_kwargs=model_kwargs, rng_key=rng_key, ) if rng_key.ndim == 1: init_state = hmc_init_fn(init_params, rng_key) else: # XXX it is safe to run hmc_init_fn under vmap despite that hmc_init_fn changes some # nonlocal variables: momentum_generator, wa_update, trajectory_len, max_treedepth, # wa_steps because those variables do not depend on traced args: init_params, rng_key. init_state = vmap(hmc_init_fn)(init_params, rng_key) sample_fn = vmap(self._sample_fn, in_axes=(0, None, None)) self._sample_fn = sample_fn return init_state def postprocess_fn(self, args, kwargs): if self._postprocess_fn is None: return identity return self._postprocess_fn(*args, **kwargs) def sample(self, state, model_args, model_kwargs): """ Run HMC from the given :data:`~numpyro.infer.hmc.HMCState` and return the resulting :data:`~numpyro.infer.hmc.HMCState`. :param HMCState state: Represents the current state. :param model_args: Arguments provided to the model. :param model_kwargs: Keyword arguments provided to the model. :return: Next `state` after running HMC. """ return self._sample_fn(state, model_args, model_kwargs) def __getstate__(self): state = self.__dict__.copy() state["_sample_fn"] = None state["_init_fn"] = None return state class NUTS(HMC): """ Hamiltonian Monte Carlo inference, using the No U-Turn Sampler (NUTS) with adaptive path length and mass matrix adaptation. .. note:: Until the kernel is used in an MCMC run, `postprocess_fn` will return the identity function. .. note:: The default init strategy ``init_to_uniform`` might not be a good strategy for some models. You might want to try other init strategies like ``init_to_median``. **References:** 1. *MCMC Using Hamiltonian Dynamics*, Radford M. Neal 2. *The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo*, Matthew D. Hoffman, and Andrew Gelman. 3. *A Conceptual Introduction to Hamiltonian Monte Carlo`*, Michael Betancourt :param model: Python callable containing Pyro :mod:`~numpyro.primitives`. If model is provided, `potential_fn` will be inferred using the model. :param potential_fn: Python callable that computes the potential energy given input parameters. The input parameters to `potential_fn` can be any python collection type, provided that `init_params` argument to `init_kernel` has the same type. :param kinetic_fn: Python callable that returns the kinetic energy given inverse mass matrix and momentum. If not provided, the default is euclidean kinetic energy. :param float step_size: Determines the size of a single step taken by the verlet integrator while computing the trajectory using Hamiltonian dynamics. If not specified, it will be set to 1. :param inverse_mass_matrix: Initial value for inverse mass matrix. This may be adapted during warmup if adapt_mass_matrix = True. If no value is specified, then it is initialized to the identity matrix. For a potential_fn with general JAX pytree parameters, the order of entries of the mass matrix is the order of the flattened version of pytree parameters obtained with `jax.tree_flatten`, which is a bit ambiguous (see more at https://jax.readthedocs.io/en/latest/pytrees.html). If `model` is not None, here we can specify a structured block mass matrix as a dictionary, where keys are tuple of site names and values are the corresponding block of the mass matrix. For more information about structured mass matrix, see `dense_mass` argument. :type inverse_mass_matrix: numpy.ndarray or dict :param bool adapt_step_size: A flag to decide if we want to adapt step_size during warm-up phase using Dual Averaging scheme. :param bool adapt_mass_matrix: A flag to decide if we want to adapt mass matrix during warm-up phase using Welford scheme. :param dense_mass: This flag controls whether mass matrix is dense (i.e. full-rank) or diagonal (defaults to ``dense_mass=False``). To specify a structured mass matrix, users can provide a list of tuples of site names. Each tuple represents a block in the joint mass matrix. For example, assuming that the model has latent variables "x", "y", "z" (where each variable can be multi-dimensional), possible specifications and corresponding mass matrix structures are as follows: + dense_mass=[("x", "y")]: use a dense mass matrix for the joint (x, y) and a diagonal mass matrix for z + dense_mass=[] (equivalent to dense_mass=False): use a diagonal mass matrix for the joint (x, y, z) + dense_mass=[("x", "y", "z")] (equivalent to full_mass=True): use a dense mass matrix for the joint (x, y, z) + dense_mass=[("x",), ("y",), ("z")]: use dense mass matrices for each of x, y, and z (i.e. block-diagonal with 3 blocks) :type dense_mass: bool or list :param float target_accept_prob: Target acceptance probability for step size adaptation using Dual Averaging. Increasing this value will lead to a smaller step size, hence the sampling will be slower but more robust. Defaults to 0.8. :param float trajectory_length: Length of a MCMC trajectory for HMC. This arg has no effect in NUTS sampler. :param int max_tree_depth: Max depth of the binary tree created during the doubling scheme of NUTS sampler. Defaults to 10. This argument also accepts a tuple of integers `(d1, d2)`, where `d1` is the max tree depth during warmup phase and `d2` is the max tree depth during post warmup phase. :param callable init_strategy: a per-site initialization function. See :ref:`init_strategy` section for available functions. :param bool find_heuristic_step_size: whether or not to use a heuristic function to adjust the step size at the beginning of each adaptation window. Defaults to False. :param bool forward_mode_differentiation: whether to use forward-mode differentiation or reverse-mode differentiation. By default, we use reverse mode but the forward mode can be useful in some cases to improve the performance. In addition, some control flow utility on JAX such as `jax.lax.while_loop` or `jax.lax.fori_loop` only supports forward-mode differentiation. See `JAX's The Autodiff Cookbook `_ for more information. """ def __init__( self, model=None, potential_fn=None, kinetic_fn=None, step_size=1.0, inverse_mass_matrix=None, adapt_step_size=True, adapt_mass_matrix=True, dense_mass=False, target_accept_prob=0.8, trajectory_length=None, max_tree_depth=10, init_strategy=init_to_uniform, find_heuristic_step_size=False, forward_mode_differentiation=False, regularize_mass_matrix=True, ): super(NUTS, self).__init__( potential_fn=potential_fn, model=model, kinetic_fn=kinetic_fn, step_size=step_size, inverse_mass_matrix=inverse_mass_matrix, adapt_step_size=adapt_step_size, adapt_mass_matrix=adapt_mass_matrix, dense_mass=dense_mass, target_accept_prob=target_accept_prob, trajectory_length=trajectory_length, init_strategy=init_strategy, find_heuristic_step_size=find_heuristic_step_size, forward_mode_differentiation=forward_mode_differentiation, regularize_mass_matrix=regularize_mass_matrix, ) self._max_tree_depth = max_tree_depth self._algo = "NUTS"