# Copyright 2020 The PyMC Developers # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. R""" Variational inference is a great approach for doing really complex, often intractable Bayesian inference in approximate form. Common methods (e.g. ADVI) lack from complexity so that approximate posterior does not reveal the true nature of underlying problem. In some applications it can yield unreliable decisions. Recently on NIPS 2017 OPVI _ framework was presented. It generalizes variational inference so that the problem is build with blocks. The first and essential block is Model itself. Second is Approximation, in some cases :math:log Q(D) is not really needed. Necessity depends on the third and fourth part of that black box, Operator and Test Function respectively. Operator is like an approach we use, it constructs loss from given Model, Approximation and Test Function. The last one is not needed if we minimize KL Divergence from Q to posterior. As a drawback we need to compute :math:loq Q(D). Sometimes approximation family is intractable and :math:loq Q(D) is not available, here comes LS(Langevin Stein) Operator with a set of test functions. Test Function has more unintuitive meaning. It is usually used with LS operator and represents all we want from our approximate distribution. For any given vector based function of :math:z LS operator yields zero mean function under posterior. :math:loq Q(D) is no more needed. That opens a door to rich approximation families as neural networks. References ---------- - Rajesh Ranganath, Jaan Altosaar, Dustin Tran, David M. Blei Operator Variational Inference https://arxiv.org/abs/1610.09033 (2016) """ import collections import itertools import warnings import aesara import aesara.tensor as at import numpy as np from aesara.graph.basic import Variable import pymc3 as pm from pymc3.aesaraf import at_rng, identity from pymc3.backends import NDArray from pymc3.blocking import ArrayOrdering, DictToArrayBijection, VarMap from pymc3.model import modelcontext from pymc3.util import ( WithMemoization, get_default_varnames, get_transformed, locally_cachedmethod, ) from pymc3.variational.updates import adagrad_window __all__ = ["ObjectiveFunction", "Operator", "TestFunction", "Group", "Approximation"] class VariationalInferenceError(Exception): """Exception for VI specific cases""" class ExplicitInferenceError(VariationalInferenceError, TypeError): """Exception for bad explicit inference""" class AEVBInferenceError(VariationalInferenceError, TypeError): """Exception for bad aevb inference""" class ParametrizationError(VariationalInferenceError, ValueError): """Error raised in case of bad parametrization""" class GroupError(VariationalInferenceError, TypeError): """Error related to VI groups""" class BatchedGroupError(GroupError): """Error with batched variables""" class LocalGroupError(BatchedGroupError, AEVBInferenceError): """Error raised in case of bad local_rv usage""" def append_name(name): def wrap(f): if name is None: return f def inner(*args, **kwargs): res = f(*args, **kwargs) res.name = name return res return inner return wrap def node_property(f): """A shortcut for wrapping method to accessible tensor""" if isinstance(f, str): def wrapper(fn): ff = append_name(f)(fn) f_ = aesara.config.change_flags(compute_test_value="off")(ff) return property(locally_cachedmethod(f_)) return wrapper else: f_ = aesara.config.change_flags(compute_test_value="off")(f) return property(locally_cachedmethod(f_)) @aesara.config.change_flags(compute_test_value="ignore") def try_to_set_test_value(node_in, node_out, s): _s = s if s is None: s = 1 s = aesara.compile.view_op(at.as_tensor(s)) if not isinstance(node_in, (list, tuple)): node_in = [node_in] if not isinstance(node_out, (list, tuple)): node_out = [node_out] for i, o in zip(node_in, node_out): if hasattr(i.tag, "test_value"): if not hasattr(s.tag, "test_value"): continue else: tv = i.tag.test_value[None, ...] tv = np.repeat(tv, s.tag.test_value, 0) if _s is None: tv = tv[0] o.tag.test_value = tv class ObjectiveUpdates(aesara.OrderedUpdates): """OrderedUpdates extension for storing loss""" loss = None def _warn_not_used(smth, where): warnings.warn(f"{smth} is not used for {where} and ignored") class ObjectiveFunction: """Helper class for construction loss and updates for variational inference Parameters ---------- op : :class:Operator OPVI Functional operator tf : :class:TestFunction OPVI TestFunction """ def __init__(self, op, tf): self.op = op self.tf = tf obj_params = property(lambda self: self.op.approx.params) test_params = property(lambda self: self.tf.params) approx = property(lambda self: self.op.approx) def updates( self, obj_n_mc=None, tf_n_mc=None, obj_optimizer=adagrad_window, test_optimizer=adagrad_window, more_obj_params=None, more_tf_params=None, more_updates=None, more_replacements=None, total_grad_norm_constraint=None, ): """Calculate gradients for objective function, test function and then constructs updates for optimization step Parameters ---------- obj_n_mc : int Number of monte carlo samples used for approximation of objective gradients tf_n_mc : int Number of monte carlo samples used for approximation of test function gradients obj_optimizer : function (loss, params) -> updates Optimizer that is used for objective params test_optimizer : function (loss, params) -> updates Optimizer that is used for test function params more_obj_params : list Add custom params for objective optimizer more_tf_params : list Add custom params for test function optimizer more_updates : dict Add custom updates to resulting updates more_replacements : dict Apply custom replacements before calculating gradients total_grad_norm_constraint : float Bounds gradient norm, prevents exploding gradient problem Returns ------- :class:ObjectiveUpdates """ if more_updates is None: more_updates = dict() resulting_updates = ObjectiveUpdates() if self.test_params: self.add_test_updates( resulting_updates, tf_n_mc=tf_n_mc, test_optimizer=test_optimizer, more_tf_params=more_tf_params, more_replacements=more_replacements, total_grad_norm_constraint=total_grad_norm_constraint, ) else: if tf_n_mc is not None: _warn_not_used("tf_n_mc", self.op) if more_tf_params: _warn_not_used("more_tf_params", self.op) self.add_obj_updates( resulting_updates, obj_n_mc=obj_n_mc, obj_optimizer=obj_optimizer, more_obj_params=more_obj_params, more_replacements=more_replacements, total_grad_norm_constraint=total_grad_norm_constraint, ) resulting_updates.update(more_updates) return resulting_updates def add_test_updates( self, updates, tf_n_mc=None, test_optimizer=adagrad_window, more_tf_params=None, more_replacements=None, total_grad_norm_constraint=None, ): if more_tf_params is None: more_tf_params = [] if more_replacements is None: more_replacements = dict() tf_target = self( tf_n_mc, more_tf_params=more_tf_params, more_replacements=more_replacements ) grads = pm.updates.get_or_compute_grads(tf_target, self.obj_params + more_tf_params) if total_grad_norm_constraint is not None: grads = pm.total_norm_constraint(grads, total_grad_norm_constraint) updates.update(test_optimizer(grads, self.test_params + more_tf_params)) def add_obj_updates( self, updates, obj_n_mc=None, obj_optimizer=adagrad_window, more_obj_params=None, more_replacements=None, total_grad_norm_constraint=None, ): if more_obj_params is None: more_obj_params = [] if more_replacements is None: more_replacements = dict() obj_target = self( obj_n_mc, more_obj_params=more_obj_params, more_replacements=more_replacements ) grads = pm.updates.get_or_compute_grads(obj_target, self.obj_params + more_obj_params) if total_grad_norm_constraint is not None: grads = pm.total_norm_constraint(grads, total_grad_norm_constraint) updates.update(obj_optimizer(grads, self.obj_params + more_obj_params)) if self.op.returns_loss: updates.loss = obj_target @aesara.config.change_flags(compute_test_value="off") def step_function( self, obj_n_mc=None, tf_n_mc=None, obj_optimizer=adagrad_window, test_optimizer=adagrad_window, more_obj_params=None, more_tf_params=None, more_updates=None, more_replacements=None, total_grad_norm_constraint=None, score=False, fn_kwargs=None, ): R"""Step function that should be called on each optimization step. Generally it solves the following problem: .. math:: \mathbf{\lambda^{\*}} = \inf_{\lambda} \sup_{\theta} t(\mathbb{E}_{\lambda}[(O^{p,q}f_{\theta})(z)]) Parameters ---------- obj_n_mc: int Number of monte carlo samples used for approximation of objective gradients tf_n_mc: int Number of monte carlo samples used for approximation of test function gradients obj_optimizer: function (grads, params) -> updates Optimizer that is used for objective params test_optimizer: function (grads, params) -> updates Optimizer that is used for test function params more_obj_params: list Add custom params for objective optimizer more_tf_params: list Add custom params for test function optimizer more_updates: dict Add custom updates to resulting updates total_grad_norm_constraint: float Bounds gradient norm, prevents exploding gradient problem score: bool calculate loss on each step? Defaults to False for speed fn_kwargs: dict Add kwargs to aesara.function (e.g. {'profile': True}) more_replacements: dict Apply custom replacements before calculating gradients Returns ------- aesara.function """ if fn_kwargs is None: fn_kwargs = {} if score and not self.op.returns_loss: raise NotImplementedError("%s does not have loss" % self.op) updates = self.updates( obj_n_mc=obj_n_mc, tf_n_mc=tf_n_mc, obj_optimizer=obj_optimizer, test_optimizer=test_optimizer, more_obj_params=more_obj_params, more_tf_params=more_tf_params, more_updates=more_updates, more_replacements=more_replacements, total_grad_norm_constraint=total_grad_norm_constraint, ) if score: step_fn = aesara.function([], updates.loss, updates=updates, **fn_kwargs) else: step_fn = aesara.function([], None, updates=updates, **fn_kwargs) return step_fn @aesara.config.change_flags(compute_test_value="off") def score_function( self, sc_n_mc=None, more_replacements=None, fn_kwargs=None ): # pragma: no cover R"""Compile scoring function that operates which takes no inputs and returns Loss Parameters ---------- sc_n_mc: int number of scoring MC samples more_replacements: Apply custom replacements before compiling a function fn_kwargs: dict arbitrary kwargs passed to aesara.function Returns ------- aesara.function """ if fn_kwargs is None: fn_kwargs = {} if not self.op.returns_loss: raise NotImplementedError("%s does not have loss" % self.op) if more_replacements is None: more_replacements = {} loss = self(sc_n_mc, more_replacements=more_replacements) return aesara.function([], loss, **fn_kwargs) @aesara.config.change_flags(compute_test_value="off") def __call__(self, nmc, **kwargs): if "more_tf_params" in kwargs: m = -1.0 else: m = 1.0 a = self.op.apply(self.tf) a = self.approx.set_size_and_deterministic(a, nmc, 0, kwargs.get("more_replacements")) return m * self.op.T(a) class Operator: R"""**Base class for Operator** Parameters ---------- approx: :class:Approximation an approximation instance Notes ----- For implementing custom operator it is needed to define :func:Operator.apply method """ has_test_function = False returns_loss = True require_logq = True objective_class = ObjectiveFunction supports_aevb = property(lambda self: not self.approx.any_histograms) T = identity def __init__(self, approx): self.approx = approx if not self.supports_aevb and approx.has_local: raise AEVBInferenceError( "%s does not support AEVB, " "please change inference method" % self ) if self.require_logq and not approx.has_logq: raise ExplicitInferenceError( "%s requires logq, but %s does not implement it" "please change inference method" % (self, approx) ) inputs = property(lambda self: self.approx.inputs) logp = property(lambda self: self.approx.logp) varlogp = property(lambda self: self.approx.varlogp) datalogp = property(lambda self: self.approx.datalogp) logq = property(lambda self: self.approx.logq) logp_norm = property(lambda self: self.approx.logp_norm) varlogp_norm = property(lambda self: self.approx.varlogp_norm) datalogp_norm = property(lambda self: self.approx.datalogp_norm) logq_norm = property(lambda self: self.approx.logq_norm) model = property(lambda self: self.approx.model) def apply(self, f): # pragma: no cover R"""Operator itself .. math:: (O^{p,q}f_{\theta})(z) Parameters ---------- f: :class:TestFunction or None function that takes z = self.input and returns same dimensional output Returns ------- TensorVariable symbolically applied operator """ raise NotImplementedError def __call__(self, f=None): if self.has_test_function: if f is None: raise ParametrizationError("Operator %s requires TestFunction" % self) else: if not isinstance(f, TestFunction): f = TestFunction.from_function(f) else: if f is not None: warnings.warn("TestFunction for %s is redundant and removed" % self, stacklevel=3) else: pass f = TestFunction() f.setup(self.approx) return self.objective_class(self, f) def __str__(self): # pragma: no cover return "%(op)s[%(ap)s]" % dict( op=self.__class__.__name__, ap=self.approx.__class__.__name__ ) def collect_shared_to_list(params): """Helper function for getting a list from usable representation of parameters Parameters ---------- params: {dict|None} Returns ------- List """ if isinstance(params, dict): return list( t[1] for t in sorted(params.items(), key=lambda t: t[0]) if isinstance(t[1], aesara.compile.SharedVariable) ) elif params is None: return [] else: raise TypeError("Unknown type %s for %r, need dict or None") class TestFunction: def __init__(self): self._inited = False self.shared_params = None @property def params(self): return collect_shared_to_list(self.shared_params) def __call__(self, z): raise NotImplementedError def setup(self, approx): pass @classmethod def from_function(cls, f): if not callable(f): raise ParametrizationError("Need callable, got %r" % f) obj = TestFunction() obj.__call__ = f return obj class Group(WithMemoization): R"""**Base class for grouping variables in VI** Grouped Approximation is used for modelling mutual dependencies for a specified group of variables. Base for local and global group. Parameters ---------- group: list List of PyMC3 variables or None indicating that group takes all the rest variables vfam: str String that marks the corresponding variational family for the group. Cannot be passed both with params params: dict Dict with variational family parameters, full description can be found below. Cannot be passed both with vfam random_seed: int Random seed for underlying random generator model : PyMC3 Model local: bool Indicates whether this group is local. Cannot be passed without params. Such group should have only one variable rowwise: bool Indicates whether this group is independently parametrized over first dim. Such group should have only one variable options: dict Special options for the group kwargs: Other kwargs for the group Notes ----- Group instance/class has some important constants: - **supports_batched** Determines whether such variational family can be used for AEVB or rowwise approx. AEVB approx is such approx that somehow depends on input data. It can be treated as conditional distribution. You can see more about in the corresponding paper mentioned in references. Rowwise mode is a special case approximation that treats every 'row', of a tensor as independent from each other. Some distributions can't do that by definition e.g. :class:Empirical that consists of particles only. - **has_logq** Tells that distribution is defined explicitly These constants help providing the correct inference method for given parametrization Examples -------- **Basic Initialization** :class:Group is a factory class. You do not need to call every ApproximationGroup explicitly. Passing the correct vfam (Variational FAMily) argument you'll tell what parametrization is desired for the group. This helps not to overload code with lots of classes. .. code:: python >>> group = Group([latent1, latent2], vfam='mean_field') The other way to select approximation is to provide params dictionary that has some predefined well shaped parameters. Keys of the dict serve as an identifier for variational family and help to autoselect the correct group class. To identify what approximation to use, params dict should have the full set of needed parameters. As there are 2 ways to instantiate the :class:Group passing both vfam and params is prohibited. Partial parametrization is prohibited by design to avoid corner cases and possible problems. .. code:: python >>> group = Group([latent3], params=dict(mu=my_mu, rho=my_rho)) Important to note that in case you pass custom params they will not be autocollected by optimizer, you'll have to provide them with more_obj_params keyword. **Supported dict keys:** - {'mu', 'rho'}: :class:MeanFieldGroup - {'mu', 'L_tril'}: :class:FullRankGroup - {'histogram'}: :class:EmpiricalGroup - {0, 1, 2, 3, ..., k-1}: :class:NormalizingFlowGroup of depth k NormalizingFlows have other parameters than ordinary groups and should be passed as nested dicts with the following keys: - {'u', 'w', 'b'}: :class:PlanarFlow - {'a', 'b', 'z_ref'}: :class:RadialFlow - {'loc'}: :class:LocFlow - {'rho'}: :class:ScaleFlow - {'v'}: :class:HouseholderFlow Note that all integer keys should be present in the dictionary. An example of NormalizingFlow initialization can be found below. **Using AEVB** Autoencoding variational Bayes is a powerful tool to get conditional :math:q(\lambda|X) distribution on latent variables. It is well supported by PyMC3 and all you need is to provide a dictionary with well shaped variational parameters, the correct approximation will be autoselected as mentioned in section above. However we have some implementation restrictions in AEVB. They require autoencoded variable to have first dimension as *batch* dimension and other dimensions should stay fixed. With this assumptions it is possible to generalize all variational approximation families as batched approximations that have flexible parameters and leading axis. Only single variable local group is supported. Params are required. >>> # for mean field >>> group = Group([latent3], params=dict(mu=my_mu, rho=my_rho), local=True) >>> # or for full rank >>> group = Group([latent3], params=dict(mu=my_mu, L_tril=my_L_tril), local=True) - An Approximation class is selected automatically based on the keys in dict. - my_mu and my_rho are usually estimated with neural network or function approximator. **Using Row-Wise Group** Batch groups have independent row wise approximations, thus using batched mean field will give no effect. It is more interesting if you want each row of a matrix to be parametrized independently with normalizing flow or full rank gaussian. To tell :class:Group that group is batched you need set batched kwarg as True. Only single variable group is allowed due to implementation details. >>> group = Group([latent3], vfam='fr', rowwise=True) # 'fr' is alias for 'full_rank' The resulting approximation for this variable will have the following structure .. math:: latent3_{i, \dots} \sim \mathcal{N}(\mu_i, \Sigma_i) \forall i **Note**: Using rowwise and user-parametrized approximation is ok, but shape should be checked beforehand, it is impossible to infer it by PyMC3 **Normalizing Flow Group** In case you use simple initialization pattern using vfam you'll not meet any changes. Passing flow formula to vfam you'll get correct flow parametrization for group .. code:: python >>> group = Group([latent3], vfam='scale-hh*5-radial*4-loc') **Note**: Consider passing location flow as the last one and scale as the first one for stable inference. Rowwise normalizing flow is supported as well .. code:: python >>> group = Group([latent3], vfam='scale-hh*2-radial-loc', rowwise=True) Custom parameters for normalizing flow can be a real trouble for the first time. They have quite different format from the rest variational families. .. code:: python >>> # int is used as key, it also tells the flow position ... flow_params = { ... # rho parametrizes scale flow, softplus is used to map (-inf; inf) -> (0, inf) ... 0: dict(rho=my_scale), ... 1: dict(v=my_v1), # Householder Flow, v is parameter name from the original paper ... 2: dict(v=my_v2), # do not miss any number in dict, or else error is raised ... 3: dict(a=my_a, b=my_b, z_ref=my_z_ref), # Radial flow ... 4: dict(loc=my_loc) # Location Flow ... } ... group = Group([latent3], params=flow_params) ... # local=True can be added in case you do AEVB inference ... group = Group([latent3], params=flow_params, local=True) **Delayed Initialization** When you have a lot of latent variables it is impractical to do it all manually. To make life much simpler, You can pass None instead of list of variables. That case you'll not create shared parameters until you pass all collected groups to Approximation object that collects all the groups together and checks that every group is correctly initialized. For those groups which have group equal to None it will collect all the rest variables not covered by other groups and perform delayed init. .. code:: python >>> group_1 = Group([latent1], vfam='fr') # latent1 has full rank approximation >>> group_other = Group(None, vfam='mf') # other variables have mean field Q >>> approx = Approximation([group_1, group_other]) **Summing Up** When you have created all the groups they need to pass all the groups to :class:Approximation. It does not accept any other parameter rather than groups .. code:: python >>> approx = Approximation(my_groups) See Also -------- :class:Approximation References ---------- - Kingma, D. P., & Welling, M. (2014). Auto-Encoding Variational Bayes. stat, 1050, 1. _ """ # needs to be defined in init shared_params = None symbolic_initial = None replacements = None input = None # defined by approximation supports_batched = True has_logq = True # some important defaults initial_dist_name = "normal" initial_dist_map = 0.0 # for handy access using class methods __param_spec__ = dict() short_name = "" alias_names = frozenset() __param_registry = dict() __name_registry = dict() @classmethod def register(cls, sbcls): assert ( frozenset(sbcls.__param_spec__) not in cls.__param_registry ), "Duplicate __param_spec__" cls.__param_registry[frozenset(sbcls.__param_spec__)] = sbcls assert sbcls.short_name not in cls.__name_registry, "Duplicate short_name" cls.__name_registry[sbcls.short_name] = sbcls for alias in sbcls.alias_names: assert alias not in cls.__name_registry, "Duplicate alias_name" cls.__name_registry[alias] = sbcls return sbcls @classmethod def group_for_params(cls, params): if pm.variational.flows.seems_like_flow_params(params): return pm.variational.approximations.NormalizingFlowGroup if frozenset(params) not in cls.__param_registry: raise KeyError( "No such group for the following params: {!r}, " "only the following are supported\n\n{}".format(params, cls.__param_registry) ) return cls.__param_registry[frozenset(params)] @classmethod def group_for_short_name(cls, name): if pm.variational.flows.seems_like_formula(name): return pm.variational.approximations.NormalizingFlowGroup if name.lower() not in cls.__name_registry: raise KeyError( "No such group: {!r}, " "only the following are supported\n\n{}".format(name, cls.__name_registry) ) return cls.__name_registry[name.lower()] def __new__(cls, group=None, vfam=None, params=None, *args, **kwargs): if cls is Group: if vfam is not None and params is not None: raise TypeError("Cannot call Group with both vfam and params provided") elif vfam is not None: return super().__new__(cls.group_for_short_name(vfam)) elif params is not None: return super().__new__(cls.group_for_params(params)) else: raise TypeError("Need to call Group with either vfam or params provided") else: return super().__new__(cls) def __init__( self, group, vfam=None, params=None, random_seed=None, model=None, local=False, rowwise=False, options=None, **kwargs, ): if local and not self.supports_batched: raise LocalGroupError("%s does not support local groups" % self.__class__) if local and rowwise: raise LocalGroupError("%s does not support local grouping in rowwise mode") if isinstance(vfam, str): vfam = vfam.lower() if options is None: options = dict() self.options = options self._vfam = vfam self._local = local self._batched = rowwise self._rng = at_rng(random_seed) model = modelcontext(model) self.model = model self.group = group self.user_params = params self._user_params = None # save this stuff to use in __init_group__ later self._kwargs = kwargs if self.group is not None: # init can be delayed self.__init_group__(self.group) @classmethod def get_param_spec_for(cls, **kwargs): res = dict() for name, fshape in cls.__param_spec__.items(): res[name] = tuple(eval(s, kwargs) for s in fshape) return res def _check_user_params(self, **kwargs): R"""*Dev* - checks user params, allocates them if they are correct, returns True. If they are not present, returns False Parameters ---------- kwargs: special kwargs needed sometimes Returns ------- bool indicating whether to allocate new shared params """ user_params = self.user_params if user_params is None: return False if not isinstance(user_params, dict): raise TypeError("params should be a dict") givens = set(user_params.keys()) needed = set(self.__param_spec__) if givens != needed: raise ParametrizationError( "Passed parameters do not have a needed set of keys, " "they should be equal, got {givens}, needed {needed}".format( givens=givens, needed=needed ) ) self._user_params = dict() spec = self.get_param_spec_for(d=self.ddim, **kwargs.pop("spec_kw", {})) for name, param in self.user_params.items(): shape = spec[name] if self.local: shape = (-1,) + shape elif self.batched: shape = (self.bdim,) + shape self._user_params[name] = at.as_tensor(param).reshape(shape) return True def _initial_type(self, name): R"""*Dev* - initial type with given name. The correct type depends on self.batched Parameters ---------- name: str name for tensor Returns ------- tensor """ if self.batched: return at.tensor3(name) else: return at.matrix(name) def _input_type(self, name): R"""*Dev* - input type with given name. The correct type depends on self.batched Parameters ---------- name: str name for tensor Returns ------- tensor """ if self.batched: return at.matrix(name) else: return at.vector(name) @aesara.config.change_flags(compute_test_value="off") def __init_group__(self, group): if not group: raise GroupError("Got empty group") if self.group is None: # delayed init self.group = group if self.batched and len(group) > 1: if self.local: # better error message raise LocalGroupError("Local groups with more than 1 variable are not supported") else: raise BatchedGroupError( "Batched groups with more than 1 variable are not supported" ) self.symbolic_initial = self._initial_type( self.__class__.__name__ + "_symbolic_initial_tensor" ) self.input = self._input_type(self.__class__.__name__ + "_symbolic_input") # I do some staff that is not supported by standard __init__ # so I have to to it by myself self.ordering = ArrayOrdering([]) self.replacements = dict() self.group = [get_transformed(var) for var in self.group] for var in self.group: if isinstance(var.distribution, pm.Discrete): raise ParametrizationError(f"Discrete variables are not supported by VI: {var}") begin = self.ddim if self.batched: if var.ndim < 1: if self.local: raise LocalGroupError("Local variable should not be scalar") else: raise BatchedGroupError("Batched variable should not be scalar") self.ordering.size += (np.prod(var.dshape[1:])).astype(int) if self.local: shape = (-1,) + var.dshape[1:] else: shape = var.dshape else: self.ordering.size += var.dsize shape = var.dshape end = self.ordering.size vmap = VarMap(var.name, slice(begin, end), shape, var.dtype) self.ordering.vmap.append(vmap) self.ordering.by_name[vmap.var] = vmap vr = self.input[..., vmap.slc].reshape(shape).astype(vmap.dtyp) vr.name = vmap.var + "_vi_replacement" self.replacements[var] = vr self.bij = DictToArrayBijection(self.ordering, {}) def _finalize_init(self): """*Dev* - clean up after init""" del self._kwargs local = property(lambda self: self._local) batched = property(lambda self: self._local or self._batched) @property def params_dict(self): # prefixed are correctly reshaped if self._user_params is not None: return self._user_params else: return self.shared_params @property def params(self): # raw user params possibly not reshaped if self.user_params is not None: return collect_shared_to_list(self.user_params) else: return collect_shared_to_list(self.shared_params) def _new_initial_shape(self, size, dim, more_replacements=None): """*Dev* - correctly proceeds sampling with variable batch size Parameters ---------- size: scalar sample size dim: scalar latent fixed dim more_replacements: dict replacements for latent batch shape Returns ------- shape vector """ if self.batched: bdim = at.as_tensor(self.bdim) bdim = aesara.clone_replace(bdim, more_replacements) return at.stack([size, bdim, dim]) else: return at.stack([size, dim]) @node_property def bdim(self): if not self.local: if self.batched: return self.ordering.vmap[0].shp[0] else: return 1 else: return next(iter(self.params_dict.values())).shape[0] @node_property def ndim(self): return self.ordering.size * self.bdim @property def ddim(self): return self.ordering.size def _new_initial(self, size, deterministic, more_replacements=None): """*Dev* - allocates new initial random generator Parameters ---------- size: scalar sample size deterministic: bool or scalar whether to sample in deterministic manner more_replacements: dict more replacements passed to shape Notes ----- Suppose you have a AEVB setup that: - input X is purely symbolic, and X.shape[0] is needed to initial second dim - to perform inference, X is replaced with data tensor, however, since X.shape[0] in initial remains symbolic and can't be replaced, you get MissingInputError - as a solution, here we perform a manual replacement for the second dim in initial. Returns ------- tensor """ if size is None: size = 1 if not isinstance(deterministic, Variable): deterministic = np.int8(deterministic) dim, dist_name, dist_map = (self.ddim, self.initial_dist_name, self.initial_dist_map) dtype = self.symbolic_initial.dtype dim = at.as_tensor(dim) size = at.as_tensor(size) shape = self._new_initial_shape(size, dim, more_replacements) # apply optimizations if possible if not isinstance(deterministic, Variable): if deterministic: return at.ones(shape, dtype) * dist_map else: return getattr(self._rng, dist_name)(size=shape) else: sample = getattr(self._rng, dist_name)(size=shape) initial = at.switch(deterministic, at.ones(shape, dtype) * dist_map, sample) return initial @node_property def symbolic_random(self): """*Dev* - abstract node that takes self.symbolic_initial and creates approximate posterior that is parametrized with self.params_dict. Implementation should take in account self.batched. If self.batched is True, then self.symbolic_initial is 3d tensor, else 2d Returns ------- tensor """ raise NotImplementedError @node_property def symbolic_random2d(self): """*Dev* - self.symbolic_random flattened to matrix""" if self.batched: return self.symbolic_random.flatten(2) else: return self.symbolic_random @aesara.config.change_flags(compute_test_value="off") def set_size_and_deterministic(self, node, s, d, more_replacements=None): """*Dev* - after node is sampled via :func:symbolic_sample_over_posterior or :func:symbolic_single_sample new random generator can be allocated and applied to node Parameters ---------- node: :class:Variable Aesara node with symbolically applied VI replacements s: scalar desired number of samples d: bool or int whether sampling is done deterministically more_replacements: dict more replacements to apply Returns ------- :class:Variable with applied replacements, ready to use """ flat2rand = self.make_size_and_deterministic_replacements(s, d, more_replacements) node_out = aesara.clone_replace(node, flat2rand) try_to_set_test_value(node, node_out, s) return node_out def to_flat_input(self, node): """*Dev* - replace vars with flattened view stored in self.inputs""" return aesara.clone_replace(node, self.replacements) def symbolic_sample_over_posterior(self, node): """*Dev* - performs sampling of node applying independent samples from posterior each time. Note that it is done symbolically and this node needs :func:set_size_and_deterministic call """ node = self.to_flat_input(node) random = self.symbolic_random.astype(self.symbolic_initial.dtype) random = at.patternbroadcast(random, self.symbolic_initial.broadcastable) def sample(post): return aesara.clone_replace(node, {self.input: post}) nodes, _ = aesara.scan(sample, random) return nodes def symbolic_single_sample(self, node): """*Dev* - performs sampling of node applying single sample from posterior. Note that it is done symbolically and this node needs :func:set_size_and_deterministic call with size=1 """ node = self.to_flat_input(node) random = self.symbolic_random.astype(self.symbolic_initial.dtype) random = at.patternbroadcast(random, self.symbolic_initial.broadcastable) return aesara.clone_replace(node, {self.input: random[0]}) def make_size_and_deterministic_replacements(self, s, d, more_replacements=None): """*Dev* - creates correct replacements for initial depending on sample size and deterministic flag Parameters ---------- s: scalar sample size d: bool or scalar whether sampling is done deterministically more_replacements: dict replacements for shape and initial Returns ------- dict with replacements for initial """ initial = self._new_initial(s, d, more_replacements) initial = at.patternbroadcast(initial, self.symbolic_initial.broadcastable) if more_replacements: initial = aesara.clone_replace(initial, more_replacements) return {self.symbolic_initial: initial} @node_property def symbolic_normalizing_constant(self): """*Dev* - normalizing constant for self.logq, scales it to minibatch_size instead of total_size""" t = self.to_flat_input(at.max([v.scaling for v in self.group])) t = self.symbolic_single_sample(t) return pm.floatX(t) @node_property def symbolic_logq_not_scaled(self): """*Dev* - symbolically computed logq for self.symbolic_random computations can be more efficient since all is known beforehand including self.symbolic_random """ raise NotImplementedError # shape (s,) @node_property def symbolic_logq(self): """*Dev* - correctly scaled self.symbolic_logq_not_scaled""" if self.local: s = self.group[0].scaling s = self.to_flat_input(s) s = self.symbolic_single_sample(s) return self.symbolic_logq_not_scaled * s else: return self.symbolic_logq_not_scaled @node_property def logq(self): """*Dev* - Monte Carlo estimate for group logQ""" return self.symbolic_logq.mean(0) @node_property def logq_norm(self): """*Dev* - Monte Carlo estimate for group logQ normalized""" return self.logq / self.symbolic_normalizing_constant def __str__(self): if self.group is None: shp = "undefined" else: shp = str(self.ddim) if self.local: shp = "None, " + shp elif self.batched: shp = str(self.bdim) + ", " + shp return f"{self.__class__.__name__}[{shp}]" @node_property def std(self): raise NotImplementedError @node_property def cov(self): raise NotImplementedError @node_property def mean(self): raise NotImplementedError group_for_params = Group.group_for_params group_for_short_name = Group.group_for_short_name class Approximation(WithMemoization): """**Wrapper for grouped approximations** Wraps list of groups, creates an Approximation instance that collects sampled variables from all the groups, also collects logQ needed for explicit Variational Inference. Parameters ---------- groups: list[Group] List of :class:Group instances. They should have all model variables model: Model Notes ----- Some shortcuts for single group approximations are available: - :class:MeanField - :class:FullRank - :class:NormalizingFlow - :class:Empirical Single group accepts local_rv keyword with dict mapping PyMC3 variables to their local Group parameters dict See Also -------- :class:Group """ def __init__(self, groups, model=None): self._scale_cost_to_minibatch = aesara.shared(np.int8(1)) model = modelcontext(model) if not model.free_RVs: raise TypeError("Model does not have FreeRVs") self.groups = list() seen = set() rest = None for g in groups: if g.group is None: if rest is not None: raise GroupError("More than one group is specified for " "the rest variables") else: rest = g else: if set(g.group) & seen: raise GroupError("Found duplicates in groups") seen.update(g.group) self.groups.append(g) if set(model.free_RVs) - seen: if rest is None: raise GroupError("No approximation is specified for the rest variables") else: rest.__init_group__(list(set(model.free_RVs) - seen)) self.groups.append(rest) self.model = model @property def has_logq(self): return all(self.collect("has_logq")) def collect(self, item, part="total"): if part == "total": return [getattr(g, item) for g in self.groups] elif part == "local": return [getattr(g, item) for g in self.groups if g.local] elif part == "global": return [getattr(g, item) for g in self.groups if not g.local] elif part == "batched": return [getattr(g, item) for g in self.groups if g.batched] else: raise ValueError("unknown part %s, expected {'local', 'global', 'total', 'batched'}") inputs = property(lambda self: self.collect("input")) symbolic_randoms = property(lambda self: self.collect("symbolic_random")) @property def scale_cost_to_minibatch(self): """*Dev* - Property to control scaling cost to minibatch""" return bool(self._scale_cost_to_minibatch.get_value()) @scale_cost_to_minibatch.setter def scale_cost_to_minibatch(self, value): self._scale_cost_to_minibatch.set_value(np.int8(bool(value))) @node_property def symbolic_normalizing_constant(self): """*Dev* - normalizing constant for self.logq, scales it to minibatch_size instead of total_size. Here the effect is controlled by self.scale_cost_to_minibatch """ t = at.max( self.collect("symbolic_normalizing_constant") + [var.scaling for var in self.model.observed_RVs] ) t = at.switch(self._scale_cost_to_minibatch, t, at.constant(1, dtype=t.dtype)) return pm.floatX(t) @node_property def symbolic_logq(self): """*Dev* - collects symbolic_logq for all groups""" return at.add(*self.collect("symbolic_logq")) @node_property def logq(self): """*Dev* - collects logQ for all groups""" return at.add(*self.collect("logq")) @node_property def logq_norm(self): """*Dev* - collects logQ for all groups and normalizes it""" return self.logq / self.symbolic_normalizing_constant @node_property def _sized_symbolic_varlogp_and_datalogp(self): """*Dev* - computes sampled prior term from model via aesara.scan""" varlogp_s, datalogp_s = self.symbolic_sample_over_posterior( [self.model.varlogpt, self.model.datalogpt] ) return varlogp_s, datalogp_s # both shape (s,) @node_property def sized_symbolic_varlogp(self): """*Dev* - computes sampled prior term from model via aesara.scan""" return self._sized_symbolic_varlogp_and_datalogp[0] # shape (s,) @node_property def sized_symbolic_datalogp(self): """*Dev* - computes sampled data term from model via aesara.scan""" return self._sized_symbolic_varlogp_and_datalogp[1] # shape (s,) @node_property def sized_symbolic_logp(self): """*Dev* - computes sampled logP from model via aesara.scan""" return self.sized_symbolic_varlogp + self.sized_symbolic_datalogp # shape (s,) @node_property def logp(self): """*Dev* - computes :math:E_{q}(logP) from model via aesara.scan that can be optimized later""" return self.varlogp + self.datalogp @node_property def varlogp(self): """*Dev* - computes :math:E_{q}(prior term) from model via aesara.scan that can be optimized later""" return self.sized_symbolic_varlogp.mean(0) @node_property def datalogp(self): """*Dev* - computes :math:E_{q}(data term) from model via aesara.scan that can be optimized later""" return self.sized_symbolic_datalogp.mean(0) @node_property def _single_symbolic_varlogp_and_datalogp(self): """*Dev* - computes sampled prior term from model via aesara.scan""" varlogp, datalogp = self.symbolic_single_sample([self.model.varlogpt, self.model.datalogpt]) return varlogp, datalogp @node_property def single_symbolic_varlogp(self): """*Dev* - for single MC sample estimate of :math:E_{q}(prior term) aesara.scan is not needed and code can be optimized""" return self._single_symbolic_varlogp_and_datalogp[0] @node_property def single_symbolic_datalogp(self): """*Dev* - for single MC sample estimate of :math:E_{q}(data term) aesara.scan is not needed and code can be optimized""" return self._single_symbolic_varlogp_and_datalogp[1] @node_property def single_symbolic_logp(self): """*Dev* - for single MC sample estimate of :math:E_{q}(logP) aesara.scan is not needed and code can be optimized""" return self.single_symbolic_datalogp + self.single_symbolic_varlogp @node_property def logp_norm(self): """*Dev* - normalized :math:E_{q}(logP)""" return self.logp / self.symbolic_normalizing_constant @node_property def varlogp_norm(self): """*Dev* - normalized :math:E_{q}(prior term)""" return self.varlogp / self.symbolic_normalizing_constant @node_property def datalogp_norm(self): """*Dev* - normalized :math:E_{q}(data term)""" return self.datalogp / self.symbolic_normalizing_constant @property def replacements(self): """*Dev* - all replacements from groups to replace PyMC random variables with approximation""" return collections.OrderedDict( itertools.chain.from_iterable(g.replacements.items() for g in self.groups) ) def make_size_and_deterministic_replacements(self, s, d, more_replacements=None): """*Dev* - creates correct replacements for initial depending on sample size and deterministic flag Parameters ---------- s: scalar sample size d: bool whether sampling is done deterministically more_replacements: dict replacements for shape and initial Returns ------- dict with replacements for initial """ if more_replacements is None: more_replacements = {} flat2rand = collections.OrderedDict() for g in self.groups: flat2rand.update(g.make_size_and_deterministic_replacements(s, d, more_replacements)) flat2rand.update(more_replacements) return flat2rand @aesara.config.change_flags(compute_test_value="off") def set_size_and_deterministic(self, node, s, d, more_replacements=None): """*Dev* - after node is sampled via :func:symbolic_sample_over_posterior or :func:symbolic_single_sample new random generator can be allocated and applied to node Parameters ---------- node: :class:Variable Aesara node with symbolically applied VI replacements s: scalar desired number of samples d: bool or int whether sampling is done deterministically more_replacements: dict more replacements to apply Returns ------- :class:Variable with applied replacements, ready to use """ _node = node optimizations = self.get_optimization_replacements(s, d) flat2rand = self.make_size_and_deterministic_replacements(s, d, more_replacements) node = aesara.clone_replace(node, optimizations) node = aesara.clone_replace(node, flat2rand) try_to_set_test_value(_node, node, s) return node def to_flat_input(self, node): """*Dev* - replace vars with flattened view stored in self.inputs""" return aesara.clone_replace(node, self.replacements) def symbolic_sample_over_posterior(self, node): """*Dev* - performs sampling of node applying independent samples from posterior each time. Note that it is done symbolically and this node needs :func:set_size_and_deterministic call """ node = self.to_flat_input(node) def sample(*post): return aesara.clone_replace(node, dict(zip(self.inputs, post))) nodes, _ = aesara.scan(sample, self.symbolic_randoms) return nodes def symbolic_single_sample(self, node): """*Dev* - performs sampling of node applying single sample from posterior. Note that it is done symbolically and this node needs :func:set_size_and_deterministic call with size=1 """ node = self.to_flat_input(node) post = [v[0] for v in self.symbolic_randoms] inp = self.inputs return aesara.clone_replace(node, dict(zip(inp, post))) def get_optimization_replacements(self, s, d): """*Dev* - optimizations for logP. If sample size is static and equal to 1: then aesara.scan MC estimate is replaced with single sample without call to aesara.scan. """ repl = collections.OrderedDict() # avoid scan if size is constant and equal to one if isinstance(s, int) and (s == 1) or s is None: repl[self.varlogp] = self.single_symbolic_varlogp repl[self.datalogp] = self.single_symbolic_datalogp return repl @aesara.config.change_flags(compute_test_value="off") def sample_node(self, node, size=None, deterministic=False, more_replacements=None): """Samples given node or nodes over shared posterior Parameters ---------- node: Aesara Variables (or Aesara expressions) size: None or scalar number of samples more_replacements: dict add custom replacements to graph, e.g. change input source deterministic: bool whether to use zeros as initial distribution if True - zero initial point will produce constant latent variables Returns ------- sampled node(s) with replacements """ node_in = node node = aesara.clone_replace(node, more_replacements) if size is None: node_out = self.symbolic_single_sample(node) else: node_out = self.symbolic_sample_over_posterior(node) node_out = self.set_size_and_deterministic(node_out, size, deterministic, more_replacements) try_to_set_test_value(node_in, node_out, size) return node_out def rslice(self, name): """*Dev* - vectorized sampling for named random variable without call to aesara.scan. This node still needs :func:set_size_and_deterministic to be evaluated """ def vars_names(vs): return {v.name for v in vs} for vars_, random, ordering in zip( self.collect("group"), self.symbolic_randoms, self.collect("ordering") ): if name in vars_names(vars_): name_, slc, shape, dtype = ordering[name] found = random[..., slc].reshape((random.shape[0],) + shape).astype(dtype) found.name = name + "_vi_random_slice" break else: raise KeyError("%r not found" % name) return found @node_property def sample_dict_fn(self): s = at.iscalar() names = [v.name for v in self.model.free_RVs] sampled = [self.rslice(name) for name in names] sampled = self.set_size_and_deterministic(sampled, s, 0) sample_fn = aesara.function([s], sampled) def inner(draws=100): _samples = sample_fn(draws) return {v_.name: s_ for v_, s_ in zip(self.model.free_RVs, _samples)} return inner def sample(self, draws=500, include_transformed=True): """Draw samples from variational posterior. Parameters ---------- draws: int Number of random samples. include_transformed: bool If True, transformed variables are also sampled. Default is False. Returns ------- trace: :class:pymc3.backends.base.MultiTrace Samples drawn from variational posterior. """ vars_sampled = get_default_varnames( self.model.unobserved_RVs, include_transformed=include_transformed ) samples = self.sample_dict_fn(draws) # type: dict points = ({name: records[i] for name, records in samples.items()} for i in range(draws)) trace = NDArray( model=self.model, vars=vars_sampled, test_point={name: records[0] for name, records in samples.items()}, ) try: trace.setup(draws=draws, chain=0) for point in points: trace.record(point) finally: trace.close() return pm.sampling.MultiTrace([trace]) @property def ndim(self): return sum(self.collect("ndim")) @property def ddim(self): return sum(self.collect("ddim")) @property def has_local(self): return any(self.collect("local")) @property def has_global(self): return any(not c for c in self.collect("local")) @property def has_batched(self): return any(not c for c in self.collect("batched")) @node_property def symbolic_random(self): return at.concatenate(self.collect("symbolic_random2d"), axis=-1) def __str__(self): if len(self.groups) < 5: return "Approximation{" + " & ".join(map(str, self.groups)) + "}" else: forprint = self.groups[:2] + ["..."] + self.groups[-2:] return "Approximation{" + " & ".join(map(str, forprint)) + "}" @property def all_histograms(self): return all(isinstance(g, pm.approximations.EmpiricalGroup) for g in self.groups) @property def any_histograms(self): return any(isinstance(g, pm.approximations.EmpiricalGroup) for g in self.groups) @node_property def joint_histogram(self): if not self.all_histograms: raise VariationalInferenceError("%s does not consist of all Empirical approximations") return at.concatenate(self.collect("histogram"), axis=-1) @property def params(self): return sum(self.collect("params"), [])