Reparameterizers¶
The pyro.infer.reparam
module contains reparameterization strategies for
the pyro.poutine.handlers.reparam()
effect. These are useful for altering
geometry of a poorlyconditioned parameter space to make the posterior better
shaped. These can be used with a variety of inference algorithms, e.g.
Auto*Normal
guides and MCMC.

class
Reparam
[source]¶ Base class for reparameterizers.

__call__
(name, fn, obs)[source]¶ Parameters:  name (str) – A sample site name.
 fn (TorchDistribution) – A distribution.
 obs (Tensor) – Observed value or None.
Returns: A pair (
new_fn
,value
).

Conjugate Updating¶

class
ConjugateReparam
(guide)[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
EXPERIMENTAL Reparameterize to a conjugate updated distribution.
This updates a prior distribution
fn
using theconjugate_update()
method. The guide may be either a distribution object or a callable inputting model*args,**kwargs
and returning a distribution object. The guide may be approximate or learned.For example consider the model and naive variational guide:
total = torch.tensor(10.) count = torch.tensor(2.) def model(): prob = pyro.sample("prob", dist.Beta(0.5, 1.5)) pyro.sample("count", dist.Binomial(total, prob), obs=count) guide = AutoDiagonalNormal(model) # learns the posterior over prob
Instead of using this learned guide, we can handcompute the conjugate posterior distribution over “prob”, and then use a simpler guide during inference, in this case an empty guide:
reparam_model = poutine.reparam(model, { "prob": ConjugateReparam(dist.Beta(1 + count, 1 + total  count)) }) def reparam_guide(): pass # nothing remains to be modeled!
Parameters: guide (Distribution or callable) – A likelihood distribution or a callable returning a guide distribution. Only a few distributions are supported, depending on the prior distribution’s conjugate_update()
implementation.
LocScale Decentering¶

class
LocScaleReparam
(centered=None, shape_params=())[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Generic decentering reparameterizer [1] for latent variables parameterized by
loc
andscale
(and possibly additionalshape_params
).This reparameterization works only for latent variables, not likelihoods.
 [1] Maria I. Gorinova, Dave Moore, Matthew D. Hoffman (2019)
 “Automatic Reparameterisation of Probabilistic Programs” https://arxiv.org/pdf/1906.03028.pdf
Parameters:  centered (float) – optional centered parameter. If None (default) learn
a persite perelement centering parameter in
[0,1]
. If 0, fully decenter the distribution; if 1, preserve the centered distribution unchanged.  shape_params (tuple or list) – list of additional parameter names to copy unchanged from the centered to decentered distribution.
Transformed Distributions¶

class
TransformReparam
[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Reparameterizer for
pyro.distributions.torch.TransformedDistribution
latent variables.This is useful for transformed distributions with complex, geometrychanging transforms, where the posterior has simple shape in the space of
base_dist
.This reparameterization works only for latent variables, not likelihoods.
Discrete Cosine Transform¶

class
DiscreteCosineReparam
(dim=1, smooth=0.0, *, experimental_allow_batch=False)[source]¶ Bases:
pyro.infer.reparam.unit_jacobian.UnitJacobianReparam
Discrete Cosine reparameterizer, using a
DiscreteCosineTransform
.This is useful for sequential models where coupling along a timelike axis (e.g. a banded precision matrix) introduces longrange correlation. This reparameterizes to a frequencydomain representation where posterior covariance should be closer to diagonal, thereby improving the accuracy of diagonal guides in SVI and improving the effectiveness of a diagonal mass matrix in HMC.
When reparameterizing variables that are approximately continuous along the time dimension, set
smooth=1
. For variables that are approximately continuously differentiable along the time axis, setsmooth=2
.This reparameterization works only for latent variables, not likelihoods.
Parameters:  dim (int) – Dimension along which to transform. Must be negative. This is an absolute dim counting from the right.
 smooth (float) – Smoothing parameter. When 0, this transforms white noise to white noise; when 1 this transforms Brownian noise to to white noise; when 1 this transforms violet noise to white noise; etc. Any real number is allowed. https://en.wikipedia.org/wiki/Colors_of_noise.
Haar Transform¶

class
HaarReparam
(dim=1, flip=False, *, experimental_allow_batch=False)[source]¶ Bases:
pyro.infer.reparam.unit_jacobian.UnitJacobianReparam
Haar wavelet reparameterizer, using a
HaarTransform
.This is useful for sequential models where coupling along a timelike axis (e.g. a banded precision matrix) introduces longrange correlation. This reparameterizes to a frequencydomain representation where posterior covariance should be closer to diagonal, thereby improving the accuracy of diagonal guides in SVI and improving the effectiveness of a diagonal mass matrix in HMC.
This reparameterization works only for latent variables, not likelihoods.
Parameters:
Unit Jacobian Transforms¶

class
UnitJacobianReparam
(transform, suffix='transformed', *, experimental_allow_batch=False)[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Reparameterizer for
Transform
objects whose Jacobian determinant is one.Parameters:
StudentT Distributions¶

class
StudentTReparam
[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Auxiliary variable reparameterizer for
StudentT
random variables.This is useful in combination with
LinearHMMReparam
because it allows StudentT processes to be treated as conditionally Gaussian processes, permitting cheap inference viaGaussianHMM
.This reparameterizes a
StudentT
by introducing an auxiliaryGamma
variable conditioned on which the result isNormal
.
Stable Distributions¶

class
LatentStableReparam
[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Auxiliary variable reparameterizer for
Stable
latent variables.This is useful in inference of latent
Stable
variables because thelog_prob()
is not implemented.This uses the ChambersMallowsStuck method [1], creating a pair of parameterfree auxiliary distributions (
Uniform(pi/2,pi/2)
andExponential(1)
) with welldefined.log_prob()
methods, thereby permitting use of reparameterized stable distributions in likelihoodbased inference algorithms like SVI and MCMC.This reparameterization works only for latent variables, not likelihoods. For likelihoodcompatible reparameterization see
SymmetricStableReparam
orStableReparam
. [1] J.P. Nolan (2017).
 Stable Distributions: Models for Heavy Tailed Data. http://fs2.american.edu/jpnolan/www/stable/chap1.pdf

class
SymmetricStableReparam
[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Auxiliary variable reparameterizer for symmetric
Stable
random variables (i.e. those for whichskew=0
).This is useful in inference of symmetric
Stable
variables because thelog_prob()
is not implemented.This reparameterizes a symmetric
Stable
random variable as a totallyskewed (skew=1
)Stable
scale mixture ofNormal
random variables. See Proposition 3. of [1] (but note we differ sinceStable
uses Nolan’s continuous S0 parameterization). [1] Alvaro Cartea and Sam Howison (2009)
 “Option Pricing with LevyStable Processes” https://pdfs.semanticscholar.org/4d66/c91b136b2a38117dd16c2693679f5341c616.pdf

class
StableReparam
[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Auxiliary variable reparameterizer for arbitrary
Stable
random variables.This is useful in inference of nonsymmetric
Stable
variables because thelog_prob()
is not implemented.This reparameterizes a
Stable
random variable as sum of two other stable random variables, one symmetric and the other totally skewed (applying Property 2.3.a of [1]). The totally skewed variable is sampled as inLatentStableReparam
, and the symmetric variable is decomposed as inSymmetricStableReparam
. [1] V. M. Zolotarev (1986)
 “Onedimensional stable distributions”
Hidden Markov Models¶

class
LinearHMMReparam
(init=None, trans=None, obs=None)[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Auxiliary variable reparameterizer for
LinearHMM
random variables.This defers to component reparameterizers to create auxiliary random variables conditioned on which the process becomes a
GaussianHMM
. If theobservation_dist
is aTransformedDistribution
this reorders those transforms so that the result is aTransformedDistribution
ofGaussianHMM
.This is useful for training the parameters of a
LinearHMM
distribution, whoselog_prob()
method is undefined. To perform inference in the presence of nonGaussian factors such asStable()
,StudentT()
orLogNormal()
, configure withStudentTReparam
,StableReparam
,SymmetricStableReparam
, etc. component reparameterizers forinit
,trans
, andscale
. For example:hmm = LinearHMM( init_dist=Stable(1,0,1,0).expand([2]).to_event(1), trans_matrix=torch.eye(2), trans_dist=MultivariateNormal(torch.zeros(2), torch.eye(2)), obs_matrix=torch.eye(2), obs_dist=TransformedDistribution( Stable(1.5,0.5,1.0).expand([2]).to_event(1), ExpTransform())) rep = LinearHMMReparam(init=SymmetricStableReparam(), obs=StableReparam()) with poutine.reparam(config={"hmm": rep}): pyro.sample("hmm", hmm, obs=data)
Parameters:
Site Splitting¶

class
SplitReparam
(sections, dim)[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Reparameterizer to split a random variable along a dimension, similar to
torch.split()
.This is useful for treating different parts of a tensor with different reparameterizers or inference methods. For example when performing HMC inference on a time series, you can first apply
DiscreteCosineReparam
orHaarReparam
, then applySplitReparam
to split into lowfrequency and highfrequency components, and finally add the lowfrequency components to thefull_mass
matrix together with globals.Parameters:  sections – Size of a single chunk or list of sizes for each chunk.
 dim (int) – Dimension along which to split. Defaults to 1.
Type:
Neural Transport¶

class
NeuTraReparam
(guide)[source]¶ Bases:
pyro.infer.reparam.reparam.Reparam
Neural Transport reparameterizer [1] of multiple latent variables.
This uses a trained
AutoContinuous
guide to alter the geometry of a model, typically for use e.g. in MCMC. Example usage:# Step 1. Train a guide guide = AutoIAFNormal(model) svi = SVI(model, guide, ...) # ...train the guide... # Step 2. Use trained guide in NeuTra MCMC neutra = NeuTraReparam(guide) model = poutine.reparam(model, config=lambda _: neutra) nuts = NUTS(model) # ...now use the model in HMC or NUTS...
This reparameterization works only for latent variables, not likelihoods. Note that all sites must share a single common
NeuTraReparam
instance, and that the model must have static structure. [1] Hoffman, M. et al. (2019)
 “NeuTralizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport” https://arxiv.org/abs/1903.03704
Parameters: guide (AutoContinuous) – A trained guide. 
transform_sample
(latent)[source]¶ Given latent samples from the warped posterior (with a possible batch dimension), return a dict of samples from the latent sites in the model.
Parameters: latent – sample from the warped posterior (possibly batched). Note that the batch dimension must not collide with plate dimensions in the model, i.e. any batch dims d <  max_plate_nesting. Returns: a dict of samples keyed by latent sites in the model. Return type: dict