class_docstr: Sampler for Bayesian regression with a spike-and-slab prior on weights.
  
  This implementation follows the sampler described in section 3.2
  of Scott and Varian, 2013 [1].
  
  ### Model
  
  This sampler assumes the regression model
  
  ```
  y ~ Normal(loc=matvec(design_matrix,  # `X` in [1].
                        weights),       # `beta` in `[1]`.
             scale=observation_noise_scale)  # `sigma_epsilon` in [1].
  ```
  
  where the design matrix has shape `[num_outputs, num_features]`, with a
  conjugate InverseGamma prior on the noise variance (eqn (6) of [1]):
  
  ```
  observation_noise_scale**2 ~ InverseGamma(
    concentration=observation_noise_variance_prior_concentration,
    scale=observation_noise_variance_prior_scale)
  ```
  
  and a spike-and-slab prior on the weights (eqns (5) and (6) of [1]):
  
  ```
  slab_weights ~ MultivariateNormal(
     loc=0.,  # `b` from [1].
     precision=(weights_prior_precision  # `Omega^{-1}` from [1].
                / observation_noise_scale**2))
  nonzeros ~ Bernoulli(probs=nonzero_prior_prob)  # `gamma` from [1].
  weights = slab_weights * nonzeros
  ```
  
  ### Example
  
  Constructing a sampler instance specifies the model priors:
  
  ```python
  sampler = spike_and_slab.SpikeSlabSampler(
    design_matrix=design_matrix,
    observation_noise_variance_prior_concentration=1.,
    observation_noise_variance_prior_scale=1.
    nonzero_prior_prob=0.1)
  ```
  
  The sampler instance itself is stateless, though some internal methods take
  or accept `SpikeSlabSamplerState` tuples representing posterior quantities
  maintained within a sampling pass. The sampler is
  invoked by passing the regression targets (`y`) and the initial sparsity
  pattern (`nonzeros`):
  
  ```
  (observation_noise_variance,
   weights) = sampler.sample_noise_variance_and_weights(
     targets=y, initial_nonzeros=tf.ones([num_features], dtype=tf.bool))
  ```
  
  This implements the stochastic search variable selection (SSVS) algorithm [2],
  sweeping over the features in random order to resample their sparsity
  indicators one by one. It then returns a sample from the joint posterior
  on the regression weights and the observation noise variance, conditioned
  on the resampled sparsity pattern.
  
  #### References
  
  [1] Steven L. Scott and Hal Varian. Predicting the Present with Bayesian
      Structural Time Series. __International Journal of Mathematical Modelling
      and Numerical Optimisation 5.1-2 (2014): 4-23.__
      https://people.ischool.berkeley.edu/~hal/Papers/2013/pred-present-with-bsts.pdf
  
  [2] George, E. I. and McCulloch, R. E. Approaches for Bayesian variable
      selection. __Statistica Sinica 7, 339–374 (1997)__.
class_docstr_tok: ["Sampler","for","Bayesian","regression","with","a","spike-and-slab","prior","on","weights",".","This","implementation","follows","the","sampler","described","in","section","3.2","of","Scott","and","Varian",",","2013","[","1","]",".","#","#","#","Model","This","sampler","assumes","the","regression","model","``","`","y","~","Normal","(","loc=matvec","(","design_matrix",",","#","`","X","`","in","[","1","]",".","weights",")",",","#","`","beta","`","in","`","[","1","]","`",".","scale=observation_noise_scale",")","#","`","sigma_epsilon","`","in","[","1","]",".","``","`","where","the","design","matrix","has","shape","`","[","num_outputs",",","num_features","]","`",",","with","a","conjugate","InverseGamma","prior","on","the","noise","variance","(","eqn","(","6",")","of","[","1","]",")",":","``","`","observation_noise_scale","*","*","2","~","InverseGamma","(","concentration=observation_noise_variance_prior_concentration",",","scale=observation_noise_variance_prior_scale",")","``","`","and","a","spike-and-slab","prior","on","the","weights","(","eqns","(","5",")","and","(","6",")","of","[","1","]",")",":","``","`","slab_weights","~","MultivariateNormal","(","loc=0.",",","#","`","b","`","from","[","1","]",".","precision=","(","weights_prior_precision","#","`","Omega^","{","-1","}","`","from","[","1","]",".","\/","observation_noise_scale","*","*","2",")",")","nonzeros","~","Bernoulli","(","probs=nonzero_prior_prob",")","#","`","gamma","`","from","[","1","]",".","weights","=","slab_weights","*","nonzeros","``","`","#","#","#","Example","Constructing","a","sampler","instance","specifies","the","model","priors",":","``","`","python","sampler","=","spike_and_slab.SpikeSlabSampler","(","design_matrix=design_matrix",",","observation_noise_variance_prior_concentration=1.",",","observation_noise_variance_prior_scale=1",".","nonzero_prior_prob=0.1",")","``","`","The","sampler","instance","itself","is","stateless",",","though","some","internal","methods","take","or","accept","`","SpikeSlabSamplerState","`","tuples","representing","posterior","quantities","maintained","within","a","sampling","pass",".","The","sampler","is","invoked","by","passing","the","regression","targets","(","`","y","`",")","and","the","initial","sparsity","pattern","(","`","nonzeros","`",")",":","``","`","(","observation_noise_variance",",","weights",")","=","sampler.sample_noise_variance_and_weights","(","targets=y",",","initial_nonzeros=tf.ones","(","[","num_features","]",",","dtype=tf.bool",")",")","``","`","This","implements","the","stochastic","search","variable","selection","(","SSVS",")","algorithm","[","2","]",",","sweeping","over","the","features","in","random","order","to","resample","their","sparsity","indicators","one","by","one",".","It","then","returns","a","sample","from","the","joint","posterior","on","the","regression","weights","and","the","observation","noise","variance",",","conditioned","on","the","resampled","sparsity","pattern",".","#","#","#","#","References","[","1","]","Steven","L.","Scott","and","Hal","Varian",".","Predicting","the","Present","with","Bayesian","Structural","Time","Series",".","__International","Journal","of","Mathematical","Modelling","and","Numerical","Optimisation","5.1-2","(","2014",")",":","4-23.__","https",":","\/\/people.ischool.berkeley.edu\/~hal\/Papers\/2013\/pred-present-with-bsts.pdf","[","2","]","George",",","E.","I.","and","McCulloch",",","R.","E.","Approaches","for","Bayesian","variable","selection",".","__Statistica","Sinica","7",",","339\u2013374","(","1997",")","__","."]
docstr: Builds the joint posterior for a sparsity pattern (eqn (7) from [1]).
code: def _get_conditional_posterior(self, sampler_state):
      """Builds the joint posterior for a sparsity pattern (eqn (7) from [1])."""
  
      @joint_distribution_auto_batched.JointDistributionCoroutineAutoBatched
      def posterior_jd():
          observation_noise_variance = yield InverseGammaWithSampleUpperBound(
              concentration=(
                  self.observation_noise_variance_posterior_concentration
              ),
              scale=sampler_state.observation_noise_variance_posterior_scale,
              upper_bound=self.observation_noise_variance_upper_bound,
              name="observation_noise_variance",
          )
          yield MVNPrecisionFactorHardZeros(
              loc=sampler_state.conditional_weights_mean,
              # Note that the posterior precision varies inversely with the
              # noise variance: in worlds with high noise we're also
              # more uncertain about the values of the weights.
              # TODO(colcarroll): Tests pass even without a square root on the
              # observation_noise_variance. Should add a test that would fail.
              precision_factor=tf.linalg.LinearOperatorLowerTriangular(
                  sampler_state.conditional_posterior_precision_chol
                  / tf.sqrt(
                      observation_noise_variance[
                          ..., tf.newaxis, tf.newaxis
                      ]
                  )
              ),
              nonzeros=sampler_state.nonzeros,
              name="weights",
          )
  
      return posterior_jd
  
imports: import collections
  import tensorflow.compat.v2
  from tensorflow_probability.python.bijectors import softplus
  from tensorflow_probability.python.distributions import bernoulli
  from tensorflow_probability.python.distributions import inverse_gamma
  from tensorflow_probability.python.distributions import joint_distribution_auto_batched
  from tensorflow_probability.python.distributions import sample
  from tensorflow_probability.python.experimental.distributions.mvn_precision_factor_linop import MultivariateNormalPrecisionFactorLinearOperator
  from tensorflow_probability.python.internal import broadcast_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import vectorization_util
  from tensorflow_probability.python.math import linalg
  from tensorflow_probability.python.mcmc.internal import util
label_desc: Use image node_id 7 for calling the SpikeSlabSampler obj's underlying member method code with example usage: obj._get_conditional_posterior(sampler_state) and returns: posterior_jd