tensorflow_probability/python/distributions/linear_gaussian_ssm.py
def backward_smoothing_pass(self,
                              filtered_means,
                              filtered_covs,
                              predicted_means,
                              predicted_covs):
    """Run the backward pass in Kalman smoother.

    The backward smoothing is using Rauch, Tung and Striebel smoother as
    as discussed in section 18.3.2 of Kevin P. Murphy, 2012, Machine Learning:
    A Probabilistic Perspective, The MIT Press. The inputs are returned by
    `forward_filter` function.

    Args:
      filtered_means: Means of the per-timestep filtered marginal
        distributions p(z_t | x_{:t}), as a Tensor of shape
        `sample_shape(x) + batch_shape + [num_timesteps, latent_size]`.
      filtered_covs: Covariances of the per-timestep filtered marginal
        distributions p(z_t | x_{:t}), as a Tensor of shape
        `batch_shape + [num_timesteps, latent_size, latent_size]`.
      predicted_means: Means of the per-timestep predictive
         distributions over latent states, p(z_{t+1} | x_{:t}), as a
         Tensor of shape `sample_shape(x) + batch_shape +
         [num_timesteps, latent_size]`.
      predicted_covs: Covariances of the per-timestep predictive
         distributions over latent states, p(z_{t+1} | x_{:t}), as a
         Tensor of shape `batch_shape + [num_timesteps, latent_size,
         latent_size]`.

    Returns:
      posterior_means: Means of the smoothed marginal distributions
        p(z_t | x_{1:T}), as a Tensor of shape
        `sample_shape(x) + batch_shape + [num_timesteps, latent_size]`,
        which is of the same shape as filtered_means.
      posterior_covs: Covariances of the smoothed marginal distributions
        p(z_t | x_{1:T}), as a Tensor of shape
        `batch_shape + [num_timesteps, latent_size, latent_size]`.
        which is of the same shape as filtered_covs.
    """
    with tf.name_scope("backward_pass"):
      filtered_means = tf.convert_to_tensor(
          value=filtered_means, name="filtered_means")
      filtered_covs = tf.convert_to_tensor(
          value=filtered_covs, name="filtered_covs")
      predicted_means = tf.convert_to_tensor(
          value=predicted_means, name="predicted_means")
      predicted_covs = tf.convert_to_tensor(
          value=predicted_covs, name="predicted_covs")

      # To scan over time dimension, we need to move 'num_timesteps' from the
      # event shape to the initial dimension of the tensor.
      filtered_means = distribution_util.move_dimension(filtered_means, -2, 0)
      filtered_covs = distribution_util.move_dimension(filtered_covs, -3, 0)
      predicted_means = distribution_util.move_dimension(predicted_means, -2, 0)
      predicted_covs = distribution_util.move_dimension(predicted_covs, -3, 0)

      # The means are assumed to be vectors. Adding a dummy index to
      # ensure the `matmul` op working smoothly.
      filtered_means = filtered_means[..., tf.newaxis]
      predicted_means = predicted_means[..., tf.newaxis]

      initial_backward_mean = predicted_means[-1, ...]
      initial_backward_cov = predicted_covs[-1, ...]

      num_timesteps = tf.shape(input=filtered_means)[0]
      initial_state = BackwardPassState(
          backward_mean=initial_backward_mean,
          backward_cov=initial_backward_cov,
          timestep=self.initial_step + num_timesteps - 1)

      update_step_fn = build_backward_pass_step(
          self.get_transition_matrix_for_timestep)

      # For backward pass, it scans the `elems` from last to first.
      posterior_states = tf.scan(update_step_fn,
                                 elems=(filtered_means,
                                        filtered_covs,
                                        predicted_means,
                                        predicted_covs),
                                 initializer=initial_state,
                                 reverse=True)

      # Move the time dimension back into the event shape.
      posterior_means = distribution_util.move_dimension(
          posterior_states.backward_mean[..., 0], 0, -2)
      posterior_covs = distribution_util.move_dimension(
          posterior_states.backward_cov, 0, -3)

      return (posterior_means, posterior_covs)
def backward_smoothing_pass(self,
                              filtered_means,
                              filtered_covs,
                              predicted_means,
                              predicted_covs):
    with tf.name_scope("backward_pass"):
      filtered_means = tf.convert_to_tensor(
          value=filtered_means, name="filtered_means")
      filtered_covs = tf.convert_to_tensor(
          value=filtered_covs, name="filtered_covs")
      predicted_means = tf.convert_to_tensor(
          value=predicted_means, name="predicted_means")
      predicted_covs = tf.convert_to_tensor(
          value=predicted_covs, name="predicted_covs")

      # To scan over time dimension, we need to move 'num_timesteps' from the
      # event shape to the initial dimension of the tensor.
      filtered_means = distribution_util.move_dimension(filtered_means, -2, 0)
      filtered_covs = distribution_util.move_dimension(filtered_covs, -3, 0)
      predicted_means = distribution_util.move_dimension(predicted_means, -2, 0)
      predicted_covs = distribution_util.move_dimension(predicted_covs, -3, 0)

      # The means are assumed to be vectors. Adding a dummy index to
      # ensure the `matmul` op working smoothly.
      filtered_means = filtered_means[..., tf.newaxis]
      predicted_means = predicted_means[..., tf.newaxis]

      initial_backward_mean = predicted_means[-1, ...]
      initial_backward_cov = predicted_covs[-1, ...]

      num_timesteps = tf.shape(input=filtered_means)[0]
      initial_state = BackwardPassState(
          backward_mean=initial_backward_mean,
          backward_cov=initial_backward_cov,
          timestep=self.initial_step + num_timesteps - 1)

      update_step_fn = build_backward_pass_step(
          self.get_transition_matrix_for_timestep)

      # For backward pass, it scans the `elems` from last to first.
      posterior_states = tf.scan(update_step_fn,
                                 elems=(filtered_means,
                                        filtered_covs,
                                        predicted_means,
                                        predicted_covs),
                                 initializer=initial_state,
                                 reverse=True)

      # Move the time dimension back into the event shape.
      posterior_means = distribution_util.move_dimension(
          posterior_states.backward_mean[..., 0], 0, -2)
      posterior_covs = distribution_util.move_dimension(
          posterior_states.backward_cov, 0, -3)

      return (posterior_means, posterior_covs)
def backward_smoothing_pass ( self , filtered_means , filtered_covs , predicted_means , predicted_covs ) : with tf . name_scope ( "backward_pass" ) : filtered_means = tf . convert_to_tensor ( value = filtered_means , name = "filtered_means" ) filtered_covs = tf . convert_to_tensor ( value = filtered_covs , name = "filtered_covs" ) predicted_means = tf . convert_to_tensor ( value = predicted_means , name = "predicted_means" ) predicted_covs = tf . convert_to_tensor ( value = predicted_covs , name = "predicted_covs" ) # To scan over time dimension, we need to move 'num_timesteps' from the # event shape to the initial dimension of the tensor. filtered_means = distribution_util . move_dimension ( filtered_means , - 2 , 0 ) filtered_covs = distribution_util . move_dimension ( filtered_covs , - 3 , 0 ) predicted_means = distribution_util . move_dimension ( predicted_means , - 2 , 0 ) predicted_covs = distribution_util . move_dimension ( predicted_covs , - 3 , 0 ) # The means are assumed to be vectors. Adding a dummy index to # ensure the `matmul` op working smoothly. filtered_means = filtered_means [ ... , tf . newaxis ] predicted_means = predicted_means [ ... , tf . newaxis ] initial_backward_mean = predicted_means [ - 1 , ... ] initial_backward_cov = predicted_covs [ - 1 , ... ] num_timesteps = tf . shape ( input = filtered_means ) [ 0 ] initial_state = BackwardPassState ( backward_mean = initial_backward_mean , backward_cov = initial_backward_cov , timestep = self . initial_step + num_timesteps - 1 ) update_step_fn = build_backward_pass_step ( self . get_transition_matrix_for_timestep ) # For backward pass, it scans the `elems` from last to first. posterior_states = tf . scan ( update_step_fn , elems = ( filtered_means , filtered_covs , predicted_means , predicted_covs ) , initializer = initial_state , reverse = True ) # Move the time dimension back into the event shape. posterior_means = distribution_util . move_dimension ( posterior_states . backward_mean [ ... , 0 ] , 0 , - 2 ) posterior_covs = distribution_util . move_dimension ( posterior_states . backward_cov , 0 , - 3 ) return ( posterior_means , posterior_covs )
Run the backward pass in Kalman smoother.

    The backward smoothing is using Rauch, Tung and Striebel smoother as
    as discussed in section 18.3.2 of Kevin P. Murphy, 2012, Machine Learning:
    A Probabilistic Perspective, The MIT Press. The inputs are returned by
    `forward_filter` function.

    Args:
      filtered_means: Means of the per-timestep filtered marginal
        distributions p(z_t | x_{:t}), as a Tensor of shape
        `sample_shape(x) + batch_shape + [num_timesteps, latent_size]`.
      filtered_covs: Covariances of the per-timestep filtered marginal
        distributions p(z_t | x_{:t}), as a Tensor of shape
        `batch_shape + [num_timesteps, latent_size, latent_size]`.
      predicted_means: Means of the per-timestep predictive
         distributions over latent states, p(z_{t+1} | x_{:t}), as a
         Tensor of shape `sample_shape(x) + batch_shape +
         [num_timesteps, latent_size]`.
      predicted_covs: Covariances of the per-timestep predictive
         distributions over latent states, p(z_{t+1} | x_{:t}), as a
         Tensor of shape `batch_shape + [num_timesteps, latent_size,
         latent_size]`.

    Returns:
      posterior_means: Means of the smoothed marginal distributions
        p(z_t | x_{1:T}), as a Tensor of shape
        `sample_shape(x) + batch_shape + [num_timesteps, latent_size]`,
        which is of the same shape as filtered_means.
      posterior_covs: Covariances of the smoothed marginal distributions
        p(z_t | x_{1:T}), as a Tensor of shape
        `batch_shape + [num_timesteps, latent_size, latent_size]`.
        which is of the same shape as filtered_covs.
Run the backward pass in Kalman smoother .