Package 'tfprobability'

Description

A list of models that can be used as the model argument in glm_fit():

Details

• Bernoulli: Bernoulli(probs=mean) where mean = sigmoid(matmul(X, weights))

• BernoulliNormalCDF: Bernoulli(probs=mean) where ⁠mean = Normal(0, 1).cdf(matmul(X, weights))⁠

• GammaExp: Gamma(concentration=1, rate=1 / mean) where mean = exp(matmul(X, weights))

• GammaSoftplus: Gamma(concentration=1, rate=1 / mean) where mean = softplus(matmul(X, weights))

• LogNormal: LogNormal(loc=log(mean) - log(2) / 2, scale=sqrt(log(2))) where mean = exp(matmul(X, weights)).

• LogNormalSoftplus: LogNormal(loc=log(mean) - log(2) / 2, scale=sqrt(log(2))) where mean = softplus(matmul(X, weights))

• Normal: Normal(loc=mean, scale=1) where mean = matmul(X, weights).

• NormalReciprocal: Normal(loc=mean, scale=1) where mean = 1 / matmul(X, weights)

• Poisson: Poisson(rate=mean) where mean = exp(matmul(X, weights)).

• PoissonSoftplus: Poisson(rate=mean) where mean = softplus(matmul(X, weights)).

Value

list of models that can be used as the model argument in glm_fit()

See Also

Other glm_fit: glm_fit.tensorflow.tensor(), glm_fit_one_step.tensorflow.tensor()

Description

Runs multiple Fisher scoring steps

Usage

glm_fit(x, ...)

Arguments

Value

A glm_fit object with parameter estimates, number of iterations, etc.

See Also

glm_fit.tensorflow.tensor()

Description

Runs one Fisher scoring step

Usage

glm_fit_one_step(x, ...)

Arguments

Value

A glm_fit object with parameter estimates, number of iterations, etc.

See Also

glm_fit_one_step.tensorflow.tensor()

Description

Runs one Fisher Scoring step

Usage

## S3 method for class 'tensorflow.tensor'
glm_fit_one_step(
  x,
  response,
  model,
  model_coefficients_start = NULL,
  predicted_linear_response_start = NULL,
  l2_regularizer = NULL,
  dispersion = NULL,
  offset = NULL,
  learning_rate = NULL,
  fast_unsafe_numerics = TRUE,
  name = NULL,
  ...
)

Arguments

Value

A glm_fit object with parameter estimates, and number of required steps.

See Also

Other glm_fit: glm_families, glm_fit.tensorflow.tensor()

Description

Runs multiple Fisher scoring steps

Usage

## S3 method for class 'tensorflow.tensor'
glm_fit(
  x,
  response,
  model,
  model_coefficients_start = NULL,
  predicted_linear_response_start = NULL,
  l2_regularizer = NULL,
  dispersion = NULL,
  offset = NULL,
  convergence_criteria_fn = NULL,
  learning_rate = NULL,
  fast_unsafe_numerics = TRUE,
  maximum_iterations = NULL,
  name = NULL,
  ...
)

Arguments

Value

A glm_fit object with parameter estimates, and number of required steps.

See Also

Other glm_fit: glm_families, glm_fit_one_step.tensorflow.tensor()

Description

Initializer which concats other intializers

Usage

initializer_blockwise(initializers, sizes, validate_args = FALSE)

Arguments

Description

Installs TensorFlow Probability

Usage

install_tfprobability(
  method = c("auto", "virtualenv", "conda"),
  conda = "auto",
  version = "default",
  tensorflow = "default",
  extra_packages = NULL,
  ...,
  pip_ignore_installed = TRUE
)

Arguments

Value

invisible

Description

layer_autoregressive takes as input a Tensor of shape ⁠[..., event_size]⁠ and returns a Tensor of shape ⁠[..., event_size, params]⁠. The output satisfies the autoregressive property. That is, the layer is configured with some permutation ord of ⁠{0, ..., event_size-1}⁠ (i.e., an ordering of the input dimensions), and the output output[batch_idx, i, ...] for input dimension i depends only on inputs x[batch_idx, j] where ord(j) < ord(i).

Usage

layer_autoregressive(
  object,
  params,
  event_shape = NULL,
  hidden_units = NULL,
  input_order = "left-to-right",
  hidden_degrees = "equal",
  activation = NULL,
  use_bias = TRUE,
  kernel_initializer = "glorot_uniform",
  validate_args = FALSE,
  ...
)

Arguments

Details

The autoregressive property allows us to use output[batch_idx, i] to parameterize conditional distributions: ⁠p(x[batch_idx, i] | x[batch_idx, ] for ord(j) < ord(i))⁠ which give us a tractable distribution over input x[batch_idx]:

⁠p(x[batch_idx]) = prod_i p(x[batch_idx, ord(i)] | x[batch_idx, ord(0:i)])⁠

For example, when params is 2, the output of the layer can parameterize the location and log-scale of an autoregressive Gaussian distribution.

Value

a Keras layer

See Also

Other layers: layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

Following Papamakarios et al. (2017), given an autoregressive model $p(x)$ with conditional distributions in the location-scale family, we can construct a normalizing flow for $p(x)$.

Usage

layer_autoregressive_transform(object, made, ...)

Arguments

Details

Specifically, suppose made is a ⁠[layer_autoregressive()]⁠ – a layer implementing a Masked Autoencoder for Distribution Estimation (MADE) – that computes location and log-scale parameters $made(x)[i]$ for each input $x[i]$. Then we can represent the autoregressive model $p(x)$ as $x = f(u)$ where $u$ is drawn from from some base distribution and where $f$ is an invertible and differentiable function (i.e., a Bijector) and $f^{-1}(x)$ is defined by:

library(tensorflow)
library(zeallot)
f_inverse <- function(x) {
  c(shift, log_scale) %<-% tf$unstack(made(x), 2, axis = -1L)
  (x - shift) * tf$math$exp(-log_scale)
}

Given a layer_autoregressive() made, a layer_autoregressive_transform() transforms an input ⁠tfd_*⁠ $p(u)$ to an output ⁠tfd_*⁠ $p(x)$ where $x = f(u)$.

Value

a Keras layer

References

Papamakarios et al. (2017)

See Also

tfb_masked_autoregressive_flow() and layer_autoregressive()

Description

k (i.e., num_components) represents the number of component OneHotCategorical distributions and d (i.e., event_size) represents the number of categories within each OneHotCategorical distribution.

Usage

layer_categorical_mixture_of_one_hot_categorical(
  object,
  event_size,
  num_components,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  sample_dtype = NULL,
  validate_args = FALSE,
  ...
)

Arguments

Details

Typical choices for convert_to_tensor_fn include:

• tfp$distributions$Distribution$sample

• tfp$distributions$Distribution$mean

• tfp$distributions$Distribution$mode

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_1d_flipout(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the Flipout estimator (Wen et al., 2018), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias. Flipout uses roughly twice as many floating point operations as the reparameterization estimator but has the advantage of significantly lower variance.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In International Conference on Learning Representations, 2018.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_1d_reparameterization(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the reparameterization estimator (Kingma and Welling, 2014), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In International Conference on Learning Representations, 2014.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_2d_flipout(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the Flipout estimator (Wen et al., 2018), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias. Flipout uses roughly twice as many floating point operations as the reparameterization estimator but has the advantage of significantly lower variance.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In International Conference on Learning Representations, 2018.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_2d_reparameterization(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the reparameterization estimator (Kingma and Welling, 2014), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In International Conference on Learning Representations, 2014.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_3d_flipout(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the Flipout estimator (Wen et al., 2018), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias. Flipout uses roughly twice as many floating point operations as the reparameterization estimator but has the advantage of significantly lower variance.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In International Conference on Learning Representations, 2018.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer creates a convolution kernel that is convolved (actually cross-correlated) with the layer input to produce a tensor of outputs. It may also include a bias addition and activation function on the outputs. It assumes the kernel and/or bias are drawn from distributions.

Usage

layer_conv_3d_reparameterization(
  object,
  filters,
  kernel_size,
  strides = 1,
  padding = "valid",
  data_format = "channels_last",
  dilation_rate = 1,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

outputs = f(inputs; kernel, bias), kernel, bias ~ posterior

where f denotes the layer's calculation. It uses the reparameterization estimator (Kingma and Welling, 2014), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In International Conference on Learning Representations, 2014.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

Usage

layer_dense_flipout(
  object,
  units,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  seed = NULL,
  ...
)

Arguments

Details

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

kernel, bias ~ posterior
outputs = activation(matmul(inputs, kernel) + bias)

It uses the Flipout estimator (Wen et al., 2018), which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias. Flipout uses roughly twice as many floating point operations as the reparameterization estimator but has the advantage of significantly lower variance.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer).

Value

a Keras layer

References

• Yeming Wen, Paul Vicol, Jimmy Ba, Dustin Tran, and Roger Grosse. Flipout: Efficient Pseudo-Independent Weight Perturbations on Mini-Batches. In International Conference on Learning Representations, 2018.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

Usage

layer_dense_local_reparameterization(
  object,
  units,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

kernel, bias ~ posterior
outputs = activation(matmul(inputs, kernel) + bias)

It uses the local reparameterization estimator (Kingma et al., 2015), which performs a Monte Carlo approximation of the distribution on the hidden units induced by the kernel and bias. The default kernel_posterior_fn is a normal distribution which factorizes across all elements of the weight matrix and bias vector. Unlike that paper's multiplicative parameterization, this distribution has trainable location and scale parameters which is known as an additive noise parameterization (Molchanov et al., 2017).

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Diederik Kingma, Tim Salimans, and Max Welling. Variational Dropout and the Local Reparameterization Trick. In Neural Information Processing Systems, 2015.

• Dmitry Molchanov, Arsenii Ashukha, Dmitry Vetrov. Variational Dropout Sparsifies Deep Neural Networks. In International Conference on Machine Learning, 2017.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer implements the Bayesian variational inference analogue to a dense layer by assuming the kernel and/or the bias are drawn from distributions.

Usage

layer_dense_reparameterization(
  object,
  units,
  activation = NULL,
  activity_regularizer = NULL,
  trainable = TRUE,
  kernel_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(),
  kernel_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  kernel_prior_fn = tfp$layers$util$default_multivariate_normal_fn,
  kernel_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  bias_posterior_fn = tfp$layers$util$default_mean_field_normal_fn(is_singular = TRUE),
  bias_posterior_tensor_fn = function(d) d %>% tfd_sample(),
  bias_prior_fn = NULL,
  bias_divergence_fn = function(q, p, ignore) tfd_kl_divergence(q, p),
  ...
)

Arguments

Details

By default, the layer implements a stochastic forward pass via sampling from the kernel and bias posteriors,

kernel, bias ~ posterior
outputs = activation(matmul(inputs, kernel) + bias)

It uses the reparameterization estimator (Kingma and Welling, 2014) which performs a Monte Carlo approximation of the distribution integrating over the kernel and bias.

The arguments permit separate specification of the surrogate posterior (q(W|x)), prior (p(W)), and divergence for both the kernel and bias distributions.

Upon being built, this layer adds losses (accessible via the losses property) representing the divergences of kernel and/or bias surrogate posteriors and their respective priors. When doing minibatch stochastic optimization, make sure to scale this loss such that it is applied just once per epoch (e.g. if kl is the sum of losses for each element of the batch, you should pass kl / num_examples_per_epoch to your optimizer). You can access the kernel and/or bias posterior and prior distributions after the layer is built via the kernel_posterior, kernel_prior, bias_posterior and bias_prior properties.

Value

a Keras layer

References

• Diederik Kingma and Max Welling. Auto-Encoding Variational Bayes. In International Conference on Learning Representations, 2014.

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_variational(), layer_variable()

Description

This layer uses variational inference to fit a "surrogate" posterior to the distribution over both the kernel matrix and the bias terms which are otherwise used in a manner similar to layer_dense(). This layer fits the "weights posterior" according to the following generative process:

[K, b] ~ Prior()
M = matmul(X, K) + b
Y ~ Likelihood(M)

Usage

layer_dense_variational(
  object,
  units,
  make_posterior_fn,
  make_prior_fn,
  kl_weight = NULL,
  kl_use_exact = FALSE,
  activation = NULL,
  use_bias = TRUE,
  ...
)

Arguments

Value

a Keras layer

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_variable()

Description

Keras layer enabling plumbing TFP distributions through Keras models

Usage

layer_distribution_lambda(
  object,
  make_distribution_fn,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

An Independent-Bernoulli Keras layer from prod(event_shape) params

Usage

layer_independent_bernoulli(
  object,
  event_shape,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  sample_dtype = NULL,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

An independent Logistic Keras layer.

Usage

layer_independent_logistic(
  object,
  event_shape,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

An independent Normal Keras layer.

Usage

layer_independent_normal(
  object,
  event_shape,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Examples

library(keras)
input_shape <- c(28, 28, 1)
encoded_shape <- 2
n <- 2
model <- keras_model_sequential(
  list(
    layer_input(shape = input_shape),
    layer_flatten(),
    layer_dense(units = n),
    layer_dense(units = params_size_independent_normal(encoded_shape)),
    layer_independent_normal(event_shape = encoded_shape)
    )
  )

Description

An independent Poisson Keras layer.

Usage

layer_independent_poisson(
  object,
  event_shape,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

Pass-through layer that adds a KL divergence penalty to the model loss

Usage

layer_kl_divergence_add_loss(
  object,
  distribution_b,
  use_exact_kl = FALSE,
  test_points_reduce_axis = NULL,
  test_points_fn = tf$convert_to_tensor,
  weight = NULL,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

When using Monte Carlo approximation (e.g., use_exact = FALSE), it is presumed that the input distribution's concretization (i.e., tf$convert_to_tensor(distribution)) corresponds to a random sample. To override this behavior, set test_points_fn.

Usage

layer_kl_divergence_regularizer(
  object,
  distribution_b,
  use_exact_kl = FALSE,
  test_points_reduce_axis = NULL,
  test_points_fn = tf$convert_to_tensor,
  weight = NULL,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

A mixture distribution Keras layer, with independent logistic components.

Usage

layer_mixture_logistic(
  object,
  num_components,
  event_shape = list(),
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

A mixture distribution Keras layer, with independent normal components.

Usage

layer_mixture_normal(
  object,
  num_components,
  event_shape = list(),
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_same_family(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

A mixture (same-family) Keras layer.

Usage

layer_mixture_same_family(
  object,
  num_components,
  component_layer,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_multivariate_normal_tri_l(), layer_one_hot_categorical()

Description

A d-variate Multivariate Normal TriL Keras layer from d+d*(d+1)/ 2 params

Usage

layer_multivariate_normal_tri_l(
  object,
  event_size,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_one_hot_categorical()

Description

Typical choices for convert_to_tensor_fn include:

• tfp$distributions$Distribution$sample

• tfp$distributions$Distribution$mean

• tfp$distributions$Distribution$mode

• tfp$distributions$OneHotCategorical$logits

Usage

layer_one_hot_categorical(
  object,
  event_size,
  convert_to_tensor_fn = tfp$distributions$Distribution$sample,
  sample_dtype = NULL,
  validate_args = FALSE,
  ...
)

Arguments

Value

a Keras layer

See Also

For an example how to use in a Keras model, see layer_independent_normal().

Other distribution_layers: layer_categorical_mixture_of_one_hot_categorical(), layer_distribution_lambda(), layer_independent_bernoulli(), layer_independent_logistic(), layer_independent_normal(), layer_independent_poisson(), layer_kl_divergence_add_loss(), layer_kl_divergence_regularizer(), layer_mixture_logistic(), layer_mixture_normal(), layer_mixture_same_family(), layer_multivariate_normal_tri_l()

Description

Simply returns a (trainable) variable, regardless of input. This layer implements the mathematical function f(x) = c where c is a constant, i.e., unchanged for all x. Like other Keras layers, the constant is trainable. This layer can also be interpretted as the special case of layer_dense() when the kernel is forced to be the zero matrix (tf$zeros).

Usage

layer_variable(
  object,
  shape,
  dtype = NULL,
  activation = NULL,
  initializer = "zeros",
  regularizer = NULL,
  constraint = NULL,
  ...
)

Arguments

Value

a Keras layer

See Also

Other layers: layer_autoregressive(), layer_conv_1d_flipout(), layer_conv_1d_reparameterization(), layer_conv_2d_flipout(), layer_conv_2d_reparameterization(), layer_conv_3d_flipout(), layer_conv_3d_reparameterization(), layer_dense_flipout(), layer_dense_local_reparameterization(), layer_dense_reparameterization(), layer_dense_variational()

Description

Create a Variational Gaussian Process distribution whose index_points are the inputs to the layer. Parameterized by number of inducing points and a kernel_provider, which should be a tf.keras.Layer with an @property that late-binds variable parameters to a tfp.positive_semidefinite_kernel.PositiveSemidefiniteKernel instance (this requirement has to do with the way that variables must be created in a keras model). The mean_fn is an optional argument which, if omitted, will be automatically configured to be a constant function with trainable variable output.

Usage

layer_variational_gaussian_process(
  object,
  num_inducing_points,
  kernel_provider,
  event_shape = 1,
  inducing_index_points_initializer = NULL,
  unconstrained_observation_noise_variance_initializer = NULL,
  mean_fn = NULL,
  jitter = 1e-06,
  name = NULL
)

Arguments

Value

a Keras layer

Description

The dual averaging policy uses a noisy step size for exploration, while averaging over tuning steps to provide a smoothed estimate of an optimal value. It is based on section 3.2 of Hoffman and Gelman (2013), which modifies the [stochastic convex optimization scheme of Nesterov (2009). The modified algorithm applies extra weight to recent iterations while keeping the convergence guarantees of Robbins-Monro, and takes care not to make the step size too small too quickly when maintaining a constant trajectory length, to avoid expensive early iterations. A good target acceptance probability depends on the inner kernel. If this kernel is HamiltonianMonteCarlo, then 0.6-0.9 is a good range to aim for. For RandomWalkMetropolis this should be closer to 0.25. See the individual kernels' docstrings for guidance.

Usage

mcmc_dual_averaging_step_size_adaptation(
  inner_kernel,
  num_adaptation_steps,
  target_accept_prob = 0.75,
  exploration_shrinkage = 0.05,
  step_count_smoothing = 10,
  decay_rate = 0.75,
  step_size_setter_fn = NULL,
  step_size_getter_fn = NULL,
  log_accept_prob_getter_fn = NULL,
  validate_args = FALSE,
  name = NULL
)

Arguments

Details

In general, adaptation prevents the chain from reaching a stationary distribution, so obtaining consistent samples requires num_adaptation_steps be set to a value somewhat smaller than the number of burnin steps. However, it may sometimes be helpful to set num_adaptation_steps to a larger value during development in order to inspect the behavior of the chain during adaptation. The step size is assumed to broadcast with the chain state, potentially having leading dimensions corresponding to multiple chains. When there are fewer of those leading dimensions than there are chain dimensions, the corresponding dimensions in the log_accept_prob are averaged (in the direct space, rather than the log space) before being used to adjust the step size. This means that this kernel can do both cross-chain adaptation, or per-chain step size adaptation, depending on the shape of the step size. For example, if your problem has a state with shape ⁠[S]⁠, your chain state has shape ⁠[C0, C1, S]⁠ (meaning that there are C0 * C1 total chains) and log_accept_prob has shape ⁠[C0, C1]⁠ (one acceptance probability per chain), then depending on the shape of the step size, the following will happen:

• Step size has shape ⁠[]⁠, ⁠[S]⁠ or ⁠[1]⁠, the log_accept_prob will be averaged across its C0 and C1 dimensions. This means that you will learn a shared step size based on the mean acceptance probability across all chains. This can be useful if you don't have a lot of steps to adapt and want to average away the noise.

• Step size has shape ⁠[C1, 1]⁠ or ⁠[C1, S]⁠, the log_accept_prob will be averaged across its C0 dimension. This means that you will learn a shared step size based on the mean acceptance probability across chains that share the coordinate across the C1 dimension. This can be useful when the C1 dimension indexes different distributions, while C0 indexes replicas of a single distribution, all sampled in parallel.

• Step size has shape ⁠[C0, C1, 1]⁠ or ⁠[C0, C1, S]⁠, then no averaging will happen. This means that each chain will learn its own step size. This can be useful when all chains are sampling from different distributions. Even when all chains are for the same distribution, this can help during the initial warmup period.

• Step size has shape ⁠[C0, 1, 1]⁠ or ⁠[C0, 1, S]⁠, the log_accept_prob will be averaged across its C1 dimension. This means that you will learn a shared step size based on the mean acceptance probability across chains that share the coordinate across the C0 dimension. This can be useful when the C0 dimension indexes different distributions, while C1 indexes replicas of a single distribution, all sampled in parallel.

Value

a Monte Carlo sampling kernel

References

• Matthew D. Hoffman, Andrew Gelman. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. In Journal of Machine Learning Research, 15(1):1593-1623, 2014.

• Yurii Nesterov. Primal-dual subgradient methods for convex problems. Mathematical programming 120.1 (2009): 221-259

• https://statmodeling.stat.columbia.edu/2017/12/15/burn-vs-warm-iterative-simulation-algorithms/

See Also

For an example how to use see mcmc_no_u_turn_sampler().

Other mcmc_kernels: mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

Roughly speaking, "effective sample size" (ESS) is the size of an iid sample with the same variance as state.

Usage

mcmc_effective_sample_size(
  states,
  filter_threshold = 0,
  filter_beyond_lag = NULL,
  name = NULL
)

Arguments

Details

More precisely, given a stationary sequence of possibly correlated random variables ⁠X_1, X_2,...,X_N⁠, each identically distributed ESS is the number such that ⁠Variance{ N**-1 * Sum{X_i} } = ESS**-1 * Variance{ X_1 }.⁠

If the sequence is uncorrelated, ESS = N. In general, one should expect ESS <= N, with more highly correlated sequences having smaller ESS.

Value

Tensor or list of Tensor objects. The effective sample size of each component of states. Shape will be ⁠states$shape[1:]⁠.

See Also

Other mcmc_functions: mcmc_potential_scale_reduction(), mcmc_sample_annealed_importance_chain(), mcmc_sample_chain(), mcmc_sample_halton_sequence()

Description

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm that takes a series of gradient-informed steps to produce a Metropolis proposal. This class implements one random HMC step from a given current_state. Mathematical details and derivations can be found in Neal (2011).

Usage

mcmc_hamiltonian_monte_carlo(
  target_log_prob_fn,
  step_size,
  num_leapfrog_steps,
  state_gradients_are_stopped = FALSE,
  step_size_update_fn = NULL,
  seed = NULL,
  store_parameters_in_results = FALSE,
  name = NULL
)

Arguments

Details

The one_step function can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, ⁠current_state[0, :]⁠ could have a different target distribution from ⁠current_state[1, :]⁠. These semantics are governed by target_log_prob_fn(current_state). (The number of independent chains is tf$size(target_log_prob_fn(current_state)).)

Value

a Monte Carlo sampling kernel

References

• Radford Neal. MCMC Using Hamiltonian Dynamics. Handbook of Markov Chain Monte Carlo, 2011.

• Bernard Delyon, Marc Lavielle, Eric, Moulines. Convergence of a stochastic approximation version of the EM algorithm, Ann. Statist. 27 (1999), no. 1, 94–128.

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

Metropolis-adjusted Langevin algorithm (MALA) is a Markov chain Monte Carlo (MCMC) algorithm that takes a step of a discretised Langevin diffusion as a proposal. This class implements one step of MALA using Euler-Maruyama method for a given current_state and diagonal preconditioning volatility matrix.

Usage

mcmc_metropolis_adjusted_langevin_algorithm(
  target_log_prob_fn,
  step_size,
  volatility_fn = NULL,
  seed = NULL,
  parallel_iterations = 10,
  name = NULL
)

Arguments

Details

Mathematical details and derivations can be found in Roberts and Rosenthal (1998) and Xifara et al. (2013).

The one_step function can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should reduce log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, ⁠current_state[0, :]⁠ could have a different target distribution from ⁠current_state[1, :]⁠. These semantics are governed by target_log_prob_fn(current_state). (The number of independent chains is tf.size(target_log_prob_fn(current_state)).)

References

• Gareth Roberts and Jeffrey Rosenthal. Optimal Scaling of Discrete Approximations to Langevin Diffusions. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 60: 255-268, 1998.

• T. Xifara et al. Langevin diffusions and the Metropolis-adjusted Langevin algorithm. arXiv preprint arXiv:1309.2983, 2013.

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

The Metropolis-Hastings algorithm is a Markov chain Monte Carlo (MCMC) technique which uses a proposal distribution to eventually sample from a target distribution.

Usage

mcmc_metropolis_hastings(inner_kernel, seed = NULL, name = NULL)

Arguments

Details

Note: inner_kernel$one_step must return kernel_results as a collections$namedtuple which must:

• have a target_log_prob field,

• optionally have a log_acceptance_correction field, and,

• have only fields which are Tensor-valued.

The Metropolis-Hastings log acceptance-probability is computed as:

log_accept_ratio = (current_kernel_results.target_log_prob
                   - previous_kernel_results.target_log_prob
                   + current_kernel_results.log_acceptance_correction)

If current_kernel_results$log_acceptance_correction does not exist, it is presumed 0 (i.e., that the proposal distribution is symmetric). The most common use-case for log_acceptance_correction is in the Metropolis-Hastings algorithm, i.e.,

accept_prob(x' | x) = p(x') / p(x) (g(x|x') / g(x'|x))
where,
p  represents the target distribution,
g  represents the proposal (conditional) distribution,
x' is the proposed state, and,
x  is current state

The log of the parenthetical term is the log_acceptance_correction. The log_acceptance_correction may not necessarily correspond to the ratio of proposal distributions, e.g, log_acceptance_correction has a different interpretation in Hamiltonian Monte Carlo.

Value

a Monte Carlo sampling kernel

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

The No U-Turn Sampler (NUTS) is an adaptive variant of the Hamiltonian Monte Carlo (HMC) method for MCMC. NUTS adapts the distance traveled in response to the curvature of the target density. Conceptually, one proposal consists of reversibly evolving a trajectory through the sample space, continuing until that trajectory turns back on itself (hence the name, 'No U-Turn'). This class implements one random NUTS step from a given current_state. Mathematical details and derivations can be found in Hoffman & Gelman (2011).

Usage

mcmc_no_u_turn_sampler(
  target_log_prob_fn,
  step_size,
  max_tree_depth = 10,
  max_energy_diff = 1000,
  unrolled_leapfrog_steps = 1,
  seed = NULL,
  name = NULL
)

Arguments

Details

The one_step function can update multiple chains in parallel. It assumes that a prefix of leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, current_state[0][0, ...] could have a different target distribution from current_state[0][1, ...]. These semantics are governed by ⁠target_log_prob_fn(*current_state)⁠. (The number of independent chains is tf$size(target_log_prob_fn(current_state)).)

Value

a Monte Carlo sampling kernel

References

• Matthew D. Hoffman, Andrew Gelman. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. 2011.

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_random_walk_metropolis(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Examples

predictors <- tf$cast( c(201,244, 47,287,203,58,210,202,198,158,165,201,157,
  131,166,160,186,125,218,146),tf$float32)
obs <- tf$cast(c(592,401,583,402,495,173,479,504,510,416,393,442,317,311,400,
  337,423,334,533,344),tf$float32)
y_sigma <- tf$cast(c(61,25,38,15,21,15,27,14,30,16,14,25,52,16,34,31,42,26,
  16,22),tf$float32)

# Robust linear regression model
robust_lm <- tfd_joint_distribution_sequential(
 list(
   tfd_normal(loc = 0, scale = 1, name = "b0"),
   tfd_normal(loc = 0, scale = 1, name = "b1"),
   tfd_half_normal(5, name = "df"),
   function(df, b1, b0)
     tfd_independent(
       tfd_student_t(
         # Likelihood
           df = tf$expand_dims(df, axis = -1L),
           loc = tf$expand_dims(b0, axis = -1L) +
                 tf$expand_dims(b1, axis = -1L) * predictors[tf$newaxis, ],
           scale = y_sigma,
           name = "st"
           ), name = "ind")), validate_args = TRUE)

 log_prob <-function(b0, b1, df) {robust_lm %>%
   tfd_log_prob(list(b0, b1, df, obs))}
 step_size0 <- Map(function(x) tf$cast(x, tf$float32), c(1, .2, .5))

 number_of_steps <- 10
 burnin <- 5
 nchain <- 50

 run_chain <- function() {
 # random initialization of the starting postion of each chain
 samples <- robust_lm %>% tfd_sample(nchain)
 b0 <- samples[[1]]
 b1 <- samples[[2]]
 df <- samples[[3]]

 # bijector to map constrained parameters to real
 unconstraining_bijectors <- list(
   tfb_identity(), tfb_identity(), tfb_exp())

 trace_fn <- function(x, pkr) {
   list(pkr$inner_results$inner_results$step_size,
     pkr$inner_results$inner_results$log_accept_ratio)
 }

 nuts <- mcmc_no_u_turn_sampler(
   target_log_prob_fn = log_prob,
   step_size = step_size0
   ) %>%
   mcmc_transformed_transition_kernel(bijector = unconstraining_bijectors) %>%
   mcmc_dual_averaging_step_size_adaptation(
     num_adaptation_steps = burnin,
     step_size_setter_fn = function(pkr, new_step_size)
       pkr$`_replace`(
         inner_results = pkr$inner_results$`_replace`(step_size = new_step_size)),
     step_size_getter_fn = function(pkr) pkr$inner_results$step_size,
     log_accept_prob_getter_fn = function(pkr) pkr$inner_results$log_accept_ratio
     )

   nuts %>% mcmc_sample_chain(
     num_results = number_of_steps,
     num_burnin_steps = burnin,
     current_state = list(b0, b1, df),
     trace_fn = trace_fn)
   }

   run_chain <- tensorflow::tf_function(run_chain)
   res <- run_chain()

Description

Given N > 1 states from each of C > 1 independent chains, the potential scale reduction factor, commonly referred to as R-hat, measures convergence of the chains (to the same target) by testing for equality of means.

Usage

mcmc_potential_scale_reduction(
  chains_states,
  independent_chain_ndims = 1,
  name = NULL
)

Arguments

Details

Specifically, R-hat measures the degree to which variance (of the means) between chains exceeds what one would expect if the chains were identically distributed. See Gelman and Rubin (1992), Brooks and Gelman (1998)].

Some guidelines:

• The initial state of the chains should be drawn from a distribution overdispersed with respect to the target.

• If all chains converge to the target, then as ⁠N --> infinity⁠, R-hat –> 1. Before that, R-hat > 1 (except in pathological cases, e.g. if the chain paths were identical).

• The above holds for any number of chains C > 1. Increasing C improves effectiveness of the diagnostic.

• Sometimes, R-hat < 1.2 is used to indicate approximate convergence, but of course this is problem dependent. See Brooks and Gelman (1998).

• R-hat only measures non-convergence of the mean. If higher moments, or other statistics are desired, a different diagnostic should be used. See Brooks and Gelman (1998).

To see why R-hat is reasonable, let X be a random variable drawn uniformly from the combined states (combined over all chains). Then, in the limit ⁠N, C --> infinity⁠, with E, Var denoting expectation and variance, ⁠R-hat = ( E[Var[X | chain]] + Var[E[X | chain]] ) / E[Var[X | chain]].⁠ Using the law of total variance, the numerator is the variance of the combined states, and the denominator is the total variance minus the variance of the the individual chain means. If the chains are all drawing from the same distribution, they will have the same mean, and thus the ratio should be one.

Value

Tensor or list of Tensors representing the R-hat statistic for the state(s). Same dtype as state, and shape equal to ⁠state$shape[1 + independent_chain_ndims:]⁠.

References

• Stephen P. Brooks and Andrew Gelman. General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics, 7(4), 1998.

• Andrew Gelman and Donald B. Rubin. Inference from Iterative Simulation Using Multiple Sequences. Statistical Science, 7(4):457-472, 1992.

See Also

Other mcmc_functions: mcmc_effective_sample_size(), mcmc_sample_annealed_importance_chain(), mcmc_sample_chain(), mcmc_sample_halton_sequence()

Description

Random Walk Metropolis is a gradient-free Markov chain Monte Carlo (MCMC) algorithm. The algorithm involves a proposal generating step proposal_state = current_state + perturb by a random perturbation, followed by Metropolis-Hastings accept/reject step. For more details see Section 2.1 of Roberts and Rosenthal (2004).

Usage

mcmc_random_walk_metropolis(
  target_log_prob_fn,
  new_state_fn = NULL,
  seed = NULL,
  name = NULL
)

Arguments

Details

The current class implements RWM for normal and uniform proposals. Alternatively, the user can supply any custom proposal generating function. The function one_step can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, ⁠current_state[0, :]⁠ could have a different target distribution from ⁠current_state[1, :]⁠. These semantics are governed by target_log_prob_fn(current_state). (The number of independent chains is tf$size(target_log_prob_fn(current_state)).)

Value

a Monte Carlo sampling kernel

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_replica_exchange_mc(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

Replica Exchange Monte Carlo is a Markov chain Monte Carlo (MCMC) algorithm that is also known as Parallel Tempering. This algorithm performs multiple sampling with different temperatures in parallel, and exchanges those samplings according to the Metropolis-Hastings criterion. The K replicas are parameterized in terms of inverse_temperature's, ⁠(beta[0], beta[1], ..., beta[K-1])⁠. If the target distribution has probability density p(x), the kth replica has density p(x)**beta_k.

Usage

mcmc_replica_exchange_mc(
  target_log_prob_fn,
  inverse_temperatures,
  make_kernel_fn,
  swap_proposal_fn = tfp$mcmc$replica_exchange_mc$default_swap_proposal_fn(1),
  state_includes_replicas = FALSE,
  seed = NULL,
  name = NULL
)

Arguments

Details

Typically beta[0] = 1.0, and ⁠1.0 > beta[1] > beta[2] > ... > 0.0⁠.

• beta[0] == 1 ==> First replicas samples from the target density, p.

• beta[k] < 1, for ⁠k = 1, ..., K-1⁠ ==> Other replicas sample from "flattened" versions of p (peak is less high, valley less low). These distributions are somewhat closer to a uniform on the support of p. Samples from adjacent replicas i, i + 1 are used as proposals for each other in a Metropolis step. This allows the lower beta samples, which explore less dense areas of p, to occasionally be used to help the beta == 1 chain explore new regions of the support. Samples from replica 0 are returned, and the others are discarded.

Value

list of next_state (Tensor or Python list of Tensors representing the state(s) of the Markov chain(s) at each result step. Has same shape as and current_state.) and kernel_results (collections$namedtuple of internal calculations used to 'advance the chain).

See Also

Other mcmc_kernels: mcmc_dual_averaging_step_size_adaptation(), mcmc_hamiltonian_monte_carlo(), mcmc_metropolis_adjusted_langevin_algorithm(), mcmc_metropolis_hastings(), mcmc_no_u_turn_sampler(), mcmc_random_walk_metropolis(), mcmc_simple_step_size_adaptation(), mcmc_slice_sampler(), mcmc_transformed_transition_kernel(), mcmc_uncalibrated_hamiltonian_monte_carlo(), mcmc_uncalibrated_langevin(), mcmc_uncalibrated_random_walk()

Description

This function uses an MCMC transition operator (e.g., Hamiltonian Monte Carlo) to sample from a series of distributions that slowly interpolates between an initial "proposal" distribution: exp(proposal_log_prob_fn(x) - proposal_log_normalizer) and the target distribution: exp(target_log_prob_fn(x) - target_log_normalizer), accumulating importance weights along the way. The product of these importance weights gives an unbiased estimate of the ratio of the normalizing constants of the initial distribution and the target distribution: E[exp(ais_weights)] = exp(target_log_normalizer - proposal_log_normalizer).

Usage

mcmc_sample_annealed_importance_chain(
  num_steps,
  proposal_log_prob_fn,
  target_log_prob_fn,
  current_state,
  make_kernel_fn,
  parallel_iterations = 10,
  name = NULL
)

Arguments

Details

Note: When running in graph mode, proposal_log_prob_fn and target_log_prob_fn are called exactly three times (although this may be reduced to two times in the future).

Value

list of next_state (Tensor or Python list of Tensors representing the state(s) of the Markov chain(s) at the final iteration. Has same shape as input current_state), ais_weights (Tensor with the estimated weight(s). Has shape matching target_log_prob_fn(current_state)), and kernel_results (collections.namedtuple of internal calculations used to advance the chain).

See Also

For an example how to use see mcmc_sample_chain().

Other mcmc_functions: mcmc_effective_sample_size(), mcmc_potential_scale_reduction(), mcmc_sample_chain(), mcmc_sample_halton_sequence()

Description

This function samples from an Markov chain at current_state and whose stationary distribution is governed by the supplied TransitionKernel instance (kernel).

Usage

mcmc_sample_chain(
  kernel = NULL,
  num_results,
  current_state,
  previous_kernel_results = NULL,
  num_burnin_steps = 0,
  num_steps_between_results = 0,
  trace_fn = NULL,
  return_final_kernel_results = FALSE,
  parallel_iterations = 10,
  seed = NULL,
  name = NULL
)

Arguments

Details

This function can sample from multiple chains, in parallel. (Whether or not there are multiple chains is dictated by the kernel.)

The current_state can be represented as a single Tensor or a list of Tensors which collectively represent the current state. Since MCMC states are correlated, it is sometimes desirable to produce additional intermediate states, and then discard them, ending up with a set of states with decreased autocorrelation. See Owen (2017). Such "thinning" is made possible by setting num_steps_between_results > 0. The chain then takes num_steps_between_results extra steps between the steps that make it into the results. The extra steps are never materialized (in calls to sess$run), and thus do not increase memory requirements.

Warning: when setting a seed in the kernel, ensure that sample_chain's parallel_iterations=1, otherwise results will not be reproducible. In addition to returning the chain state, this function supports tracing of auxiliary variables used by the kernel. The traced values are selected by specifying trace_fn. By default, all kernel results are traced but in the future the default will be changed to no results being traced, so plan accordingly. See below for some examples of this feature.

Value

list of:

• checkpointable_states_and_trace: if return_final_kernel_results is TRUE. The return value is an instance of CheckpointableStatesAndTrace.

• all_states: if return_final_kernel_results is FALSE and trace_fn is NULL. The return value is a Tensor or Python list of Tensors representing the state(s) of the Markov chain(s) at each result step. Has same shape as input current_state but with a prepended num_results-size dimension.

• states_and_trace: if return_final_kernel_results is FALSE and trace_fn is not NULL. The return value is an instance of StatesAndTrace.

References

• Art B. Owen. Statistically efficient thinning of a Markov chain sampler. Technical Report, 2017.

See Also

Other mcmc_functions: mcmc_effective_sample_size(), mcmc_potential_scale_reduction(), mcmc_sample_annealed_importance_chain(), mcmc_sample_halton_sequence()

Examples

dims <- 10
  true_stddev <- sqrt(seq(1, 3, length.out = dims))
  likelihood <- tfd_multivariate_normal_diag(scale_diag = true_stddev)

  kernel <- mcmc_hamiltonian_monte_carlo(
    target_log_prob_fn = likelihood$log_prob,
    step_size = 0.5,
    num_leapfrog_steps = 2
  )

  states <- kernel %>% mcmc_sample_chain(
    num_results = 1000,
    num_burnin_steps = 500,
    current_state = rep(0, dims),
    trace_fn = NULL
  )

  sample_mean <- tf$reduce_mean(states, axis = 0L)
  sample_stddev <- tf$sqrt(
    tf$reduce_mean(tf$math$squared_difference(states, sample_mean), axis = 0L))

Description

Warning: The sequence elements take values only between 0 and 1. Care must be taken to appropriately transform the domain of a function if it differs from the unit cube before evaluating integrals using Halton samples. It is also important to remember that quasi-random numbers without randomization are not a replacement for pseudo-random numbers in every context. Quasi random numbers are completely deterministic and typically have significant negative autocorrelation unless randomization is used.

Usage

mcmc_sample_halton_sequence(
  dim,
  num_results = NULL,
  sequence_indices = NULL,
  dtype = tf$float32,
  randomized = TRUE,
  seed = NULL,
  name = NULL
)

Arguments