TensorFlow Probability is a library for statistical computation and probabilistic modeling built on top of TensorFlow.

Its building blocks include a vast range of distributions and invertible transformations (bijectors), probabilistic layers that may be used in keras models, and tools for probabilistic reasoning including variational inference and Markov Chain Monte Carlo.


Install the released version of tfprobability from CRAN:


To install tfprobability from github, do


Then, use the install_tfprobability() function to install TensorFlow and TensorFlow Probability python modules.

you will automatically get the current stable version of TensorFlow Probability together with TensorFlow. Correspondingly, if you need nightly builds,

install_tfprobability(version = "nightly")

will get you the nightly build of TensorFlow as well as TensorFlow Probability.


High-level application of tfprobability to tasks like

  • probabilistic (multi-level) modeling with MCMC and/or variational inference,
  • uncertainty estimation for neural networks,
  • time series modeling with state space models, or
  • density estimation with autoregressive flows

are described in the vignettes/articles and/or featured on the TensorFlow for R blog.

This introductory text illustrates the lower-level building blocks: distributions, bijectors, and probabilistic keras layers.



Distributions are objects with methods to compute summary statistics, (log) probability, and (optionally) quantities like entropy and KL divergence.

Example: Binomial distribution

# create a binomial distribution with n = 7 and p = 0.3
d <- tfd_binomial(total_count = 7, probs = 0.3)

# compute mean
d %>% tfd_mean()
# compute variance
d %>% tfd_variance()
# compute probability
d %>% tfd_prob(2.3)

Example: Hidden Markov Model

# Represent a cold day with 0 and a hot day with 1.
# Suppose the first day of a sequence has a 0.8 chance of being cold.
# We can model this using the categorical distribution:
initial_distribution <- tfd_categorical(probs = c(0.8, 0.2))
# Suppose a cold day has a 30% chance of being followed by a hot day
# and a hot day has a 20% chance of being followed by a cold day.
# We can model this as:
transition_distribution <- tfd_categorical(
  probs = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE) %>% 
# Suppose additionally that on each day the temperature is
# normally distributed with mean and standard deviation 0 and 5 on
# a cold day and mean and standard deviation 15 and 10 on a hot day.
# We can model this with:
observation_distribution <- tfd_normal(loc = c(0, 15), scale = c(5, 10))
# We can combine these distributions into a single week long
# hidden Markov model with:
d <- tfd_hidden_markov_model(
  initial_distribution = initial_distribution,
  transition_distribution = transition_distribution,
  observation_distribution = observation_distribution,
  num_steps = 7
# The expected temperatures for each day are given by:
d %>% tfd_mean()  # shape [7], elements approach 9.0
# The log pdf of a week of temperature 0 is:
d %>% tfd_log_prob(rep(0, 7)) 


Bijectors are invertible transformations that allow to derive data likelihood under the transformed distribution from that under the base distribution. For an in-detail explanation, see Getting into the flow: Bijectors in TensorFlow Probability on the TensorFlow for R blog.

Affine bijector

# create an affine transformation that shifts by 3.33 and scales by 0.5
b <- tfb_affine_scalar(shift = 3.33, scale = 0.5)

# apply the transformation
x <- c(100, 1000, 10000)
b %>% tfb_forward(x)

Discrete cosine transform bijector

# create a bijector to that performs the discrete cosine transform (DCT)
b <- tfb_discrete_cosine_transform()

# run on sample data
x <- matrix(runif(3))
b %>% tfb_forward(x)

Keras layers

tfprobality wraps distributions in Keras layers so we can use them seemlessly in a neural network, and work with tensors as targets as usual. For example, we can use layer_kl_divergence_add_loss to have the network take care of the KL loss automatically, and train a variational autoencoder with just negative log likelihood only, like this:


encoded_size <- 2
input_shape <- c(2L, 2L, 1L)
train_size <- 100
x_train <- array(runif(train_size * Reduce(`*`, input_shape)), dim = c(train_size, input_shape))

# encoder is a keras sequential model
encoder_model <- keras_model_sequential() %>%
  layer_flatten(input_shape = input_shape) %>%
  layer_dense(units = 10, activation = "relu") %>%
  layer_dense(units = params_size_multivariate_normal_tri_l(encoded_size)) %>%
  layer_multivariate_normal_tri_l(event_size = encoded_size) %>%
  # last layer adds KL divergence loss
      distribution = tfd_independent(
        tfd_normal(loc = c(0, 0), scale = 1),
        reinterpreted_batch_ndims = 1
      weight = train_size)

# decoder is a keras sequential model
decoder_model <- keras_model_sequential() %>%
  layer_dense(units = 10,
              activation = 'relu',
              input_shape = encoded_size) %>%
  layer_dense(params_size_independent_bernoulli(input_shape)) %>%
  layer_independent_bernoulli(event_shape = input_shape,
                              convert_to_tensor_fn = tfp$distributions$Bernoulli$logits)

# keras functional model uniting them both
vae_model <- keras_model(inputs = encoder_model$inputs,
                         outputs = decoder_model(encoder_model$outputs[1]))

# VAE loss now is just log probability of the data
vae_loss <- function (x, rv_x)
    - (rv_x %>% tfd_log_prob(x))

vae_model %>% compile(
  optimizer = "adam",
  loss = vae_loss

vae_model %>% fit(x_train, x_train, batch_size = 25, epochs = 1)