# tfprobability: R interface to TensorFlow Probability

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.

## Installation

Install the released version of `tfprobability` from CRAN:

``install.packages("tfprobability")``

To install `tfprobability` from github, do

``devtools::install_github("rstudio/tfprobability")``

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

``````library(tfprobability)
install_tfprobability()``````

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.

## Usage

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.

``````library(tfprobability)
library(tensorflow)``````

### Distributions

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()
#> tf.Tensor(2.1000001, shape=(), dtype=float32)
# compute variance
d %>% tfd_variance()
#> tf.Tensor(1.47, shape=(), dtype=float32)
# compute probability
d %>% tfd_prob(2.3)
#> tf.Tensor(0.303791, shape=(), dtype=float32)``````

#### 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) %>%
tf\$cast(tf\$float32)
)
# 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
#> tf.Tensor([3.        6.        7.4999995 8.249999  8.625001  8.812501  8.90625  ], shape=(7), dtype=float32)
# The log pdf of a week of temperature 0 is:
d %>% tfd_log_prob(rep(0, 7))
#> tf.Tensor(-19.855635, shape=(), dtype=float32)``````

### Bijectors

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_shift(3.33)(tfb_scale(0.5))

# apply the transformation
x <- c(100, 1000, 10000)
b %>% tfb_forward(x)
#> tf.Tensor([  53.33  503.33 5003.33], shape=(3), dtype=float32)``````

#### 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)
#> tf.Tensor(
#> [[0.5221709 ]
#>  [0.5336635 ]
#>  [0.06735111]], shape=(3, 1), dtype=float32)``````

### 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:

``````library(keras)

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(
loss = vae_loss
)

vae_model
#> Model: "model"
#> ________________________________________________________________________________
#>  Layer (type)                       Output Shape                    Param #
#> ================================================================================
#>  flatten_input (InputLayer)         [(None, 2, 2, 1)]               0
#>  flatten (Flatten)                  (None, 4)                       0
#>  dense_1 (Dense)                    (None, 10)                      50
#>  dense (Dense)                      (None, 5)                       55
#>  multivariate_normal_tri_l (Multiva  ((None, 2),                    0
#>  riateNormalTriL)                    (None, 2))
#>  kl_divergence_add_loss (KLDivergen  (None, 2)                      0