ComputesY = g(X) s.t. X = g^-1(Y) = (Y - mean(Y)) / std(Y)

Applies Batch Normalization (Ioffe and Szegedy, 2015) to samples from a data distribution. This can be used to stabilize training of normalizing flows (Papamakarios et al., 2016; Dinh et al., 2017)

tfb_batch_normalization(
  batchnorm_layer = NULL,
  training = TRUE,
  validate_args = FALSE,
  name = "batch_normalization"
)

Arguments

batchnorm_layer	tf$layers$BatchNormalization layer object. If NULL, defaults to tf$layers$BatchNormalization(gamma_constraint=tf$nn$relu(x) + 1e-6). This ensures positivity of the scale variable.
training	If TRUE, updates running-average statistics during call to inverse().
validate_args	Logical, default FALSE. Whether to validate input with asserts. If validate_args is FALSE, and the inputs are invalid, correct behavior is not guaranteed.
name	name prefixed to Ops created by this class.

Value

a bijector instance.

Details

When training Deep Neural Networks (DNNs), it is common practice to normalize or whiten features by shifting them to have zero mean and scaling them to have unit variance.

The inverse() method of the BatchNormalization bijector, which is used in the log-likelihood computation of data samples, implements the normalization procedure (shift-and-scale) using the mean and standard deviation of the current minibatch.

Conversely, the forward() method of the bijector de-normalizes samples (e.g. X*std(Y) + mean(Y) with the running-average mean and standard deviation computed at training-time. De-normalization is useful for sampling.

During training time, BatchNormalization.inverse and BatchNormalization.forward are not guaranteed to be inverses of each other because inverse(y) uses statistics of the current minibatch, while forward(x) uses running-average statistics accumulated from training. In other words, tfb_batch_normalization()$inverse(tfb_batch_normalization()$forward(...)) and tfb_batch_normalization()$forward(tfb_batch_normalization()$inverse(...)) will be identical when training=FALSE but may be different when training=TRUE.

References

• Sergey Ioffe and Christian Szegedy. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. In International Conference on Machine Learning, 2015.

• Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio. Density Estimation using Real NVP. In International Conference on Learning Representations, 2017.

• George Papamakarios, Theo Pavlakou, and Iain Murray. Masked Autoregressive Flow for Density Estimation. In Neural Information Processing Systems, 2017.

See also

For usage examples see tfb_forward(), tfb_inverse(), tfb_inverse_log_det_jacobian().

Other bijectors: tfb_absolute_value(), tfb_affine_linear_operator(), tfb_affine_scalar(), tfb_affine(), tfb_ascending(), tfb_blockwise(), tfb_chain(), tfb_cholesky_outer_product(), tfb_cholesky_to_inv_cholesky(), tfb_correlation_cholesky(), tfb_cumsum(), tfb_discrete_cosine_transform(), tfb_expm1(), tfb_exp(), tfb_ffjord(), tfb_fill_scale_tri_l(), tfb_fill_triangular(), tfb_glow(), tfb_gompertz_cdf(), tfb_gumbel_cdf(), tfb_gumbel(), tfb_identity(), tfb_inline(), tfb_invert(), tfb_iterated_sigmoid_centered(), tfb_kumaraswamy_cdf(), tfb_kumaraswamy(), tfb_lambert_w_tail(), tfb_masked_autoregressive_default_template(), tfb_masked_autoregressive_flow(), tfb_masked_dense(), tfb_matrix_inverse_tri_l(), tfb_matvec_lu(), tfb_normal_cdf(), tfb_ordered(), tfb_pad(), tfb_permute(), tfb_power_transform(), tfb_rational_quadratic_spline(), tfb_rayleigh_cdf(), tfb_real_nvp_default_template(), tfb_real_nvp(), tfb_reciprocal(), tfb_reshape(), tfb_scale_matvec_diag(), tfb_scale_matvec_linear_operator(), tfb_scale_matvec_lu(), tfb_scale_matvec_tri_l(), tfb_scale_tri_l(), tfb_scale(), tfb_shifted_gompertz_cdf(), tfb_shift(), tfb_sigmoid(), tfb_sinh_arcsinh(), tfb_sinh(), tfb_softmax_centered(), tfb_softplus(), tfb_softsign(), tfb_split(), tfb_square(), tfb_tanh(), tfb_transform_diagonal(), tfb_transpose(), tfb_weibull_cdf(), tfb_weibull()