tfd_exp_inverse_gamma {tfprobability}

ExpInverseGamma distribution.

Description

The ExpInverseGamma distribution is defined over the real numbers such that X ~ ExpInverseGamma(..) => exp(X) ~ InverseGamma(..). The distribution is logically equivalent to tfb_log()(tfd_inverse_gamma(..)), but can be sampled with much better precision.

Usage

tfd_exp_inverse_gamma(
  concentration,
  scale = NULL,
  log_scale = NULL,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "ExpGamma"
)

Arguments

concentration

Floating point tensor, the concentration params of the distribution(s). Must contain only positive values.

scale

Floating point tensor, the scale params of the distribution(s). Must contain only positive values. Mutually exclusive with log_scale.

log_scale

Floating point tensor, the natural logarithm of the scale params of the distribution(s). Mutually exclusive with scale.

validate_args

Logical, default FALSE. When TRUE distribution parameters are checked for validity despite possibly degrading runtime performance. When FALSE invalid inputs may silently render incorrect outputs. Default value: FALSE.

allow_nan_stats

Logical, default TRUE. When TRUE, statistics (e.g., mean, mode, variance) use the value NaN to indicate the result is undefined. When FALSE, an exception is raised if one or more of the statistic's batch members are undefined.

name

name prefixed to Ops created by this class.

Details

Mathematical Details

The probability density function (pdf) is very similar to ExpGamma,

pdf(x; alpha, beta > 0) = exp(-x)**(alpha - 1) exp(-exp(-x) beta) / Z - x
Z = Gamma(alpha) beta**(-alpha)

where:

• concentration = alpha,

• scale = beta,

• Z is the normalizing constant, and,

• Gamma is the gamma function.

The cumulative density function (cdf) is,

cdf(x; alpha, beta, x) = 1 - GammaInc(alpha, beta exp(-x)) / Gamma(alpha)

where GammaInc is the upper incomplete Gamma function.

Distribution parameters are automatically broadcast in all functions. Samples of this distribution are reparameterized (pathwise differentiable). The derivatives are computed using the approach described in Figurnov et al, 2018.

Value

a distribution instance.

References

• Michael Figurnov, Shakir Mohamed, Andriy Mnih. Implicit Reparameterization Gradients. arXiv preprint arXiv:1805.08498, 2018.

See Also

For usage examples see e.g. tfd_sample(), tfd_log_prob(), tfd_mean().

Other distributions: tfd_autoregressive(), tfd_batch_reshape(), tfd_bates(), tfd_bernoulli(), tfd_beta_binomial(), tfd_beta(), tfd_binomial(), tfd_categorical(), tfd_cauchy(), tfd_chi2(), tfd_chi(), tfd_cholesky_lkj(), tfd_continuous_bernoulli(), tfd_deterministic(), tfd_dirichlet_multinomial(), tfd_dirichlet(), tfd_empirical(), tfd_exp_gamma(), tfd_exponential(), tfd_gamma_gamma(), tfd_gamma(), tfd_gaussian_process_regression_model(), tfd_gaussian_process(), tfd_generalized_normal(), tfd_geometric(), tfd_gumbel(), tfd_half_cauchy(), tfd_half_normal(), tfd_hidden_markov_model(), tfd_horseshoe(), tfd_independent(), tfd_inverse_gamma(), tfd_inverse_gaussian(), tfd_johnson_s_u(), tfd_joint_distribution_named_auto_batched(), tfd_joint_distribution_named(), tfd_joint_distribution_sequential_auto_batched(), tfd_joint_distribution_sequential(), tfd_kumaraswamy(), tfd_laplace(), tfd_linear_gaussian_state_space_model(), tfd_lkj(), tfd_log_logistic(), tfd_log_normal(), tfd_logistic(), tfd_mixture_same_family(), tfd_mixture(), tfd_multinomial(), tfd_multivariate_normal_diag_plus_low_rank(), tfd_multivariate_normal_diag(), tfd_multivariate_normal_full_covariance(), tfd_multivariate_normal_linear_operator(), tfd_multivariate_normal_tri_l(), tfd_multivariate_student_t_linear_operator(), tfd_negative_binomial(), tfd_normal(), tfd_one_hot_categorical(), tfd_pareto(), tfd_pixel_cnn(), tfd_poisson_log_normal_quadrature_compound(), tfd_poisson(), tfd_power_spherical(), tfd_probit_bernoulli(), tfd_quantized(), tfd_relaxed_bernoulli(), tfd_relaxed_one_hot_categorical(), tfd_sample_distribution(), tfd_sinh_arcsinh(), tfd_skellam(), tfd_spherical_uniform(), tfd_student_t_process(), tfd_student_t(), tfd_transformed_distribution(), tfd_triangular(), tfd_truncated_cauchy(), tfd_truncated_normal(), tfd_uniform(), tfd_variational_gaussian_process(), tfd_vector_diffeomixture(), tfd_vector_exponential_diag(), tfd_vector_exponential_linear_operator(), tfd_vector_laplace_diag(), tfd_vector_laplace_linear_operator(), tfd_vector_sinh_arcsinh_diag(), tfd_von_mises_fisher(), tfd_von_mises(), tfd_weibull(), tfd_wishart_linear_operator(), tfd_wishart_tri_l(), tfd_wishart(), tfd_zipf()