The so-called 'horseshoe' distribution is a Cauchy-Normal scale mixture,
proposed as a sparsity-inducing prior for Bayesian regression. It is
symmetric around zero, has heavy (Cauchy-like) tails, so that large
coefficients face relatively little shrinkage, but an infinitely tall spike at
0, which pushes small coefficients towards zero. It is parameterized by a
positive scalar scale parameter: higher values yield a weaker
sparsity-inducing effect.
tfd_horseshoe( scale, validate_args = FALSE, allow_nan_stats = TRUE, name = "Horseshoe" )
| scale | Floating point tensor; the scales of the distribution(s). Must contain only positive values. |
|---|---|
| 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. |
a distribution instance.
Mathematical details
The Horseshoe distribution is centered at zero, with scale parameter $lambda$. It is defined by:
horseshoe(scale = lambda) ~ Normal(0, lamda * sigma)
where sigma ~ half_cauchy(0, 1)
Carvalho, Polson, Scott. Handling Sparsity via the Horseshoe (2008).
Barry, Parlange, Li. Approximation for the exponential integral (2000).
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_exp_inverse_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_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()