tfd_lkj: LKJ distribution on correlation matrices
In tfprobability: Interface to 'TensorFlow Probability'

tfd_lkj

R Documentation

LKJ distribution on correlation matrices

Description

This is a one-parameter of distributions on correlation matrices. The probability density is proportional to the determinant raised to the power of the parameter: pdf(X; eta) = Z(eta) * det(X) ** (eta - 1), where Z(eta) is a normalization constant. The uniform distribution on correlation matrices is the special case eta = 1.

Usage

tfd_lkj(
  dimension,
  concentration,
  input_output_cholesky = FALSE,
  validate_args = FALSE,
  allow_nan_stats = TRUE,
  name = "LKJ"
)

Arguments

`dimension`	`integer`. The dimension of the correlation matrices to sample.
`concentration`	`float` or `double` `Tensor`. The positive concentration parameter of the LKJ distributions. The pdf of a sample matrix `X` is proportional to `det(X) ** (concentration - 1)`.
`input_output_cholesky`	`Logical`. If `TRUE`, functions whose input or output have the semantics of samples assume inputs are in Cholesky form and return outputs in Cholesky form. In particular, if this flag is `TRUE`, input to `log_prob` is presumed of Cholesky form and output from `sample` is of Cholesky form. Setting this argument to `TRUE` is purely a computational optimization and does not change the underlying distribution. Additionally, validation checks which are only defined on the multiplied-out form are omitted, even if `validate_args` is `TRUE`. Default value: `FALSE` (i.e., input/output does not have Cholesky semantics).
`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

The distribution is named after Lewandowski, Kurowicka, and Joe, who gave a sampler for the distribution in Lewandowski, Kurowicka, Joe, 2009.

Value

a distribution instance.

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_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_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()