Joint distribution parameterized by distribution-making functions

This distribution enables both sampling and joint probability computation from a single model specification.

tfd_joint_distribution_sequential(model, validate_args = FALSE, name = NULL)

Arguments

model	list of either tfp$distributions$Distribution instances and/or functions which take the k previous distributions and returns a new tfp$distributions$Distribution instance.
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.
name	name prefixed to Ops created by this class.

Value

a distribution instance.

Details

A joint distribution is a collection of possibly interdependent distributions. Like tf$keras$Sequential, the JointDistributionSequential can be specified via a list of functions (each responsible for making a tfp$distributions$Distribution-like instance). Unlike tf$keras$Sequential, each function can depend on the output of all previous elements rather than only the immediately previous.

Mathematical Details

The JointDistributionSequential implements the chain rule of probability.

That is, the probability function of a length-d vector x is,

p(x) = prod{ p(x[i] | x[:i]) : i = 0, ..., (d - 1) }

The JointDistributionSequential is parameterized by a list comprised of either:

1. tfp$distributions$Distribution-like instances or,

2. callables which return a tfp$distributions$Distribution-like instance. Each list element implements the i-th full conditional distribution, p(x[i] | x[:i]). The "conditioned on" elements are represented by the callable's required arguments. Directly providing a Distribution-like nstance is a convenience and is semantically identical a zero argument callable. Denote the i-th callables non-default arguments as args[i]. Since the callable is the conditional manifest, 0 <= len(args[i]) <= i - 1. When len(args[i]) < i - 1, the callable only depends on a subset of the previous distributions, specifically those at indexes: range(i - 1, i - 1 - num_args[i], -1).

Name resolution: The names of JointDistributionSequentialcomponents are defined by explicitname arguments passed to distributions (tfd.Normal(0., 1., name='x')) and/or by the argument names in distribution-making functions (lambda x: tfd.Normal(x., 1.)). Both approaches may be used in the same distribution, as long as they are consistent; referring to a single component by multiple names will raise a ValueError`. Unnamed components will be assigned a dummy name.

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_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_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()