The HiddenMarkovModel distribution implements a (batch of) hidden Markov models where the initial states, transition probabilities and observed states are all given by user-provided distributions.

tfd_hidden_markov_model(
initial_distribution,
transition_distribution,
observation_distribution,
num_steps,
validate_args = FALSE,
allow_nan_stats = TRUE,
name = "HiddenMarkovModel"
)

## Arguments

initial_distribution A Categorical-like instance. Determines probability of first hidden state in Markov chain. The number of categories must match the number of categories of transition_distribution as well as both the rightmost batch dimension of transition_distribution and the rightmost batch dimension of observation_distribution. A Categorical-like instance. The rightmost batch dimension indexes the probability distribution of each hidden state conditioned on the previous hidden state. A tfp$distributions$Distribution-like instance. The rightmost batch dimension indexes the distribution of each observation conditioned on the corresponding hidden state. The number of steps taken in Markov chain. An integer. 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. 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 prefixed to Ops created by this class.

## Value

a distribution instance.

## Details

This model assumes that the transition matrices are fixed over time. In this model, there is a sequence of integer-valued hidden states: z[0], z[1], ..., z[num_steps - 1] and a sequence of observed states: x[0], ..., x[num_steps - 1].

The distribution of z[0] is given by initial_distribution. The conditional probability of z[i + 1] given z[i] is described by the batch of distributions in transition_distribution. For a batch of hidden Markov models, the coordinates before the rightmost one of the transition_distribution batch correspond to indices into the hidden Markov model batch. The rightmost coordinate of the batch is used to select which distribution z[i + 1] is drawn from. The distributions corresponding to the probability of z[i + 1] conditional on z[i] == k is given by the elements of the batch whose rightmost coordinate is k.

Similarly, the conditional distribution of z[i] given x[i] is given by the batch of observation_distribution. When the rightmost coordinate of observation_distribution is k it gives the conditional probabilities of x[i] given z[i] == k. The probability distribution associated with the HiddenMarkovModel distribution is the marginal distribution of x[0],...,x[num_steps - 1].

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_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()