Markov chain Monte Carlo (MCMC) methods are considered the gold standard of Bayesian inference; under suitable conditions and in the limit of infinitely many draws they generate samples from the true posterior distribution. HMC (Neal, 2011) uses gradients of the model's log-density function to propose samples, allowing it to exploit posterior geometry. However, it is computationally more expensive than variational inference and relatively sensitive to tuning.
sts_fit_with_hmc(
observed_time_series,
model,
num_results = 100,
num_warmup_steps = 50,
num_leapfrog_steps = 15,
initial_state = NULL,
initial_step_size = NULL,
chain_batch_shape = list(),
num_variational_steps = 150,
variational_optimizer = NULL,
variational_sample_size = 5,
seed = NULL,
name = NULL
)list of:
samples: list of Tensors representing posterior samples of model
parameters, with shapes [concat([[num_results], chain_batch_shape, param.prior.batch_shape, param.prior.event_shape]) for param in model.parameters].
kernel_results: A (possibly nested) list of Tensors representing
internal calculations made within the HMC sampler.
float tensor of shape
concat([sample_shape, model.batch_shape, [num_timesteps, 1]]) where
sample_shape corresponds to i.i.d. observations, and the trailing [1]
dimension may (optionally) be omitted if num_timesteps > 1. May
optionally be an instance of sts_masked_time_series, which includes
a mask tensor to specify timesteps with missing observations.
An instance of StructuralTimeSeries representing a
time-series model. This represents a joint distribution over
time-series and their parameters with batch shape [b1, ..., bN].
Integer number of Markov chain draws. Default value: 100.
Integer number of steps to take before starting to
collect results. The warmup steps are also used to adapt the step size
towards a target acceptance rate of 0.75. Default value: 50.
Integer number of steps to run the leapfrog integrator
for. Total progress per HMC step is roughly proportional to step_size * num_leapfrog_steps.
Default value: 15.
Optional Python list of Tensors, one for each model
parameter, representing the initial state(s) of the Markov chain(s). These
should have shape tf$concat(list(chain_batch_shape, param$prior$batch_shape, param$prior$event_shape)).
If NULL, the initial state is set automatically using a sample from a variational posterior.
Default value: NULL.
list of tensors, one for each model parameter,
representing the step size for the leapfrog integrator. Must
broadcast with the shape of initial_state. Larger step sizes lead to
faster progress, but too-large step sizes make rejection exponentially
more likely. If NULL, the step size is set automatically using the
standard deviation of a variational posterior. Default value: NULL.
Batch shape (list or int) of chains to run in parallel.
Default value: list() (i.e., a single chain).
int number of steps to run the variational
optimization to determine the initial state and step sizes. Default value: 150.
Optional tf$train$Optimizer instance to use in
the variational optimization. If NULL, defaults to tf$train$AdamOptimizer(0.1).
Default value: NULL.
integer number of Monte Carlo samples to use
in estimating the variational divergence. Larger values may stabilize
the optimization, but at higher cost per step in time and memory.
Default value: 1.
integer to seed the random number generator.
name prefixed to ops created by this function. Default value: NULL (i.e., 'fit_with_hmc').
This method attempts to provide a sensible default approach for fitting StructuralTimeSeries models using HMC. It first runs variational inference as a fast posterior approximation, and initializes the HMC sampler from the variational posterior, using the posterior standard deviations to set per-variable step sizes (equivalently, a diagonal mass matrix). During the warmup phase, it adapts the step size to target an acceptance rate of 0.75, which is thought to be in the desirable range for optimal mixing (Betancourt et al., 2014).
Other sts-functions:
sts_build_factored_surrogate_posterior(),
sts_build_factored_variational_loss(),
sts_decompose_by_component(),
sts_decompose_forecast_by_component(),
sts_forecast(),
sts_one_step_predictive(),
sts_sample_uniform_initial_state()
# \donttest{
observed_time_series <-
rep(c(3.5, 4.1, 4.5, 3.9, 2.4, 2.1, 1.2), 5) +
rep(c(1.1, 1.5, 2.4, 3.1, 4.0), each = 7) %>%
tensorflow::tf$convert_to_tensor(dtype = tensorflow::tf$float64)
day_of_week <- observed_time_series %>% sts_seasonal(num_seasons = 7)
local_linear_trend <- observed_time_series %>% sts_local_linear_trend()
model <- observed_time_series %>%
sts_sum(components = list(day_of_week, local_linear_trend))
states_and_results <- observed_time_series %>%
sts_fit_with_hmc(
model,
num_results = 10,
num_warmup_steps = 5,
num_variational_steps = 15)
# }
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