The $optimize() method of a CmdStanModel object runs Stan's optimizer to obtain a posterior mode (penalized maximum likelihood) estimate.

Any argument left as NULL will default to the default value used by the installed version of CmdStan. See the CmdStan User’s Guide for more details.

optimize(
  data = NULL,
  seed = NULL,
  refresh = NULL,
  init = NULL,
  save_latent_dynamics = FALSE,
  output_dir = NULL,
  sig_figs = NULL,
  threads = NULL,
  algorithm = NULL,
  init_alpha = NULL,
  iter = NULL,
  tol_obj = NULL,
  tol_rel_obj = NULL,
  tol_grad = NULL,
  tol_rel_grad = NULL,
  tol_param = NULL,
  history_size = NULL
)

Arguments

data

(multiple options) The data to use for the variables specified in the data block of the Stan program. One of the following:

  • A named list of R objects (like for RStan). Internally this list is then written to JSON for CmdStan using write_stan_json().

  • A path to a data file compatible with CmdStan (JSON or R dump). See the appendices in the CmdStan manual for details on using these formats.

  • NULL or an empty list if the Stan program has no data block.

seed

(positive integer) A seed for the (P)RNG to pass to CmdStan.

refresh

(non-negative integer) The number of iterations between printed screen updates. If refresh = 0, only error messages will be printed.

init

(multiple options) The initialization method to use for the variables declared in the parameters block of the Stan program:

  • A real number x>0. This initializes all parameters randomly between [-x,x] (on the unconstrained parameter space);

  • The number 0. This initializes all parameters to 0;

  • A character vector of paths (one per chain) to JSON or Rdump files containing initial values for all or some parameters. See write_stan_json() to write R objects to JSON files compatible with CmdStan.

  • A list of lists containing initial values for all or some parameters. For MCMC the list should contain a sublist for each chain. For optimization and variational inference there should be just one sublist. The sublists should have named elements corresponding to the parameters for which you are specifying initial values. See Examples.

  • A function that returns a single list with names corresponding to the parameters for which you are specifying initial values. The function can take no arguments or a single argument chain_id. For MCMC, if the function has argument chain_id it will be supplied with the chain id (from 1 to number of chains) when called to generate the initial values. See Examples.

save_latent_dynamics

(logical) Should auxiliary diagnostic information about the latent dynamics be written to temporary diagnostic CSV files? This argument replaces CmdStan's diagnostic_file argument and the content written to CSV is controlled by the user's CmdStan installation and not CmdStanR (for some algorithms no content may be written). The default is FALSE, which is appropriate for almost every use case. To save the temporary files created when save_latent_dynamics=TRUE see the $save_latent_dynamics_files() method.

output_dir

(string) A path to a directory where CmdStan should write its output CSV files. For interactive use this can typically be left at NULL (temporary directory) since CmdStanR makes the CmdStan output (posterior draws and diagnostics) available in R via methods of the fitted model objects. The behavior of output_dir is as follows:

  • If NULL (the default), then the CSV files are written to a temporary directory and only saved permanently if the user calls one of the $save_* methods of the fitted model object (e.g., $save_output_files()). These temporary files are removed when the fitted model object is garbage collected (manually or automatically).

  • If a path, then the files are created in output_dir with names corresponding to the defaults used by $save_output_files().

sig_figs

(positive integer) The number of significant figures used when storing the output values. By default, CmdStan represent the output values with 6 significant figures. The upper limit for sig_figs is 18. Increasing this value will result in larger output CSV files and thus an increased usage of disk space.

threads

(positive integer) If the model was compiled with threading support, the number of threads to use in parallelized sections (e.g., when using the Stan functions reduce_sum() or map_rect()).

algorithm

(string) The optimization algorithm. One of "lbfgs", "bfgs", or "newton". The control parameters below are only available for "lbfgs" and "bfgs. For their default values and more details see the CmdStan User's Guide. The default values can also be obtained by running cmdstanr_example(method="optimize")$metadata().

init_alpha

(positive real) The initial step size parameter.

iter

(positive integer) The maximum number of iterations.

tol_obj

(positive real) Convergence tolerance on changes in objective function value.

tol_rel_obj

(positive real) Convergence tolerance on relative changes in objective function value.

tol_grad

(positive real) Convergence tolerance on the norm of the gradient.

tol_rel_grad

(positive real) Convergence tolerance on the relative norm of the gradient.

tol_param

(positive real) Convergence tolerance on changes in parameter value.

history_size

(positive integer) The size of the history used when approximating the Hessian. Only available for L-BFGS.

Details

CmdStan can find the posterior mode (assuming there is one). If the posterior is not convex, there is no guarantee Stan will be able to find the global mode as opposed to a local optimum of log probability. For optimization, the mode is calculated without the Jacobian adjustment for constrained variables, which shifts the mode due to the change of variables. Thus modes correspond to modes of the model as written.

-- CmdStan User's Guide

Value

A CmdStanMLE object.

See also

The CmdStanR website (mc-stan.org/cmdstanr) for online documentation and tutorials.

The Stan and CmdStan documentation:

Other CmdStanModel methods: model-method-check_syntax, model-method-compile, model-method-generate-quantities, model-method-sample_mpi, model-method-sample, model-method-variational

Examples

# \dontrun{ library(cmdstanr) library(posterior) library(bayesplot) color_scheme_set("brightblue") # Set path to cmdstan # (Note: if you installed CmdStan via install_cmdstan() with default settings # then setting the path is unnecessary but the default below should still work. # Otherwise use the `path` argument to specify the location of your # CmdStan installation.) set_cmdstan_path(path = NULL)
#> CmdStan path set to: /Users/jgabry/.cmdstanr/cmdstan-2.25.0
# Create a CmdStanModel object from a Stan program, # here using the example model that comes with CmdStan file <- file.path(cmdstan_path(), "examples/bernoulli/bernoulli.stan") mod <- cmdstan_model(file)
#> Model executable is up to date!
mod$print()
#> data { #> int<lower=0> N; #> int<lower=0,upper=1> y[N]; #> } #> parameters { #> real<lower=0,upper=1> theta; #> } #> model { #> theta ~ beta(1,1); // uniform prior on interval 0,1 #> y ~ bernoulli(theta); #> }
# Data as a named list (like RStan) stan_data <- list(N = 10, y = c(0,1,0,0,0,0,0,0,0,1)) # Run MCMC using the 'sample' method fit_mcmc <- mod$sample( data = stan_data, seed = 123, chains = 2, parallel_chains = 2 )
#> Running MCMC with 2 parallel chains... #> #> Chain 1 Iteration: 1 / 2000 [ 0%] (Warmup) #> Chain 1 Iteration: 100 / 2000 [ 5%] (Warmup) #> Chain 1 Iteration: 200 / 2000 [ 10%] (Warmup) #> Chain 1 Iteration: 300 / 2000 [ 15%] (Warmup) #> Chain 1 Iteration: 400 / 2000 [ 20%] (Warmup) #> Chain 1 Iteration: 500 / 2000 [ 25%] (Warmup) #> Chain 1 Iteration: 600 / 2000 [ 30%] (Warmup) #> Chain 1 Iteration: 700 / 2000 [ 35%] (Warmup) #> Chain 1 Iteration: 800 / 2000 [ 40%] (Warmup) #> Chain 1 Iteration: 900 / 2000 [ 45%] (Warmup) #> Chain 1 Iteration: 1000 / 2000 [ 50%] (Warmup) #> Chain 1 Iteration: 1001 / 2000 [ 50%] (Sampling) #> Chain 1 Iteration: 1100 / 2000 [ 55%] (Sampling) #> Chain 1 Iteration: 1200 / 2000 [ 60%] (Sampling) #> Chain 1 Iteration: 1300 / 2000 [ 65%] (Sampling) #> Chain 1 Iteration: 1400 / 2000 [ 70%] (Sampling) #> Chain 1 Iteration: 1500 / 2000 [ 75%] (Sampling) #> Chain 1 Iteration: 1600 / 2000 [ 80%] (Sampling) #> Chain 1 Iteration: 1700 / 2000 [ 85%] (Sampling) #> Chain 1 Iteration: 1800 / 2000 [ 90%] (Sampling) #> Chain 1 Iteration: 1900 / 2000 [ 95%] (Sampling) #> Chain 1 Iteration: 2000 / 2000 [100%] (Sampling) #> Chain 2 Iteration: 1 / 2000 [ 0%] (Warmup) #> Chain 2 Iteration: 100 / 2000 [ 5%] (Warmup) #> Chain 2 Iteration: 200 / 2000 [ 10%] (Warmup) #> Chain 2 Iteration: 300 / 2000 [ 15%] (Warmup) #> Chain 2 Iteration: 400 / 2000 [ 20%] (Warmup) #> Chain 2 Iteration: 500 / 2000 [ 25%] (Warmup) #> Chain 2 Iteration: 600 / 2000 [ 30%] (Warmup) #> Chain 2 Iteration: 700 / 2000 [ 35%] (Warmup) #> Chain 2 Iteration: 800 / 2000 [ 40%] (Warmup) #> Chain 2 Iteration: 900 / 2000 [ 45%] (Warmup) #> Chain 2 Iteration: 1000 / 2000 [ 50%] (Warmup) #> Chain 2 Iteration: 1001 / 2000 [ 50%] (Sampling) #> Chain 2 Iteration: 1100 / 2000 [ 55%] (Sampling) #> Chain 2 Iteration: 1200 / 2000 [ 60%] (Sampling) #> Chain 2 Iteration: 1300 / 2000 [ 65%] (Sampling) #> Chain 2 Iteration: 1400 / 2000 [ 70%] (Sampling) #> Chain 2 Iteration: 1500 / 2000 [ 75%] (Sampling) #> Chain 2 Iteration: 1600 / 2000 [ 80%] (Sampling) #> Chain 2 Iteration: 1700 / 2000 [ 85%] (Sampling) #> Chain 2 Iteration: 1800 / 2000 [ 90%] (Sampling) #> Chain 2 Iteration: 1900 / 2000 [ 95%] (Sampling) #> Chain 2 Iteration: 2000 / 2000 [100%] (Sampling) #> Chain 1 finished in 0.0 seconds. #> Chain 2 finished in 0.0 seconds. #> #> Both chains finished successfully. #> Mean chain execution time: 0.0 seconds. #> Total execution time: 0.1 seconds.
# Use 'posterior' package for summaries fit_mcmc$summary()
#> # A tibble: 2 x 10 #> variable mean median sd mad q5 q95 rhat ess_bulk ess_tail #> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> #> 1 lp__ -7.28 -7.00 0.739 0.342 -8.80 -6.75 1.00 815. 621. #> 2 theta 0.254 0.235 0.123 0.123 0.0809 0.485 1.00 752. 589.
# Get posterior draws draws <- fit_mcmc$draws() print(draws)
#> # A draws_array: 1000 iterations, 2 chains, and 2 variables #> , , variable = lp__ #> #> chain #> iteration 1 2 #> 1 -6.8 -6.8 #> 2 -7.3 -6.8 #> 3 -7.1 -7.0 #> 4 -7.1 -8.5 #> 5 -7.1 -7.8 #> #> , , variable = theta #> #> chain #> iteration 1 2 #> 1 0.30 0.230 #> 2 0.13 0.199 #> 3 0.16 0.165 #> 4 0.37 0.074 #> 5 0.15 0.103 #> #> # ... with 995 more iterations
# Convert to data frame using posterior::as_draws_df as_draws_df(draws)
#> # A draws_df: 1000 iterations, 2 chains, and 2 variables #> lp__ theta #> 1 -6.8 0.30 #> 2 -7.3 0.13 #> 3 -7.1 0.16 #> 4 -7.1 0.37 #> 5 -7.1 0.15 #> 6 -7.5 0.12 #> 7 -7.2 0.38 #> 8 -6.8 0.22 #> 9 -7.0 0.34 #> 10 -6.8 0.22 #> # ... with 1990 more draws #> # ... hidden reserved variables {'.chain', '.iteration', '.draw'}
# Plot posterior using bayesplot (ggplot2) mcmc_hist(fit_mcmc$draws("theta"))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# Call CmdStan's diagnose and stansummary utilities fit_mcmc$cmdstan_diagnose()
#> Processing csv files: /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpGraDrG/bernoulli-202012171339-1-29cea2.csv, /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpGraDrG/bernoulli-202012171339-2-29cea2.csv #> #> Checking sampler transitions treedepth. #> Treedepth satisfactory for all transitions. #> #> Checking sampler transitions for divergences. #> No divergent transitions found. #> #> Checking E-BFMI - sampler transitions HMC potential energy. #> E-BFMI satisfactory for all transitions. #> #> Effective sample size satisfactory. #> #> Split R-hat values satisfactory all parameters. #> #> Processing complete, no problems detected.
fit_mcmc$cmdstan_summary()
#> Input files: /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpGraDrG/bernoulli-202012171339-1-29cea2.csv, /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpGraDrG/bernoulli-202012171339-2-29cea2.csv #> Inference for Stan model: bernoulli_model #> 2 chains: each with iter=(1000,1000); warmup=(0,0); thin=(1,1); 2000 iterations saved. #> #> Warmup took (0.0080, 0.0080) seconds, 0.016 seconds total #> Sampling took (0.022, 0.020) seconds, 0.042 seconds total #> #> Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat #> #> lp__ -7.3 3.1e-02 0.74 -8.8 -7.0 -6.8 586 13956 1.0 #> accept_stat__ 0.92 5.0e-03 0.14 0.61 0.97 1.0 7.3e+02 1.7e+04 1.0e+00 #> stepsize__ 1.0 9.0e-02 0.090 0.93 1.1 1.1 1.0e+00 2.4e+01 2.6e+13 #> treedepth__ 1.4 1.2e-02 0.52 1.0 1.0 2.0 1.9e+03 4.4e+04 1.0e+00 #> n_leapfrog__ 2.6 4.0e-01 1.5 1.0 3.0 7.0 1.4e+01 3.3e+02 1.0e+00 #> divergent__ 0.00 nan 0.00 0.00 0.00 0.00 nan nan nan #> energy__ 7.8 4.0e-02 1.0 6.8 7.4 10.0 6.9e+02 1.6e+04 1.0e+00 #> #> theta 0.25 4.5e-03 0.12 0.081 0.23 0.49 755 17981 1.00 #> #> Samples were drawn using hmc with nuts. #> For each parameter, N_Eff is a crude measure of effective sample size, #> and R_hat is the potential scale reduction factor on split chains (at #> convergence, R_hat=1).
# For models fit using MCMC, if you like working with RStan's stanfit objects # then you can create one with rstan::read_stan_csv() # stanfit <- rstan::read_stan_csv(fit_mcmc$output_files()) # Run 'optimize' method to get a point estimate (default is Stan's LBFGS algorithm) # and also demonstrate specifying data as a path to a file instead of a list my_data_file <- file.path(cmdstan_path(), "examples/bernoulli/bernoulli.data.json") fit_optim <- mod$optimize(data = my_data_file, seed = 123)
#> Initial log joint probability = -9.51104 #> Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes #> 6 -5.00402 0.000103557 2.55661e-07 1 1 9 #> Optimization terminated normally: #> Convergence detected: relative gradient magnitude is below tolerance #> Finished in 0.1 seconds.
fit_optim$summary()
#> # A tibble: 2 x 2 #> variable estimate #> <chr> <dbl> #> 1 lp__ -5.00 #> 2 theta 0.2
# Run 'variational' method to approximate the posterior (default is meanfield ADVI) fit_vb <- mod$variational(data = stan_data, seed = 123)
#> ------------------------------------------------------------ #> EXPERIMENTAL ALGORITHM: #> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ #> Gradient evaluation took 1.7e-05 seconds #> 1000 transitions using 10 leapfrog steps per transition would take 0.17 seconds. #> Adjust your expectations accordingly! #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) #> Iteration: 50 / 250 [ 20%] (Adaptation) #> Iteration: 100 / 250 [ 40%] (Adaptation) #> Iteration: 150 / 250 [ 60%] (Adaptation) #> Iteration: 200 / 250 [ 80%] (Adaptation) #> Success! Found best value [eta = 1] earlier than expected. #> Begin stochastic gradient ascent. #> iter ELBO delta_ELBO_mean delta_ELBO_med notes #> 100 -6.262 1.000 1.000 #> 200 -6.263 0.500 1.000 #> 300 -6.307 0.336 0.007 MEDIAN ELBO CONVERGED #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED. #> Finished in 0.1 seconds.
fit_vb$summary()
#> # A tibble: 3 x 7 #> variable mean median sd mad q5 q95 #> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> #> 1 lp__ -7.18 -6.94 0.588 0.259 -8.36 -6.75 #> 2 lp_approx__ -0.515 -0.221 0.692 0.303 -2.06 -0.00257 #> 3 theta 0.263 0.246 0.115 0.113 0.106 0.481
# Plot approximate posterior using bayesplot mcmc_hist(fit_vb$draws("theta"))
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
# Specifying initial values as a function fit_mcmc_w_init_fun <- mod$sample( data = stan_data, seed = 123, chains = 2, refresh = 0, init = function() list(theta = runif(1)) )
#> Running MCMC with 2 sequential chains... #> #> Chain 1 finished in 0.0 seconds. #> Chain 2 finished in 0.0 seconds. #> #> Both chains finished successfully. #> Mean chain execution time: 0.0 seconds. #> Total execution time: 0.2 seconds.
fit_mcmc_w_init_fun_2 <- mod$sample( data = stan_data, seed = 123, chains = 2, refresh = 0, init = function(chain_id) { # silly but demonstrates optional use of chain_id list(theta = 1 / (chain_id + 1)) } )
#> Running MCMC with 2 sequential chains... #> #> Chain 1 finished in 0.0 seconds. #> Chain 2 finished in 0.0 seconds. #> #> Both chains finished successfully. #> Mean chain execution time: 0.0 seconds. #> Total execution time: 0.2 seconds.
fit_mcmc_w_init_fun_2$init()
#> [[1]] #> [[1]]$theta #> [1] 0.5 #> #> #> [[2]] #> [[2]]$theta #> [1] 0.3333333 #> #>
# Specifying initial values as a list of lists fit_mcmc_w_init_list <- mod$sample( data = stan_data, seed = 123, chains = 2, refresh = 0, init = list( list(theta = 0.75), # chain 1 list(theta = 0.25) # chain 2 ) )
#> Running MCMC with 2 sequential chains... #> #> Chain 1 finished in 0.0 seconds. #> Chain 2 finished in 0.0 seconds. #> #> Both chains finished successfully. #> Mean chain execution time: 0.0 seconds. #> Total execution time: 0.2 seconds.
fit_optim_w_init_list <- mod$optimize( data = stan_data, seed = 123, init = list( list(theta = 0.75) ) )
#> Initial log joint probability = -11.6657 #> Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes #> 6 -5.00402 0.000237915 9.55309e-07 1 1 9 #> Optimization terminated normally: #> Convergence detected: relative gradient magnitude is below tolerance #> Finished in 0.1 seconds.
fit_optim_w_init_list$init()
#> [[1]] #> [[1]]$theta #> [1] 0.75 #> #>
# }