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

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 Interface User's Guide

Usage

$optimize(
  data = NULL,
  seed = NULL,
  refresh = NULL,
  init = NULL,
  save_latent_dynamics = FALSE,
  output_dir = NULL,
  algorithm = NULL,
  init_alpha = NULL,
  iter = NULL
)

Arguments shared by all fitting methods

The following arguments can be specified for any of the fitting methods (sample, optimize, variational). Arguments left at NULL default to the default used by the installed version of CmdStan.

  • data: (multiple options) The data to use. 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.

  • 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.

  • init: (multiple options) The initialization method:

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

    • 0 initializes to 0;

    • A character vector of paths (one per chain) to JSON or Rdump files. See write_stan_json() to write R objects to JSON files compatible with CmdStan.

  • 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 (and for some algorithms no content may be written). The default is save_latent_dynamics=FALSE, which is appropriate for almost every use case (all diagnostics recommended for users to check are always saved, e.g., divergences for HMC). 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 (e.g., 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()).

    • If a path then the files are created in output_dir with names corresponding the defaults used by $save_output_files() (and similar methods like $save_latent_dynamics_files()).

Arguments unique to the optimize method

In addition to the arguments above, the $optimize() method also has its own set of arguments. These arguments are described briefly here and in greater detail in the CmdStan manual. Arguments left at NULL default to the default used by the installed version of CmdStan.

  • algorithm: (string) The optimization algorithm. One of "lbfgs", "bfgs", or "newton".

  • iter: (positive integer) The number of iterations.

  • init_alpha: (nonnegative real) The line search step size for first iteration. Not applicable if algorithm="newton".

Value

The $optimize() method returns 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-compile, model-method-sample, model-method-variational

Examples

# \dontrun{ # 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-2.23.0
# Create a CmdStanModel object from a Stan program, # here using the example model that comes with CmdStan stan_program <- file.path(cmdstan_path(), "examples/bernoulli/bernoulli.stan") mod <- cmdstan_model(stan_program)
#> 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, cores = 2 )
#> Running MCMC with 2 chain(s) on 2 core(s)... #> #> Running ./bernoulli 'id=1' random 'seed=123' data \ #> 'file=/var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/standata-29292a0abc9d.json' \ #> output \ #> 'file=/var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-e4fcfb.csv' \ #> 'method=sample' 'save_warmup=0' 'algorithm=hmc' 'engine=nuts' adapt \ #> 'engaged=1' #> Running ./bernoulli 'id=2' random 'seed=124' data \ #> 'file=/var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/standata-29292a0abc9d.json' \ #> output \ #> 'file=/var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-2-e4fcfb.csv' \ #> 'method=sample' 'save_warmup=0' 'algorithm=hmc' 'engine=nuts' adapt \ #> 'engaged=1' #> 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 0.2 seconds. #> Chain 2 finished in 0.2 seconds. #> #> Both chains finished successfully. #> Mean chain execution time: 0.2 seconds. #> Total execution time: 0.2 seconds.
# Use 'posterior' package for summaries fit_mcmc$summary()
#> # A tibble: 2 x 10 #> variable mean median sd mad q5 q95 rhat ess_bulk ess_tail #> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> #> 1 lp__ -7.28 -7.00 0.739 0.342 -8.80 -6.75 1.00 815. 621. #> 2 theta 0.254 0.235 0.123 0.123 0.0809 0.485 1.00 752. 589.
# Call CmdStan's diagnose and stansummary utilities fit_mcmc$cmdstan_diagnose()
#> Running bin/diagnose \ #> /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-e4fcfb.csv \ #> /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-2-e4fcfb.csv #> Processing csv files: /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-e4fcfb.csv, /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-2-e4fcfb.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$cmdstan_summary()
#> Running bin/stansummary \ #> /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-e4fcfb.csv \ #> /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-2-e4fcfb.csv #> Inference for Stan model: bernoulli_model #> 2 chains: each with iter=(1000,1000); warmup=(0,0); thin=(1,1); 2000 iterations saved. #> #> Warmup took (0.0064, 0.0062) seconds, 0.013 seconds total #> Sampling took (0.014, 0.013) seconds, 0.027 seconds total #> #> Mean MCSE StdDev 5% 50% 95% N_Eff N_Eff/s R_hat #> lp__ -7.3 3.1e-02 0.74 -8.8 -7.0 -6.8 5.9e+02 2.2e+04 1.0e+00 #> accept_stat__ 0.92 5.0e-03 0.14 0.61 0.97 1.0 7.3e+02 2.7e+04 1.0e+00 #> stepsize__ 1.0 9.0e-02 0.090 0.93 1.1 1.1 1.0e+00 3.7e+01 2.6e+13 #> treedepth__ 1.4 1.2e-02 0.52 1.0 1.0 2.0 1.9e+03 6.9e+04 1.0e+00 #> n_leapfrog__ 2.6 4.0e-01 1.5 1.0 3.0 7.0 1.4e+01 5.2e+02 1.0e+00 #> divergent__ 0.00 nan 0.00 0.00 0.00 0.00 nan nan nan #> energy__ 7.8 4.0e-02 1.0 6.8 7.4 10.0 6.9e+02 2.6e+04 1.0e+00 #> theta 0.25 4.5e-03 0.12 0.081 0.23 0.49 7.6e+02 2.8e+04 1.0e+00 #> #> Samples were drawn using hmc with nuts. #> For each parameter, N_Eff is a crude measure of effective sample size, #> and R_hat is the potential scale reduction factor on split chains (at #> convergence, R_hat=1). #>
# For models fit using MCMC, if you like working with RStan's stanfit objects # then you can create one with rstan::read_stan_csv() if (require(rstan, quietly = TRUE)) { stanfit <- rstan::read_stan_csv(fit_mcmc$output_files()) print(stanfit) }
#> Inference for Stan model: bernoulli-202005121301-1-e4fcfb. #> 2 chains, each with iter=2000; warmup=1000; thin=1; #> post-warmup draws per chain=1000, total post-warmup draws=2000. #> #> mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat #> theta 0.25 0.00 0.12 0.06 0.16 0.23 0.33 0.53 754 1 #> lp__ -7.28 0.03 0.74 -9.50 -7.45 -7.00 -6.80 -6.75 586 1 #> #> Samples were drawn using NUTS(diag_e) at Tue May 12 13:01:46 2020. #> For each parameter, n_eff is a crude measure of effective sample size, #> and Rhat is the potential scale reduction factor on split chains (at #> convergence, Rhat=1).
# 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$optimize(data = my_data_file, seed = 123)
#> method = optimize #> optimize #> algorithm = lbfgs (Default) #> lbfgs #> init_alpha = 0.001 (Default) #> tol_obj = 9.9999999999999998e-13 (Default) #> tol_rel_obj = 10000 (Default) #> tol_grad = 1e-08 (Default) #> tol_rel_grad = 10000000 (Default) #> tol_param = 1e-08 (Default) #> history_size = 5 (Default) #> iter = 2000 (Default) #> save_iterations = 0 (Default) #> id = 1 #> data #> file = /Users/jgabry/.cmdstanr/cmdstan-2.23.0/examples/bernoulli/bernoulli.data.json #> init = 2 (Default) #> random #> seed = 123 #> output #> file = /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-9cd6b0.csv #> diagnostic_file = (Default) #> refresh = 100 (Default) #> #> Initial log joint probability = -9.51104 #> Iter log prob ||dx|| ||grad|| alpha alpha0 # evals Notes #> 6 -5.00402 0.000103557 2.55661e-07 1 1 9 #> Optimization terminated normally: #> Convergence detected: relative gradient magnitude is below tolerance
#> Optimization method is experimental and the structure of returned object may change.
fit_optim$summary()
#> # A tibble: 2 x 2 #> variable estimate #> <chr> <dbl> #> 1 lp__ -5.00 #> 2 theta 0.2
# Run 'variational' to approximate the posterior (default is meanfield ADVI) fit_vb <- mod$variational(data = stan_data, seed = 123)
#> method = variational #> variational #> algorithm = meanfield (Default) #> meanfield #> iter = 10000 (Default) #> grad_samples = 1 (Default) #> elbo_samples = 100 (Default) #> eta = 1 (Default) #> adapt #> engaged = 1 (Default) #> iter = 50 (Default) #> tol_rel_obj = 0.01 (Default) #> eval_elbo = 100 (Default) #> output_samples = 1000 (Default) #> id = 1 #> data #> file = /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/standata-29292dd2beaa.json #> init = 2 (Default) #> random #> seed = 123 #> output #> file = /var/folders/h6/14xy_35x4wd2tz542dn0qhtc0000gn/T/RtmpMwcfcG/bernoulli-202005121301-1-e3a266.csv #> diagnostic_file = (Default) #> refresh = 100 (Default) #> #> ------------------------------------------------------------ #> EXPERIMENTAL ALGORITHM: #> This procedure has not been thoroughly tested and may be unstable #> or buggy. The interface is subject to change. #> ------------------------------------------------------------ #> #> #> #> Gradient evaluation took 1.9e-05 seconds #> 1000 transitions using 10 leapfrog steps per transition would take 0.19 seconds. #> Adjust your expectations accordingly! #> #> #> Begin eta adaptation. #> Iteration: 1 / 250 [ 0%] (Adaptation) #> Iteration: 50 / 250 [ 20%] (Adaptation) #> Iteration: 100 / 250 [ 40%] (Adaptation) #> Iteration: 150 / 250 [ 60%] (Adaptation) #> Iteration: 200 / 250 [ 80%] (Adaptation) #> Success! Found best value [eta = 1] earlier than expected. #> #> Begin stochastic gradient ascent. #> iter ELBO delta_ELBO_mean delta_ELBO_med notes #> 100 -6.262 1.000 1.000 #> 200 -6.263 0.500 1.000 #> 300 -6.307 0.336 0.007 MEDIAN ELBO CONVERGED #> #> Drawing a sample of size 1000 from the approximate posterior... #> COMPLETED.
#> Variational method is experimental and the structure of returned object may change.
fit_vb$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
# }