Add method to create inits from fit or draws objects

[avehtari]

Especially useful now that Pathfinder is useful for initializing MCMC. To show what I mean I show below what I came up quickly for testing purposes

pth5 <- model5$pathfinder(data = standata5, init=0.1, num_paths=10, single_path_draws=40,
                          history_size=50, max_lbfgs_iters=100)

# create a fit object (should now work also with pathfinder object 
fit5 <- model5$sample(data=standata5, chains=1, iter_sampling=1, fixed_param=TRUE, refresh=0)
# get parameter names so that we don't need to include thousands of generated quantities variables
# it would sufficient to get just the parameter names without dimensions, so in that sense the instantiated fit would 
# not be needed, but I guess this is now the only way? The downside is that it requires compiling model methods
params <- names(fit5$variable_skeleton(transformed_parameters = FALSE, generated_quantities = FALSE))
# see the function definition below, argument `variables` follows CmdStanR argument naming
init5 <- create_inits(pth5, variables=params)

#' Function to form a list of list of initial values from a draws object.
#' Arguments `variable` and  `ndraws` follow posterior package argument naming
as_inits <- function(draws, variable=NULL, ndraws=4) {
  ndraws <- min(ndraws(draws),ndraws)
  if (is.null(variable)) {variable = variables(draws)}
  draws <- draws |> as_draws_rvars()
  inits <- lapply(1:ndraws,
                  function(drawid) {
                    sapply(variable,
                           function(var) {
                             drop(draws_of(subset_draws(draws, variable=var, draw=drawid)[[1]]))
                           })
                  })
  inits
}

#' Function to form a list of list of initial values from a Pathfinder object.
#' Something like this will be eventually available in `cmdstanr` package.
create_inits <- function(pthf, variables=NULL, ndraws=4) {
g  if (is.null(variables)) {
    # set variable names to be list of parameter names
    variables <- names(pthf$variable_skeleton(transformed_parameters = FALSE,
                                              generated_quantities = FALSE))
  }
  draws <- pthf$draws(format="df")
  draws <- draws |>
    mutate_variables(lw = lp__ - lp_approx__)
  ndist <- n_distinct(extract_variable(draws,"lw"))
  if (ndist < ndraws) {
    stop(paste0("Not enough distinct draws (", ndist, ") to create inits."))
  }
  if (ndist < 0.95*ndraws(draws)) {
    # Resampling has been done in Stan, compute weights for distinct draws
    # (these are now non Pareto smoothed as we have lost the original information)
    draws <- draws |>
      group_by(lw) |>
      summarise(.draw=min(.draw)) |>
      left_join(draws, by = ".draw") |>
      as_draws_df() |>
      mutate_variables(lw = lw.x,
                       w = exp(lw-max(lw)))
  } else {
    # Resampling was not done in Stan, compute Pareto smoothed weights
    draws <- draws |>
      mutate_variables(w=pareto_smooth(exp(lw-max(lw)), tail="right"))
  }
  draws |>
    weight_draws(weights=extract_variable(draws,"w"), log=FALSE) |>
    resample_draws(ndraws=ndraws, method = "simple_no_replace") |>
    as_inits(variable=variables, ndraws=ndraws)
}

There is a corresponding CmdStanPy method `create_inits`

EDIT: updated the code to support both `psis_resample=TRUE` and `psis_resample=FALSE`, and support matrix and array type parameters.

[andrjohns]

@jgabry I'll tackle this as well

[jgabry]

Awesome, thanks @andrjohns!

[jgabry]

Just did the 0.7.0 release. Happy to another one whenever these additional features are ready. Thanks for working on this!

[reuning]

fwiw, I'd love this feature (currently working on using pathfinder to initialize a large model). If there is anything I can do to help let me know.

[andrjohns]

@avehtari The cmdstanpy implementation of create_inits just returns a random draw from the existing pathfinder estimates, but your example above is performing an additional PSIS step before selecting the first nchain draws as inits.

Ideally both of the interfaces should be consistent here. Doesn't the multi-pathfinder call already perform PSIS resampling on the results? Is there a benefit to repeating it here?

[avehtari]

When I made the issue, 1) PSIS resampling was often failing in CmdStan, 2) there was no option for sample without replacement which would be better for getting unique initial values. Now 1 has been fixed, and maybe 2, too?

[avehtari]

Birthdays case study illustrates the use of the above functions
https://users.aalto.fi/~ave/casestudies/Birthdays/birthdays.html

[jgabry]

@andrjohns Just checking in on this. Are you still planning on working on it? Let me know if it would be helpful to chat about the implementation.

[SteveBronder]

I'm finishing this up hopefully this week

[jgabry]

Awesome thanks Steve!

[avehtari]

Closed by #937