stochastic MAP in stan

[David Blei]

stanimaniacs,

thanks to the stan development team, implementing stochastic MAP

estimation in stan is easy. there was a little trickiness to getting

it to work, so i thought i'd share.

best

dave

---

you'll need

- a subsample(b) function that grabs a subsample of size b from your

  data set

- a stepsize(t) function that gets the t-th stepsize. (to start, you

  can even just choose a constant stepsize.)

here is a skeleton of the program:

# model_filename = stan model

# subsample(b)   = fun that returns a sample of b data points from the data

# n              = data set size

# batch_size     = size for each subsample to analyze on each iteration

# niter          = number of iterations

# stepsize(t)    = fun that returns the stepsize at iteration t

# model          = (opt) a pre-compiled model

stochastic.map <- function(model_filename, subsample, n, batch_size,

                           niter, stepsize, model = NULL)

{

  # compile the model (if needed) and initial parameters.

  # here, parameters are initialized to zero.

  if (is.null(model))

  {

    dummy_subsample <- sample.documents(data, batch_size)

    model <- stan(model_filename, data = dummy_subsample, chains=0)

  }

  nparams <- sum(unlist(model@par_dims))

  params <- rep(0, nparams)

  grad_scale <- n / batch_size

  # run stochastic gradient ascent by subsampling a batch, computing a

  # noisy gradient, and taking a step.  at each point, compute the

  # the per-data log probability as a score to track.

  score <- numeric(niter)

  for (t in 1:niter)

  {

    batch <- subsample(batch_size)

    iter_model <- stan(fit = model, data = batch, chains = 0)

    grad <- grad_scale * grad_log_prob(iter_model, params)

    params <- params + stepsize(t) * grad

    score[t] <- log_prob(iter_model, params) / batch_size

  }

  # return the model object (in case we want to run again)

  #        the params vector

  #        the score trajectory

  list(model = model, params = params, score = score)

}

[Daniel Lee]

Awesome!

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[Daniel Lee]

Dave, thanks for putting together stochastic MAP. What's really neat is how clean it is, once Stan has abstracted away the model and the gradients. It reads like pseudo-code.

For users that are diving into Stan at this level, if you have suggestions / requests /improvements for the API, please feel free to bring it up.

Daniel

[Andrew Gelman]

Once we've implemented black box VB, MAP will be a thing of the past.

[Jiqiang Guo]

Thanks for sharing.  Just one minor comment for getting the number of parameters.  Please see below.  

On Tue, Mar 26, 2013 at 6:20 PM, David Blei <david...@gmail.com> wrote:

This is fine for some models. But log_prob and grad_log_prob are defined on the unconstrained parameter space.  The number of unconstrained parameters might be different from what is obtained here.  Function "get_num_upars" can be used instead, that is

nparams <- get_num_upars

  params <- rep(0, nparams)

  grad_scale <- n / batch_size

  # run stochastic gradient ascent by subsampling a batch, computing a

  # noisy gradient, and taking a step.  at each point, compute the

  # the per-data log probability as a score to track.

  score <- numeric(niter)

  for (t in 1:niter)

  {

    batch <- subsample(batch_size)

    iter_model <- stan(fit = model, data = batch, chains = 0)

    grad <- grad_scale * grad_log_prob(iter_model, params)

    params <- params + stepsize(t) * grad

    score[t] <- log_prob(iter_model, params) / batch_size

  }

 

  # return the model object (in case we want to run again)

  #        the params vector

  #        the score trajectory

  list(model = model, params = params, score = score)

}

[David Blei]

hi andrew

i agree completely.  if we had black box variational inference, i would never use MAP.

best

dave