Package 'graDiEnt'

GetAlgoParams

Description

Get control parameters for optim_SQGDE function.

Usage

GetAlgoParams(
  n_params,
  n_particles = NULL,
  n_diff = 2,
  n_iter = 1000,
  init_sd = 0.01,
  init_center = 0,
  n_cores_use = 1,
  step_size = NULL,
  jitter_size = 1e-06,
  crossover_rate = 1,
  parallel_type = "none",
  return_trace = FALSE,
  thin = 1,
  purify = Inf,
  adapt_scheme = NULL,
  give_up_init = 100,
  stop_check = 10,
  stop_tol = 1e-04,
  converge_crit = "stdev"
)

Arguments

n_params	The number of parameters estimated/optimized, this integer value NEEDS to be specified.
n_particles	The number of particles (population size), 3*n_params is the default value.
n_diff	The number of mutually exclusive vector pairs to stochastically approximate the gradient.
n_iter	The number of iterations to run the algorithm, 1000 is default.
init_sd	A positive scalar or n_params-dimensional numeric vector, determines the standard deviation of the Gaussian initialization distribution. The default value is 0.01.
init_center	A scalar or n_params-dimensional numeric vector, determines the mean of the Gaussian initialization distribution. The default value is 0.
n_cores_use	An integer specifying the number of cores used when using parallelization. The default value is 1.
step_size	A positive scalar, jump size or "F" in the DE crossover step notation. The default value is 2.38/sqrt(2*n_params).
jitter_size	A positive scalar that determines the jitter (noise) size. Noise is added during adaption step from Uniform(-jitter_size,jitter_size) distribution. 1e-6 is the default value. Set to 0 to turn off jitter.
crossover_rate	A numeric scalar on the interval (0,1]. Determines the probability a parameter on a chain is updated on a given crossover step, sampled from a Bernoulli distribution. The default value is 1.
parallel_type	A string specifying parallelization type. 'none','FORK', or 'PSOCK' are valid values. 'none' is default value. 'FORK' does not work with Windows OS.
return_trace	A boolean, if true, the function returns particle trajectories. This is helpful for assessing convergence or debugging model code. The trace will be an iteration/thin $x$ n_particles $x$ n_params array containing parameter values and an iteration/thin $x$ n_particles array containing particle weights.
thin	A positive integer. Only every 'thin'-th iteration will be stored in memory. The default value is 1. Increasing thin will reduce the memory required when running the algorithim for longer.
purify	A positive integer. On every 'purify'-th iteration the particle weights are recomputed. This is useful if the objective function is stochastic/noisy. If the objective function is deterministic, this computation is redundant. Purify is set to Inf by default, disabling it.
adapt_scheme	A string that must be 'rand','current', or 'best' that determines the DE adaption scheme/strategy. 'rand' uses rand/1/bin DE-like scheme where a random particle and the particle-based quasi-gradient approximation are used to generate proposal updates for a given particle. 'current' uses current/1/bin, and 'best' uses best/1/bin which follow an analogous adaption scheme to rand. 'rand' is the default value.
give_up_init	An integer for how many failed initialization attempts before stopping the optimization routine. 100 is the default value.
stop_check	An integer for how often to check the convergence criterion. The default is 10 iterations.
stop_tol	A convergence metric must be less than value to be labeled as converged. The default is 1e-4.
converge_crit	A string denoting the convergence metric used, valid metrics are 'stdev' (standard deviation of population weight in the last stop_check iterations) and 'percent' (percent improvement in median particle weight in the last stop_check iterations). 'stdev' is the default.

Value

A list of control parameters for the optim_SQGDE function.

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optim_SQGDE

Description

Runs Stochastic Quasi-Gradient Differential Evolution (SQG-DE; Sala, Baldanzini, and Pierini, 2018) to minimize an objective function f(x). To maximize a function f(x), simply pass g(x)=-f(x) to ObjFun argument.

Usage

optim_SQGDE(ObjFun, control_params = GetAlgoParams(), ...)

Arguments

ObjFun	A scalar-returning function to minimize whose first argument is a real-valued n_params-dimensional vector.
control_params	control parameters for SQG-DE algo. see GetAlgoParams function documentation for more details. The only argument you NEED to pass here is n_params.
...	additional arguments to pass ObjFun.

Value

list containing solution and it's corresponding weight (i.e. f(solution)).

Examples

##############
# Maximum Likelihood Example
##############

# simulate from model
dataExample=matrix(rnorm(1000,c(-1,1,0,1),c(1,1,1,1)),ncol=4,byrow = TRUE)

# list parameter names
param_names_example=c("mu_1","mu_2","mu_3","mu_4")

# negative log likelihood
ExampleObjFun=function(x,data,param_names){
  out=0

  names(x) <- param_names

  # log likelihoods
  out=out+sum(dnorm(data[,1],x["mu_1"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,2],x["mu_2"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,3],x["mu_3"],sd=1,log=TRUE))
  out=out+sum(dnorm(data[,4],x["mu_4"],sd=1,log=TRUE))

  return(out*-1)
}

########################
# run optimization
out <- optim_SQGDE(ObjFun = ExampleObjFun,
                   control_params = GetAlgoParams(n_params = length(param_names_example),
                                             n_iter = 250,
                                              n_particles = 12,
                                              n_diff = 2,
                                              return_trace = TRUE),
                   data = dataExample,
                   param_names = param_names_example)
old_par <- par() # save graphic state for user
# plot particle trajectory

par(mfrow=c(2,2))
matplot(out$particles_trace[,,1],type='l')
matplot(out$particles_trace[,,2],type='l')
matplot(out$particles_trace[,,3],type='l')
matplot(out$particles_trace[,,4],type='l')

#SQG DE solution
out$solution

#analytic solution
apply(dataExample, 2, mean)

par(old_par) # restore user graphic state

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