Use a Genetic Algorithm to Estimate a Finite-state Machine Model

evolve_model uses a genetic algorithm to estimate a finite-state machine model, primarily for understanding and predicting decision-making.

evolve_model(data, test_data = NULL, drop_nzv = FALSE,
        measure = c("accuracy", "sens", "spec", "ppv"),
        states = NULL, cv = FALSE, max_states = NULL, k = 2,
        actions = NULL, seed = NULL, popSize = 75,
        pcrossover = 0.8, pmutation = 0.1, maxiter = 50,
        run = 25, parallel = FALSE, priors = NULL,
        verbose = TRUE, return_best = TRUE, ntimes = 1)

Arguments

data	A data.frame that has columns named "period" and "outcome" (period is the time period that the outcome action was taken), and one to three additional columns, containing predictors. All of the 3-5 columns should be named. The period and outcome columns should be integer vectors and the columns with the predictor variable data should be logical vectors (TRUE, FALSE). If the predictor variable data is not logical, it will coerced to logical with base::as.logical().
test_data	Optional data.frame that has "period" and "outcome" columns, with one to three additional columns containing predictors. All of the (3-5 columns) should be named. The outcome variable is the decision the decision-maker took for that period. This data.frame should be in the same format and have the same order of columns as the data.frame passed to the required data argument.
drop_nzv	Optional logical vector length one specifying whether predictors variables with variance in provided data near zero should be dropped before model building. Default is FALSE. See caret::nearZeroVar(), which calls: caret::nzv().
measure	Optional length one character vector that is either: "accuracy", "sens", "spec", or "ppv". This specifies what measure of predictive performance to use for training and evaluating the model. The default measure is "accuracy". However, accuracy can be a problematic measure when the classes are imbalanced in the samples, i.e. if a class the model is trying to predict is very rare. Alternatives to accuracy are available that illuminate different aspects of predictive power. Sensitivity answers the question, `` given that a result is truly an event, what is the probability that the model will predict an event?'' Specificity answers the question, ``given that a result is truly not an event, what is the probability that the model will predict a negative?'' Positive predictive value answers, ``what is the percent of predicted positives that are actually positive?''
states	Optional numeric vector with the number of states. If not provided, will be set to max(data$outcome).
cv	Optional logical vector length one for whether cross-validation should be conducted on training data to select optimal number of states. This can drastically increase computation time because if TRUE, it will run evolve_model k*max_states times to estimate optimal value for states. Ties are broken by choosing the smaller number of states. Default is FALSE.
max_states	Optional numeric vector length one only relevant if cv==TRUE. It specifies how up to how many states that cross-validation should search through. If not provided, will be set to states + 1.
k	Optional numeric vector length one only relevant if cv==TRUE, specifying number of folds for cross-validation.
actions	Optional numeric vector with the number of actions. If not provided, then actions will be set as the number of unique values in the outcome vector.
seed	Optional numeric vector length one.
popSize	Optional numeric vector length one specifying the size of the GA population. A larger number will increase the probability of finding a very good solution but will also increase the computation time. This is passed to the GA::ga() function of the GA package.
pcrossover	Optional numeric vector length one specifying probability of crossover for GA. This is passed to the GA::ga() function of the GA package.
pmutation	Optional numeric vector length one specifying probability of mutation for GA. This is passed to the GA::ga() function of the GA package.
maxiter	Optional numeric vector length one specifying max number of iterations for stopping the GA evolution. A larger number will increase the probability of finding a very good solution but will also increase the computation time. This is passed to the GA::ga() function of the GA package. maxiter is scaled by how many parameters are in the model: maxiter <- maxiter + ((maxiter*(nBits^2)) / maxiter).
run	Optional numeric vector length one specifying max number of consecutive iterations without improvement in best fitness score for stopping the GA evolution. A larger number will increase the probability of finding a very good solution but will also increase the computation time. This is passed to the GA::ga() function of the GA package.
parallel	Optional logical vector length one. For running the GA evolution in parallel. Depending on the number of cores registered and the memory on your machine, this can make the process much faster, but only works for Unix-based machines that can fork the processes.
priors	Optional numeric matrix of solutions strings to be included in the initialization. User needs to use a decoder function to translate prior decision models into bits and then provide them. If this is not specified, then random priors are automatically created.
verbose	Optional logical vector length one specifying whether helpful messages should be displayed on the user's console or not.
return_best	Optional logical vector length one specifying whether to return just the best model or all models. Only relevant if ntimes > 1. Default is TRUE.
ntimes	Optional integer vector length one specifying the number of times to estimate model. Default is 1 time.

Value

Returns an S4 object of class ga_fsm. See ga_fsm for the details of the slots (objects) that this type of object will have and for information on the methods that can be used to summarize the calling and execution of evolve_model(), including summary, print, and plot. Timing measurement is in seconds.

Details

This is the main function of the datafsm package. It relies on the GA package for genetic algorithm optimization. evolve_model takes data on predictors and data on the outcome. It automatically creates a fitness function that takes the data, an action vector evolve_model generates, and a state matrix evolve_model generates as input and returns numeric vector of the same length as the outcome. evolve_model then computes a fitness score for that potential solution FSM by comparing it to the provided outcome. This is repeated for every FSM in the population and then the probability of selection for the next generation is proportional to the fitness scores. The default is also for the function to call itself recursively while varying the number of states inside a cross-validation loop in order to estimate the optimal number of states.

If parallel is set to TRUE, then these evaluations are distributed across the available processors of the computer using the doParallel package, otherwise, the evaluations of fitness are conducted sequentially. Because this fitness function that evolve_model creates must loop through all the data every time it is evaluated and we need to evaluate many possible solution FSMs, the fitness function is implemented in C++ so it is very fast.

evolve_model uses a stochastic meta-heuristic optimization routine to estimate the parameters that define a FSM model. Generalized simulated annealing, or tabu search could work, but they are more difficult to parallelize. The current version uses the GA package's genetic algorithm because GAs perform well in rugged search spaces to solve integer optimization problems, are a natural complement to our binary string representation of FSMs, and are easily parallelized.

This function evolves the models on training data and then, if a test set is provided, uses the best solution to make predictions on test data. Finally, the function returns the GA object and the decoded version of the best string in the population. See ga_fsm for the details of the slots (objects) that this type of object will have.

References

Luca Scrucca (2013). GA: A Package for Genetic Algorithms in R. Journal of Statistical Software, 53(4), 1-37. URL https://www.jstatsoft.org/v53/i04/.

Examples

if (FALSE) {
# Create data:
cdata <- data.frame(period = rep(1:10, 1000),
                   outcome = rep(1:2, 5000),
                   my.decision1 = sample(1:0, 10000, TRUE),
                   other.decision1 = sample(1:0, 10000, TRUE))
(res <- evolve_model(cdata, cv=FALSE))
summary(res)
plot(res, action_label = c("C", "D"))
library(GA)
plot(estimation_details(res))
}

# In scripts, it can makes sense to set parallel to
# 'as.logical(Sys.info()['sysname'] != 'Windows')'.