findLabels: Mixed Membership Post-Processing

Description

Finds the permutation of labels that minimizes the weighted squared error loss between the fitted theta and a comparison model.

Usage

findLabels(model, training, exhaustive = TRUE)

Arguments

model

the fitted mixedMemModel object

training

the comparison theta. This should be an array the same dimensions as model$theta

exhaustive

a boolean for whether an exhaustive search should be performed. If false, a greedy algorithim is used instead

Value

perm optimal permutation of the labels with respect to squared error loss loss the sum of squared error loss of the optimal permutation weighted by relative frequency

Details

Mixed Membership models are invariant to permutations of the sub-population labels and the ordering of the labels in a fitted model is dependent on the initialization points of the variational EM algorithim. The findLabels function selects an optimal permutation of the labels to match a given comparison model. The loss function is the weighted sum of squared differences where the weights are determined by the relative frequency of each group. $Loss = \sum_j \sum_k \alpha_k/\alpha_0 [\sum_v (\hat\theta_{k,v} - \theta_{k,v})^2]$ where $\alpha_0 = \sum_k \alpha_k$ If K, number of sub-populations, is small, the method can search through all K! permutations and select the permutation which minimizes the loss. If K is large, a greedy algorithim can be used instead. This algorithim selects the best match for each fitted sub-population starting with the group with the largest fitted relative frequency.

Examples

Run this code

# See mixedMemModel documentation for how to generate data and instantiate a mixedMemModel object
# After the data as been generated, we initialize theta to a permutation of the true labeling
set.seed(123)
perm = sample.int(K, size = K, replace = FALSE)
theta1 = theta[,perm,]
test_model <- mixedMemModel(Total = Total, J = J,Rj = Rj, Nijr= Nijr, K = K, Vj = Vj,dist = dist,
 obs = obs, alpha = alpha, theta = theta1)
out <- mmVarFit(test_model)
opt.perm <- findLabels(out, theta)
opt.perm

# produce mixedMemModel object with labels permuted to match ground truth
out = permuteLabels(out, opt.perm$perm)