build_vae_correlated {ML2Pvae}

Build a VAE that fits to a normal, full covariance N(m,S) latent distribution

Description

Build a VAE that fits to a normal, full covariance N(m,S) latent distribution

Usage

build_vae_correlated(
  num_items,
  num_skills,
  Q_matrix,
  mean_vector = rep(0, num_skills),
  covariance_matrix = diag(num_skills),
  model_type = 2,
  enc_hid_arch = c(ceiling((num_items + num_skills)/2)),
  hid_enc_activations = rep("sigmoid", length(enc_hid_arch)),
  output_activation = "sigmoid",
  kl_weight = 1,
  learning_rate = 0.001
)

Arguments

num_items

an integer giving the number of items on the assessment; also the number of nodes in the input/output layers of the VAE

num_skills

an integer giving the number of skills being evaluated; also the dimensionality of the distribution learned by the VAE

Q_matrix

a binary, num_skills by num_items matrix relating the assessment items with skills

mean_vector

a vector of length num_skills specifying the mean of each latent trait; the default of rep(0, num_skills) should almost always be used

covariance_matrix

a symmetric, positive definite, num_skills by num_skills matrix giving the covariance of the latent traits

model_type

either 1 or 2, specifying a 1 parameter (1PL) or 2 parameter (2PL) model; if 1PL, then all decoder weights are fixed to be equal to one

enc_hid_arch

a vector detailing the size of hidden layers in the encoder; the number of hidden layers is determined by the length of this vector

hid_enc_activations

a vector specifying the activation function in each hidden layer in the encoder; must be the same length as enc_hid_arch

output_activation

a string specifying the activation function in the output of the decoder; the ML2P model always used 'sigmoid'

kl_weight

an optional weight for the KL divergence term in the loss function

learning_rate

an optional parameter for the adam optimizer

Value

returns three keras models: the encoder, decoder, and vae

Examples

Q <- matrix(c(1,0,1,1,0,1,1,0), nrow = 2, ncol = 4)
cov <- matrix(c(.7,.3,.3,1), nrow = 2, ncol = 2)
models <- build_vae_correlated(4, 2, Q,
          mean_vector = c(-0.5, 0), covariance_matrix = cov,
          enc_hid_arch = c(6, 3), hid_enc_activation = c('sigmoid', 'relu'),
          output_activation = 'tanh',
          kl_weight = 0.1)
vae <- models[[3]]