# YAP: Yet Another Probabilistic Neural Network

By the end of 2019, I finally managed to wrap up my third R package YAP (https://github.com/statcompute/yap) that implements the Probabilistic Neural Network (Specht, 1990) for the N-category pattern recognition with N > 2. Similar to GRNN, PNN shares same benefits of instantaneous training, simple structure, and global convergence.

Below is a demonstration showing how to use the YAP package and a comparison between the multinomial regression and the PNN. As shown below, both approaches delivered very comparable predictive performance. In this particular example, PNN even performed slightly better in terms of the cross-entropy for a separate testing dataset.

```data("Heating", package = "mlogit")
Y <- Heating[, 2]
X <- scale(Heating[, 3:15])
idx <- with(set.seed(1), sample(seq(nrow(X)), nrow(X) / 2))

### FIT A MULTINOMIAL REGRESSION AS A BENCHMARK ###
m1 <- nnet::multinom(Y ~ ., data = data.frame(X, Y)[idx, ], model = TRUE)
# cross-entropy for the testing set
yap::logl(y_pred = predict(m1, newdata = X, type = "prob")[-idx, ], y_true = yap::dummies(Y)[-idx, ])
# 1.182727

### FIT A PNN ###
n1 <- yap::pnn.fit(x = X[idx, ], y = Y[idx])
parm <- yap::pnn.search_logl(n1, yap::gen_latin(1, 10, 20), nfolds = 5)
n2 <- yap::pnn.fit(X[idx, ], Y[idx], sigma = parm\$best\$sigma)
# cross-entropy for the testing set
yap::logl(y_pred = yap::pnn.predict(n2, X)[-idx, ], y_true = yap::dummies(Y)[-idx, ])
# 1.148456
```