HW6 done

Author: Chetanfs

Learning from Data HW6 Neural Network Weights.R

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+
+# Problem 9/10
+
+### following function relates number of nodes in first hidden layer to  overall num of weights given
+### constraints of the neural network described in problems 9/10 of
+### https://work.caltech.edu/homework/hw6.pdf
+### Assumes that if you have less than 17 nodes in layer 1, nodes are laid out symmetrically
+numWeights <- function(x) {
+  if (x <= 16)
+    10*(x-1)+(x-1)^2*(36/x-1)+(36/x-1)*(x-1)+x
+  else
+    10*(x-1)+(x-1)*(36-x-1)+(36-x-1)+36-x
+}
+
+### Let's plot to find min/max
+plot(1:36, unlist(lapply(1:36, numWeights)))
+
+### Or if you don't like pictures
+which.min(unlist(lapply(1:36, numWeights))) # min is at 1 node per layer
+which.max(unlist(lapply(1:36, numWeights))) # max is at 23 nodes
+
+
+

Learning from Data HW6.docx

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+library(data.table)
+
+dt <- data.table(a=runif(10E4), b=runif(10E4))
+dt[,mean(pmin(a, b))]