R code |

R code for some examples in the videos:

Code for recurrent neural network (RNN). Note that this code is for educational purposes only and is therefore not intended to be used to predict the stock market.

library(rnn)
rm(list=ls())
y = c(9, 7, 6, 10, 8, 7, 11, 9, 6, 12, 10, 7, 11, 9, 7) # Time series data
yn = (y - min(y)) / (max(y) - min(y))
plot(yn,type="l", las=1, xlab="Time", ylab="Normalized data")
points(yn,pch=16)

step=5 # Time steps
train_size=9 # Numb of time points to train

# Prepare training data
X_train = NULL
Y_train = NULL
i=1
for (k in step:train_size){
X_train[[i]]=yn[(k-step+1):k]
Y_train[[i]]=yn[(k-step+2):(k+1)]
i=i+1
}
X_train=do.call(rbind, X_train)
Y_train=do.call(rbind, Y_train)

XM=array(X_train,dim=c(dim(X_train)[1],step,1)) # Data, samples, time, variables
YM=array(Y_train,dim=c(dim(Y_train)[1],step,1)) # Data, samples, time, variables

set.seed(3)
model = trainr(Y = YM,X = XM, learningrate = 0.1,
hidden_dim = 10, numepochs = 15000, use_bias = TRUE)

# Predict training data and plot
train=yn[1:train_size] # Train data
xp=array(train,dim=c(1,length(train),1)) # Prepare traning data to predict
Yp_train = as.vector(predictr(model, xp)) # Predict traning data
t2=2:(length(Yp_train)+1) # Time steps for plot
lines(t2, Yp_train, type = "l", col = "red")
points(t2, Yp_train,pch=16,col="red")

# Predict validation data and plot
X_valid=yn[(train_size+1):(length(yn)-1)]# Validation data
xpv=array(X_valid,dim=c(1,length(X_valid),1)) # Prepare validation data to predict
Yp_valid = as.vector(predictr(model, xpv))
t3=(t2[length(t2)]+1):length(yn)
lines(t3, Yp_valid, type = "l", col = "green")
points(t3, Yp_valid,pch=16,col="green")

#Calculate SSE of validation data
Y_valid=yn[(train_size+2):(length(yn))]# Validation data
sum((Yp_valid-Y_valid)^2)

k=100000 # Number of simulations
n=5 # Sample size
p_values=rep(0,k) # Initialize vector
p_valuesWMW=rep(0,k) # Initialize vector
for (i in 1:k){
  X1=rnorm(n,0,1)     # Group A
  X2=rnorm(n,0.3,1)  # Group B
  p_values[i]=t.test(X1,X2,var.equal=TRUE)$p.val
  p_valuesWMW[i]=wilcox.test(X1,X2)$p.val
}
power_t_test=sum(p_values<0.05)/k
round(power_t_test,2)*100
power_WMW_test=sum(p_valuesWMW<0.05)/k
round(power_WMW_test,2)*100

How to solve ordinary differential equations (ODEs) in R (deSolve)

library(deSolve)
rm(list=ls()) # Clear the memory
############# ODE function #########
my_ode=function(t,state,parms){
  with(as.list(state),{
    dndt=rep(0,length(state))
    #-------My Equations----------------
    dndt[1] = -k*N
    #-------------------------------------
    return(list(dndt)) # Return
  })
}
############ END of function ##########
N=70                # Initial value = 70 mg
init=c(N=N)     # Create a vector with initial values
k=0.2                # Exponential decay constant (/h)
t=seq(0,30,1)  # Run for 30 time steps
out = ode(y =init, times = t, func = my_ode, parms = NULL)
plot(out,type="l",xlab="Time (h)",ylab="Caffeine (mg)")

Neural networks with continuous output | ANN vs Regression

rm(list=ls())
normalize <- function(x) {
return ((x - min(x)) / (max(x) - min(x)))
}

Age=c(1,2,2,3,4,5,6,7,8,9,10,10,11)
Price=c(29,25,21,18,15,15,12,10,7,5,6,4,4)

df=data.frame(Age,Price,Price_n=normalize(Price),Age_n=normalize(Age))
plot(Age, Price, ylab="Price",xlab="Age",col="blue",cex=1.2,ylim=c(0,35),xlim=c(0,12))
set.seed(378) # To get the same numbers as in my example
library(neuralnet)
nn <- neuralnet(Price_n ~ Age_n, data=df, hidden=c(2), linear.output=TRUE, 
threshold=1e-4,rep=20,act.fct = "logistic")
i=which.min(nn$result.matrix[1,]) # Select network with the lowest error 
x=seq(0,1,0.01)
df2=data.frame(Age=x)
yy=predict(nn,df2, rep = i)* abs(diff(range(Price))) + min(Price)# Change back to original scale
tt=x*abs(diff(range(Age))) + min(Age)# Change back to original scale
lines(tt,yy)
yhat=predict(nn,data.frame(Age=normalize(Age)), rep = i)* abs(diff(range(Price))) + min(Price)
(SSE=sum((Price-yhat)^2))
plot(nn,rep=i)

R code

Pages