Question

Suppose we have a dataset DD in a regression problem.

1. What will happen to the in-sample error of linear regression using polynomials of degree dd as d→∞d→∞?

2. What will happen to the out-of-sample error of linear regression as dd increases?

You can use the output of the code below to help you form your answer.

CODE BELOW:

xmin,xmax = 0,4*np.pi
x = np.linspace(xmin,xmax,1000)
D = 14

N = 100
shuff = np.random.permutation(len(x))
x_pts = np.array(sorted(x[shuff][:N]))

K = 200
train_vals = np.zeros(D*K).reshape(K,D)
test_vals = np.zeros(D*K).reshape(K,D)
noise = np.random.randn(N)
y = np.sin(x_pts)+ noise/7

for k in range(K):
    shuff = np.random.permutation(len(x))
    x_pts = np.array(sorted(x[shuff][:N]))
    noise = np.random.randn(N)
    y = np.sin(x_pts)+ noise/7
    for i,deg in enumerate(range(D)):
        X = np.ones(N*deg).reshape(N,deg)
        for j in range(1,deg):
            X[:,j] = x_pts**j
        X_train,X_test,y_train,y_test = test_train_split(X,y,0.13)

        w = linear_fit(X_train,y_train)

        g_train = linear_predict(X_train,w)
        g_test = linear_predict(X_test,w)

        r_train = RMSE(g_train,y_train)
        r_test = RMSE(g_test,y_test)
        train_vals[k][i] = r_train
        test_vals[k][i] = r_test

tr_vals = np.mean(train_vals,axis=0)
te_vals = np.mean(test_vals,axis=0)

plt.plot(range(D),tr_vals)
plt.title("In sample error as a function of model complexity")
plt.xlabel("Polynomial degree")
plt.ylabel("RMSE")
plt.show()
plt.title("Out of sample error as a function of model complexity")
plt.plot(range(D),te_vals)
plt.xlabel("Polynomial degree")
plt.ylabel("RMSE")

plt.axis([0,D,0,2])
plt.show()

Answer 1

#include<stdio.h>
#include<stdlib.h>
struct node{
   int data;
   struct node *next;
};
void printlist(struct node *h){
   while(h != NULL){
       printf("%d ",h->data);
       h = h->next;
   }
}

int main(){
   struct node *start=NULL;
   int a,i;
   printf("Enter the no.of Nodes:");
   scanf("%d",&a);
   for(i=0;i<a;i++){
       struct node *newNode = (struct node *)malloc(sizeof(struct node));
       printf("Enter the data:");
       scanf("%d",&newNode->data);
       newNode->next = NULL;
       if(start==NULL)
           start = newNode;
       else{
           struct node *ptr = start;
           while(ptr->next!=NULL)
               ptr = ptr->next;
           ptr->next = newNode;
       }
   }
   printf("Linked List is:\n");
   printlist(start);
   printf("\nEnter the reversing the list:\n");
   struct node *current = start,*pre = NULL,*nex;
   while(current!=NULL){
       nex = current->next;
       current->next = pre;
       pre = current;
       current = nex;
   }
   start = pre;
   printlist(start);
}