Consider the following setting. You are provided with n training examples: (x1, y1), (x2, y2), · · · , (xn, yn), where xi is the input example, and yi is the class label (+1 or -1). However, the training data is highly imbalanced (say 90% of the examples are negative and 10% of the examples are positive) and we care more about the accuracy of positive examples. How will you modify the perceptron algorithm to solve this learning problem? Please justify your answer.
ANSWER:
GIVEN THAT:
To consider the following setting. You are provided with n training examples: (x1, y1), (x2, y2), · · · , (xn, yn), where xi is the input.
There are many solution paths available for this problem. Some of them are :
i).Oversampling Minority Class:-
The minority class is used multiple times to train the perceptron.
This way the minority input is amplified.
ii).Undersampling Majority Class:-
Remove some of the training tuples from majority class on random.
This will reduce the excessive effect of majority class on the
perceptron model.
iii).Modify Algorithm to be sensitive to Minority
classes:-
Even a single misclassification in minority class has a huge cost
because there are already very few cases of it.
Increase the misclassification costs
Consider the following setting. You are provided with n training examples: (x1, y1), (x2, y2), ·...
The training data consists of N pairs (x1,y1),(x2,y2),··· ,(xN,yN), with xi ∈
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number. Is the parameter identifiable?.Compute the maximum likelihood estimate. If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where Yi=1(Xi<=0.5).What distribution does Yi follow? What is the parameter of this distribution? Compute MLE and the method of moments and Fisher information.
Let X1,X2,X3..Xn be iid of f(x)= theta. x^(theta-1), with x(0,1) and theta being a positive number. Is the parameter identifiable?.Compute the maximum likelihood estimate. If instead of X1,X2,,, We observe, Y1,Y2,...Yn, where Yi=1(Xi<=0.5).What distribution does Yi follow? What is the parameter of this distribution? Compute MLE and the method of moments and Fisher information.
Consider a random sample (X1, Y1),(X2, Y2), . . . ,(Xn, Yn) where Y | X = x is modeled by a N(β0 + βx, σ2 ) distribution, where β0, β1 and σ 2 are unknown. (a) Prove that the mle of β1 is an unbiased estimator of β1. (b) Prove that the mle of β0 is an unbiased estimator of β0.
Suppose you are given the following feature vectors: x1 = (1,0), x2 = (4,2), x3 = (0,-1), x4 = (-1,-1), x5 = (-2,1) Their corresponding labels are y1 = 1, y2 = 1, y3 = -1, y4 = -1, y5 = -1 Note: there is no bias term in this problem. Suppose we run perceptron on this dataset starting with w0 = (0,0). Write down the values of w1,w2,w3,w4 and w5 after each training instance, that is, wi is the...