The following images are handwritten instances of the digits 0 and 1 . The images are small, 8 pixels by 8 pixels, and each pixel contains a gray level from the range [0,7]. Rather than use individual pixel values, which can lead to very high-dimensional feature vectors, a simpler way to represent images for use with regression models is to calculate a histogram for each image and use this as the feature vector instead. In this case the histograms simply count the frequency of occurrence of each possible gray level in each image. The table that follows shows the histograms for a small dataset of 10 images split between examples of digits 0 and 1. A logistic regression model has been trained to classify digits as either 0 or 1 . The weights in this model are as follows: In78]71 This model has been used to make predictions for the instances in the training set above. These predictions, and the related calculations required for calculating error and w[j] error values are shown in the following table. In the table, the w[j] errors are calculated as W(j)L(W)=(yi(zi))(zi)(1(zi))xi[j] which is the gradient fo W[j] estimated using least squared error (LSE) instead of MLE. xi[j] is the i th feature of j th sample point. (a) Some of the model predictions are missing in the preceding table (marked with a ?). Calculate these. (b) Some of the Error and Squared Error values are missing in the preceding table (marked with a ?). Calculate these values. (c) Some of the w[j] error values are missing in the preceding table (marked with a?). Calculate these. (d) Calculate a new set of weights for this model using a learning rate of 0.01 with LSE. (e) The following table shows handwritten examples of the digits 7 and 8 and their corresponding histogram values. i. Calculate the output of the model (using the updated weights calculated in the previous part) for these two instances. ii. Comment on the appropriateness of these outputs. (f) Now calculate new weights using MLE and one sample point ID = 0 only instead of step (d) and repeat step (e). Use the same learning rate