ECE495- Midterm Solved

Q1. ADS Fundamentals [
1a. A vehicle is equipped with a stop-and-go pilot, which can fully operate a vehicle on a highway in traffic jams, but with a fallback-ready user. Which level(s) of driving automation is this driving automation system operating at? [1 mark]

Q2. Computer Vision Fundamentals
 

2a. Compute 1-D cross-correlation by applying the following filter [0 2 1] to the following signal [0 1 3 0] (assume enough zero padding to show all non-zero output). [2 marks]

2b. Assume that the output of cross-correlating the 1-D filter [2 3 2] with some input signal resulted in the following output signal [7 10 7]. What would be the output signal have we used convolution instead of cross-correlation and why? [1 mark]

. What is the name of the following filter and what is it computing? [1 mark]

. Why is the Canny filter using double thresholding? [1 mark]

g.1 What is each of the individual sinusoids corresponding to in the input image?

Consider the following representation in Hough space (polar coordinates).

2h. Which of the following value profiles represent black in HSV? (select all that apply) [1 mark]

1.    0,high,high

2.    any,low,low

3.    any,low,high

4.    60,high,high

5.    any,high,low

6.    any,any,low
Starting with the probabilistic model for linear regression (assume single input x and single out y), show that maximizing the likelihood for a dataset (x, y) (with i.i.d. datapoints) is equivalent to minimizing the sum of squared errors. Hint: go via negative log likelihood [5 marks]

3b. What is the regression loss (as used in class) for a data point with label 0.4 and predicted output 0.7? [1 mark]

Apply what you’ve learned in lecture and Assignment 2) Given the following set of input vector X, ground truth vector Y, and weight matrices W1, W2, B1, and B2 of a 2 layer fully connected neural network, what is the inference probability of the correct class? What is the cross-entropy loss value? Assume ReLU activation on the first hidden layer and softmax activation on the output layer. Show each step of the computation. Hint: Use numerically stable softmax and assume e−1 ≈ 0.37 and e−7 ≈ 0.00 [5 marks]

3d. Consider the computational graph below for the following function

                                                                          f(x1, x2) = ln(3x1 + e2x2)                                                   (8)

Draw the computational graph and annotate it with the forward pass (above the arrows) and backward pass (below the arrows) for x1 = 1 and x2 = 0 (propagate the gradient back to each function input). Recall

dex = ex              (9) dx

                                                                                      dln(x)       1

=     (10) dx x

Assume ln(4) ≈ 1.39 [5 marks]

Consider a convolutional layer with an input volume of depth 4 and output volume of depth 128. How many convolutional filters does the layer contain? What is the depth of each filter? [2 marks]