• We have the constant data matrix X E RXa. Each row X; is a d-dimensional data vector.• We have the vector w e Rª and noise vector e E R".• We observe yi ER as the output for each row in the input data matrix X;: yi == w" x; + €;Given the model definition above, please derive the following:Q3.1: Ridge Regression can be formulated as:w* = argmin,weR E – w" x1)² + 4,||w|;,(yiiwhere 1, > 0 is the hyperparameter to control the L2 regularization of w. The loss function for Ridge Regression isJ(w, 1,) = E,(yi – w x1)? + A,||w|3 Derive the closed form for the optimal w* in terms of X, y and 1,.

Input : Load the data. Apply ridge regression and find optimal w.

Answered: • We have the constant data matrix X E…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question Study the dataset given in file ‘x03.csv’, read it in as a data frame. Use the linear regression method to find a possible linear relation between blood pressure and age. First plot the given sample points, then plot the linear model graph as only 2 variables; blood pressure and age are in the dataset. Finally, plot the residuals points and counts of the residuals, and evaluate the normality assumption for the dataset. x03.csv x03.csv Index Systolic age bp 1 1 39 144 2 1 47 220 3 1 45 138 4 1 47 145 5 1 65 162 6 1 46 142 7 1 67 170 8 1 42 124 9 1 67 158 10 1 56 154 11 1 64 162 12 1 56 150 13 1 59 140 14 1 34 110 15 1 42 128 16 1 48 130 17 1 45 135 18 1 17 114 19 1 20 116 20 1 19 124 21 1 36 136 22 1 50 142 23 1 39 120 24 1 21 120 25 1 44 160 26 1 53 158 27 1 63 144 28 1 29 130 29 1 25 125 30 1 69 175
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Question 3. Regression need answer of part b Consider real-valued variables X and Y. The Y variable is generated, conditional on X, from the fol- lowing process: E~N(0,0²) YaX+e where every e is an independent variable, called a noise term, which is drawn from a Gaussian distri- bution with mean 0, and standard deviation σ. This is a one-feature linear regression model, where a is the only weight parameter. The conditional probability of Y has distribution p(YX, a) ~ N(aX, 0²), so it can be written as p(YX,a) = exp(- (-202 (Y-ax)²) 1 ν2πσ The following questions are all about this model. MLE estimation (a) Assume we have a training dataset of n pairs (X, Y) for i = 1..n, and σ is known. Which ones of the following equations correctly represent the maximum likelihood problem for estimating a? Say yes or no to each one. More than one of them should have the answer "yes." a 1 [Solution: no] arg max > 2πσ 1 [Solution: yes] arg max II a [Solution: no] arg max a [Solution: yes] arg max a 1…
You are provided with last year’s data showing which high school students chose standard or advanced coursework. The predictor variables include their writing score, math score, and science scores from previous years. Your task is to build a model that predicts if this year's incoming students are in advanced or standard coursework given the above predictor variables. Which model is suitable for this task? Linear regression k-means Clustering Logistic Regression Regression tree
1. If a stone is thrown vertically with an initial speed u, its vertical displacements after a time t has elapsed is given by the formula: s(t) = ut – gt/2 (Air resistance has been ignored) Model this equation with a simulink diagram to obtain a plot for the vertical displacement s with time t. Where g=9.8 , u=40. Hints: First, consider the blocks needed to build the model. A Ramp block to input the time signal t, from the Sources library. A Math function block (double click on it and select square) to get t', from the Math library. A Gain block to multiply the input signal by u, from the Math library. A Gain block to multiply the square of the input signal by g/2, from the Math library. A Sum block to subtract the two quantities, also from the Math library. A Scope block to display the output, from the Sinks library. Next, gather the blocks into your model window. Note that the output will not display a cleared output so right click on the display and select autoscale.
• Implement and test: • Logistic regression (LR) with L1 regularization • LR is differentiable • But L1 norm is not • Use proximal gradient descent • For L1 norm, that’s soft-thresholding • Use tensorflow library • Dataset – the same as in HW2: • Classify two digits from MNIST dataset • See: tensorflow_minimizeF.py • Performs projected gradient descent on a simple function • The function has global minimum at • w1=-0.25, w2=2 • But the feasible set Q is: w1>=0, w2>=0 • For this function, the best solution is w1=0, w2=2 • The code does the following, in a loop: • Gradient step on the function, followed up by proximal step • Here, the proximal step is just “make w nonnegative” by replacing negative values with 0, the closest non-negative value • Feasible set Q is set of all vectors with nonnegative coordinates, i.e., for 2D, w1>=0, w2>=0 • In your actual code, you should use soft-thresholding instead • See: tensorflow_leastSquares.py • Performs gradient descent on a function…
Q1 Consider an x-by-y logical containing n number of 0's and m number of 1's. Additionally, consider an x-by-y matrix (double). Which of the following outputs is true if the matrix is indexed with the logical? Select one: a. Output is a m-by-1 double b. Output is a n-by-1 double c. Output is an x-by-y double d. Output is an m-by-n double e. Output is an x-by-y logical Q2 Consider a text file that contains 19 rows of header text followed by 23 rows of numerical data. How many times will the fgetl() function need to be called to import the 9th row of numerical data in the text file? Select one: a. 23 b. 28 c. 14 d. 9 e. 1 Q3 Consider x to be an m-by-n matrix with m > n. Which of the following statements is true regarding y = ones(length(x))? Select one: a. The output of y will be an n-by-n matrix b. The output of y will be an m-by-m matrix c. The output of y will be an n-by-m matrix d. The output of y will be a 1-by-n vector e. The…
4) In the working set model, for: ... 1345 6 03 23 204032921..., if DELTA = 6, then the working set at time t1 (... 04 03 ...) is А. (6, 0, 3, 2] В. (2, 3, 0, 4} С. (0, 4, 3, 2, 9) D. {4, 5, 6, 0, 3, 2}
Which of the following statements is/are true about Earth Mover's Distance (EMD) when applied for domain adaptation O EMD assumes the source and target data belong to Gaussian distributions and determines the difference between the parameters of the Gaussian distributions. O EMD is a non-parametric technique, i.e., the EMD technique does not need the parameters of the source and target data distributions (for e.g. mean and covariance as in a Gaussian distribution) in order to estimate the distribution difference. EMD can be used as part of an objective function to train a neural network to align the features of the source and target datasets in domain adaptation. EMD is estimated by projecting the source and target data to a high-dimensional (infinite dimensional) space and then determining the distance between the means of the projected data in the high-dimensional space.
Demonstrate a clever way to generate a d-block diagonal matrix in MATLAB. The matrix should be of size A which has row = d^2 and col = d^2. d starts at 5 and increases by an increment of 5 until 50. The d-blocks in the diagonal matrix are size d by d.
Consider the following code:> x <- matrix(rnorm(n = 500), ncol = 5)> varx <- var(x)Starting with varx, use two applications of the sweep() function, one dividing each row of the matrix andthe other dividing each column, of a covariance matrix to obtain R, the correlation matrix.
After calculating Mean Square Error (MSE) and Mean Absolute Error (MAE) for a linear model, we observe that the value of MSE is much larger than the value of MAE. What are the possible reasons? Both A and B C. The data is not linear O B. There are outliers in the dataset O A. MAE is in y unit but MSE is squared

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