edX-Learning-From-Data-Solutions:作业答案

# Code For Week #2 This homework was about the Hoeffding Inequality, noisy target functions and linear regression with nonlinear transformations. ## Plots ### Linear Regression To make sure my implementation of linear regression worked, I did a scatter plot with ![N=10][n10] points uniformly distributed in ![between -1 and 1][interval] along with the regression line, and a contour plot with the squared error surface with a point marking the optimal ![w][w].   ### Linear Regression + Perceptron Learning Algorithm (PLA) This plot shows the difference between the target function ![f][f] in magenta, the ![g][g] found via linear regression in yellow, and the ![gd][gd] found via PLA in green (it uses the weight vector of ![g][g] as the initial weights).  ### Linear Regression With Nonlinear Transformation This plot shows the difference between the noisy target function ![f][target] in magenta and the hypothesis ![g][g] in green, found via linear regression on the ![Z][Z] space after applying the transformation ![trans][trans].  [w]: http://latex.codecogs.com/gif.latex?w [wd]: http://latex.codecogs.com/gif.latex?w%27 [f]: http://latex.codecogs.com/gif.latex?f [g]: http://latex.codecogs.com/gif.latex?g [gd]: http://latex.codecogs.com/gif.latex?g%27 [n10]: http://latex.codecogs.com/gif.latex?N%3D10 [interval]: http://latex.codecogs.com/gif.latex?%5B-1%2C1%5D%5Ctimes%5B-1%2C1%5D [target]: http://latex.codecogs.com/gif.latex?f(x_1%2C%20x_2)%20%3D%20sign(x_1%5E2%20%2B%20x_2%5E2%20-%200.6) [Z]: http://latex.codecogs.com/gif.latex?Z [trans]: http://latex.codecogs.com/gif.latex?%5CPhi(x)%20%3D%20(1%2C%20x_1%2C%20x_2%2C%20x_1x_2%2C%20x_1%5E2%2C%20x_2%5E2)