![[Solved] ECE471 Assignment 1-linear regression of a noisy sinewave using a set of gaussian basis](https://assignmentchef.com/wp-content/uploads/2022/08/downloadzip.jpg)
Perform linear regression of a noisy sinewave using a set of gaussian basis
005 functions with learned location and scale parameters. Model parameters are
006 learned with stochastic gradient descent. Use of automatic differentiation is
007
008 required. Hint: note your limits!
009
010
011 Problem Statement Consider a set of scalars {x1,x2,,xN} drawn from U(0,1) 012 and a corresponding set {y1,y2,,yN} where:
013
| 014015016017018019020021022 | yi = sin(2xi)+ iand i is drawn from N(0,noise). Given the following functional form:yi = wjj (xi | j,j)+ b Mj=1with: | (1)(2) |
023
024(3)
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| 026027 | find estimates b, {j}, {j}, and {wj} that minimize the loss function: |
028
029(4)
030
031 for all (xi,yi) pairs. Estimates for the parameters must be found using stochastic
032 gradient descent. A framework that supports automatic differentiation must be
033
034 used. Set N = 50,noise = 0.1. Select M as appropriate. Produce two plots. First,
035 show the data-points, a noiseless sinewave, and the manifold produced by the
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regression model. Second, show each of the M basis functions. Plots must be of
037
038 suitable visual quality.
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