[Solved] NCTU-CS Assignment #3 -Linear Regression & Logistic Regression

Objective

• Linear Regression

• 1. Data Generation
     • Randomly generate 1000 (1)“>(1)(1)

&#x2212;1.5&lt;xi&lt;1.0“>1.5<xi<1.01.5<xi<1.0, N“>NN represents Normal distribution

• 1. Data Preprocessing 10%
     • Generate degree-x&#x005E;“>x^x^ from x&#x005E;i=[1xixi2&#x2026;xiK]“>x^i=1xix2ixKix^i=[1xixi2xiK]
       • 1. • You must experiments K“>KK settings, hint
         2. Model Construction 20%
            • Linear Regression
              • Which makes predictions s.t.“>s.t.s.t.
       1. • You must construct Linear Regression models to fit and predict data generated by y&#x005E;“>y^y^ for LaTeX“>LaTeXLaTeX
          • Use &#x2217;“> to represent multiplication operations
          • Use x“>xx
          • Limit the floating-point numeric weights to be 1.54323423456“>1.543234234561.54323423456 but 1+&#x2212;3.36&#x00D7;xi“>1+3.36xi1+3.36xi

• Logistic Regression 45% + (10%)

• 1. Data Generation 15%
     • Randomly generate 1000 (2)“>(2)(2)

yi“>yiyi is randomly assigned as 1“>11.

• 1. Model Construction 20%
     • Logistic Regression
       • Whose divider L“>LL to perform classification

1. • • Takes L2-norm as the objective function to optimize weight w=argminw&#x2032;||y&#x2212;Mw&#x2032;(x)||2“>w=argminw||yMw(x)||2w=argminw||yMw(x)||2
       • 1. • Construct a Logistic Regression model to predict [xi0xi1]T“>[xi0xi1]T[xi0xi1]T generated from equation yi=L(4.2+7.7&#x00D7;xi0+6.9&#x00D7;xi1)“>yi=L(4.2+7.7xi0+6.9xi1)yi=L(4.2+7.7xi0+6.9xi1)
              • 1. • Bonus show the decision boundary with a figure (10%)
              • Finish during class 20%
              • • Submit your report and source codes to the newE3 system before class ends.
                • Finish time will be determined by the submission time.