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機器學習導論 - Part I


Instructor


Course information

Textbook:

There is no required textbook.

Reference:


Grading Policy

  1. In class (5%)
    • (2%) Either be on duty for one lecture or share your lecture notes.
    • (3%) Other in-class activities.
  2. Assignments (15%)

Course calander:

週一 週四
9/13 課程介紹 - Lin 9/16 Lin
9/20 Holiday 9/23 Lin, Youtube - MLE
9/27 Lin 9/30 Lin
10/4 Lin 10/7 Lin
10/11 Holiday 10/14 Lin

Assignments

  • Assignment 0 - Slef-practice on python (No hand-in)
  • Assignment 1

    Extract the size and price data of your homwtown, use linear regressoin to find the best linear model

    You should

    • Specify and describe properly your data
    • Explain how the data is extracted
    • submit a 'ipynb file' to E3
  • Assignment 2

    You should submit a single PDF file to e3.

    1. Show that
      12πσ2exp((xμ)22σ2)dx=1
    2. Given sample
      {xi}i=1N
      from random distribution
      N(μ,σ)
      , show that the critical point for the likelihood function found in class is indeed a global maximum.
  • Assignment 3
    1. (ipynb) Explore the data (or try to find real data from somewhere) and find a way to see the data such that it has a two-dimensional curve-like structure.

      You should

      • Specify and describe properly your data
      • Explain how the data is obtained and extracted

      In particular, you should make sure the explanation is clear enough so that the graph and data can be reproduced by the coursemate

    2. (PDF) For binary classification problem, consider the cost function as mean square error and derive the corresponding gradient descent rule.
    3. (PDF) Consider the cross entropy loss for classification problem of
      2
      classes where the feature is
      R2
      data. Derive the corresponding gradient descent rule.
      • Remark:
        xiR2
        ,
        yiR2
        ,
        h(xi)R2
        .
  • Assignment 4
    1. Show that
      R212π|Σ|1/2exp(12(xμ)TΣ1(xμ))dx=1,

      where
      Σ
      is a
      2×2
      symmetric positive definite matrix.
    2. Let
      fC2(R)
      that satisfies
      f(x)0
      for all
      xR
      . Show that
      f
      is convex.
  • Assignment 5
    1. Find a function
      f(x,y)
      such that
      (x0,y0)
      is a critical point, i.e.,
      f(x0,y0)=0
      , besides,
      x2f(x0,y0)<0
      and
      y2f(x0,y0)<0
      , but
      f
      does not attain a local maximum at
      (x0,y0)
      .