People Innovation Excellence


Consider the following data, i.e., the return from a particular industry firm’s stock and the corresponding returns from the market portfolio for the past 15 years:

Year Stock’s Return (%) Market Return (%)
1 16.02 21.05
2 12.17 17.25
3 11.48 13.1
4 17.62 18.23
5 20.01 21.52
6 14 13.26
7 13.22 15.84
8 17.79 22.18
9 15.46 16.26
10 8.09 5.64
11 11 10.55
12 18.52 17.86
13 14.05 12.75
14 8.79 9.13
15 11.6 13.87

The question is, given the data, i.e., the pairs (or tuples) of market return and stock’s return throughout the past 15 years, can we predict stock’s return if we know the market return?  To answer this question, let’s “learn” from the pattern given by the data. The following is the plot of market return against the stock’s return:

After doing the “learning” (estimation of the coefficient of the regression) process from the data we now have an equation, a “machine” that have learned from the past data, to predict the value of Y (or stock’s return) given a particular value of X.  Say for example, for X = 20 % then the stock’s return (Y) = 3.83911 + 0.666258 (20) = 17.16427 %.  As new information is generated, i.e., new pairs of X and Y from the real world, then the “machine” can also be having to learn from this new data, that is to generate a new estimators and hence a new updated equation.  The process called learning, hence “machine learning”, learning from actual data that supervised the learning process.

Some Notes:

  • Input X can be probabilistic as in our example; Probabilistic meaning X follows a particular probability distribution; X also could be a vector (more than one X).
  • The function f(x) could be specific as in our example, a linear function, and the process of learning follows, i.e., linear regression. Some other functions and the process of learning are:
    1. The function is not specifically modeled as in Artificial Neural Network (ANN).
    2. It is a Neural Network Model, but the input might include images. This is called Convolutional Neural Network (CNN).
    3. In some cases, the machine is unsupervised; hence “unsupervised learning”. In addition to the current advancement in this area, some of these techniques are actually are in statistics even though they are not called “machines”. For example, Cluster analysis; discriminant analysis, etc.(Ir. Togar Alam Napitupulu, MS., MSc., PhD)

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