2.1 The Purpose of Machine Learning
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Fig. 2.2 Left: a sample in MNIST [18]. Right: a sample in CIFAR-10 [19]
2.1.1 Mathematical Formulation of Data
Given supervised/unsupervised data, the goal is to design a learning machine that
extracts its features and is able to predict properties of unknown data. To find a way
to construct such a machine, we need to mathematically formulate what we mean
by “predicting properties of unknown data.” For this reason, let us try the following
thought experiment.
Two dice
Suppose we have two dice here.
• Dice A rolls every number 1, · · · , 6 with a probability of 1/6.
• Dice B has only the number 6 with probability 1.
Then we repeat the following steps:
1. Choose A or B with a probability of 1/2, set d = 0 for A, d = 1 for B.
2. Roll the dice and name the pip as x.
3. Record (x, d).
Then we may obtain the following data.
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Fig. 2.2 Left: a sample in MNIST [18]. Right: a sample in CIFAR-10 [19]
2.1.1 Mathematical Formulation of Data
Given supervised/unsupervised data, the goal is to design a learning machine that
extracts its features and is able to predict properties of unknown data. To find a way
to construct such a machine, we need to mathematically formulate what we mean
by “predicting properties of unknown data.” For this reason, let us try the following
thought experiment.
Two dice
Suppose we have two dice here.
• Dice A rolls every number 1, · · · , 6 with a probability of 1/6.
• Dice B has only the number 6 with probability 1.
Then we repeat the following steps:
1. Choose A or B with a probability of 1/2, set d = 0 for A, d = 1 for B.
2. Roll the dice and name the pip as x.
3. Record (x, d).
Then we may obtain the following data.