Machine learning watermelon book study notes 1.3 hypothesis space

The two basic methods of scientific reasoning are
summarized ( $induction$ ): the generalization process from special to general(deduction deductionfrom specific facts)
$deduction$ ): general to special specialization process (deduction from basic principles)

Inductive learning:
broad sense: learning from examples,
narrow sense: learning concepts from training data ( $concept$ ), "concept learning", "concept formation"

Boolean concept learning : the most basic concept learning is/not 0/1

serial number	Color	Root	Knock	Good melon
1	Turquoise	Curl up	Voice	Yes
2	Jet black	Curl up	Voice	Yes
3	Turquoise	Stiff	Crisp	no
4	Jet black	Slightly curled up	Dull	no

Learning goal: good melon
Determinants: color, root, knocking
Boolean expression: good melon $\leftrightarrow$ (color=?)^ (root=?) ^ (knock=?) here? Indicates a value that has not yet been determined.

'Remember' training samples, mechanical learning, rote learning, what to do with melons that you haven't seen before?
Consider the learning process as a hypothesis in all hypothesis ( $hypothesis$ ) is a process of diligent search in the space composed of, the
search goal: to find a hypothesis that'matches' with the training set. Once the representation of the hypothesis is determined, the hypothesis space and its scale are also determined.
Example: The hypothesis space is formed by possible values ​​of the form "(color=?)^ (root=?) ^(knock=?)" For example, the color is composed of three possible values ​​of cyan, black and black knocking; also consider that whatever value may be appropriate for the color, use the wildcard character$‘\ast \text{'}$ Means, for example,$Goodmelon\leftrightarrow (ColorZe=\ast )\wedge (Rootpedicle=Curledshrink)\wedge (Knockingsound=Mixsound)$ , that is, good melon meet back condition, color and anything can be.

In addition, considering extreme cases, there is no good melon, $\varnothing tableshows$

If there are 3, 3, and 3 possible values ​​for the knocking sound of the color and luster, the hypothetical space size faced is $4\times 4\times 4\times 4+1=65$ (I am not very clear here. I understand that 4 is 3 plus a wildcard option, and the last one is when all are wildcard options.)
Many strategies can be used to search the hypothesis space
from top to bottom, From general to special,
bottom-up, from special to general
, the hypothesis that is inconsistent with the positive example and the hypothesis that is consistent with the negative example can be deleted continuously in the process of searchingfrom the general to the special. In the end, the hypothesis consistent with the training set will be obtained, and the result learned by i.

Real problems face a larger hypothesis space, but the learning process is based on a limited sample training set, so it may be consistent with multiple hypotheses and training sets, that is, there is a'hypothesis set' that is consistent with the training set, which is called version space For example, in the watermelon problem, the version space corresponding to the training set corresponding to the table is as follows;