﻿ Inductive inference for all possibilities

# Inductive inference for all possibilities

## ■ Enumeration of all hypotheses

Ignore computational complexity and combinatorial explosion.
List all hypotheses for best inductive reasoning.
1. Coordinate transformation in all ways.
2. Focus on all explanatory variables.
3. Assume all repeating units.
4. Assume all iteration ranges.

## ■ Coordinate transformation in all ways

1. Change scale on only one variable
such as taking logarithmic values.
2. Coordinate rotation with multiple variables
3. Changing expressions across multiple variables
polar coordinates, etc.
4. Scaling and translation
Since this does not affect the inference result, it can be ignored.
5. Mapping of injective functions from objective variables
1-5. Injective mapping from objective variable to function with all variables as arguments
However, if the distance of the target variable is within the interval of 0, it does not have to be injective.
If there is a difference in distance, there must also be a difference in the transformed values.
The “variable” here includes not only the objective variable but also the explanatory variable.
You may do something like taking the difference between the "objective variable" and the "objective variable" of another sample.

## ■All explanatory variables

An explanatory variable is a value associated with an objective variable.
1. Information given by the questioner and the value associated with the objective variable
2. The value associated with the objective variable in the information possessed by the respondent
3. Freely, the value associated with the target variable
Example: Predicting the outcome of a coin toss, assuming matching a list of numbers in a random book
4. Mapping functions of single or multiple explanatory variables as arguments
It doesn't have to be single shot.
1-4. Any unique value for the target variable

## ■All repeating units

Regularity at regular intervals and the like are “repeating units”.
1. Is a constant value
2. A constant value appears repeatedly at a constant period
3. A constant series of numbers repeats at a constant cycle
If the period is determined, the value is automatically determined, so only the period needs to be determined.
The constant period does not have to be a constant interval, and may be, for example, the period of the Fibonacci sequence.
You also need to specify the position of the reference, which is the beginning of the cycle.

## ■All repeat ranges

It is not necessary to consider all the samples given.
For example, you can use only the most recent data and ignore older data.
Basically, the range can be specified freely.
However, avoid specifying a range that connects multiple ranges with "OR".
Multiple ranges should be divided into two hypotheses and inferred from each.
For example, if you specify a range that connects two ranges with "OR", the hypothesis will be satisfied once when each of the two ranges is satisfied once.