Machine Learning in terms of probability is quite important, but the probability of the difficulty is that it is not intuitive, then from another angle, we call "God perspective", the probability into the area, and this will become intuitive;
1. The definition of probability
Probability, by definition is a possibility of a quantitative event, this is our most intuitive feelings;
The following from a more classic case as introducing --- Monty Hall Problem:
ABC has three doors, one of which is a right door, there is a high car open, the remaining two, the door to the wrong door for goat:
Prerequisite: dice corresponding to the door 1, 2; 3, 4 corresponding to the dice the door 2, the door 3 corresponding to 5,6 dice
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- Moderator by rolling dice to determine which of the door into the luxury car
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- Players roll the dice by the decision to open that door
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- After the player selection, the host will open the remaining two doors in the wrong door, and then ask whether the player changed his mind
Let's look at the probability of:
- If you choose correctly the first time, the error must re-election
- If you choose the wrong the first time, must be properly re-election
Therefore, the "first choice wrong," the probability is "right after the re-election," the probability of re-election of its accuracy rate is 2/3
But in fact, there will be another misunderstanding:
After the first selection, the host opened the wrong door, so this time leaving a false door and a right door, then the probability of re-election is this:
If the host opens the door wrong door 1;
- Gate 2 is the correct answer probability: 1/2
- Gate 3 is the probability of correct answer: 1/2
But think carefully, this probability is built on the basis of the players not selected for the first time carried on;
2. airship perspective Monty Hall Problem
As the above errors, the probability of an abstract thing, sometimes we fall into this myth out
Probability is an abstract concept, if we only rely on intuition, it is difficult to clearly understand the nature of
Our thinking is this:
1. Conversion perspective on this issue (here is the airship perspective)
2. Try to put the problems into a form can actually measure
The scene is this:
- The play set 360 hall venue 120 has a door 1 is the correct answer, the venue 120 is a correct answer of the door 2, the door 3 venue 120 is the correct answer
- Then the door 1 is the correct answer venue 120, 40 1 challenger select gate, select gate 40 2 challengers, challenger select gate 40 3
| Challenger choose door 1 | Challenger choose door 2 | Challenger selection door 3 | ||||
|---|---|---|---|---|---|---|
| host | Open the door 2 | Open the door 3 | Open the door 1 | Open the door 3 | Open the door 1 | Open the door 2 |
| Gate 1 is the correct answer | 20 venues | 20 venues | 0 venue | 40 venues | 0 venue | 40 venues |
| Gate 2 is the correct answer | 0 venue | 40 venues | 20 venues | 20 venues | 40 venues | 0 venue |
| Gate 3 is the correct answer | 40 venues | 0 venue | 40 venues | 0 venue | 20 venues | 20 venues |
According to the table, let's just restore errors:
- 1. challenger select gate 3
- 2. The host opened the door 1 has 60 venues
- 3. Gate 2 which is the correct answer is 40, the door 3 is the correct answer is 20, so that it was just wrong
3. God probability perspective
This time we need to look at a triple concept:
What is the perspective on the ground, in fact, a bird's eye view, every venue (in fact, a world, can also be considered a possible scenario is the emergence of a world), for a particular world, the world's current screenplay has been locked;
cite a simple example:
a random throw a dice, a total of six kinds of results: 1 is a result of the world, the result is a world of 2, 3, 4, empathy , 5,6 is also true ... and we from the "perspective on the ground," overlooking the world;Scene: the coin
- The results of the coin toss each world is always the same
- Then people do not know which one is living in the world, it will produce uncertainty
So far, we have an abstract concept: probability, into the concept of a quantifiable (area quantification)
We come here with a few mathematical symbols:
So would know that the first and third parameters meaning triples, where the second parameter for the time being skipped
This probability will be transformed into an area, any quantifiable things, than the abstract concept to understand more comfortable and profound;
4. The probability distribution of the random variable &
4.1 random variable
A sub-set of note here is just a point on the plane, we call basic sample points or more appropriate event will be some analogy, throwing coins into the face-up area there are numerous points, and the current events should be positive up event, but merely constitute a sample point a point events only;
4.2 probability distribution
Random variable is based on the specific parallel world, the relative probability distributions only consider the area, such as throwing a coin:
- Front: 0.5
- Reverse: 0.5
5. Independence of events
In fact, this definition may put it this way: Event A and time B, if P (A | B) = P (A | non-B), then we believe that events A and B are independent
To introduce several equivalence table v:
- A and B independently of each other
- P (A | B) = P (A | non-B)
- P(A|B) = P(A)
- P(A,B) = P(A)P(B)
- P (A, B): P (A, non-B) = P (non-A, B): P (non-A, non-B)
So determine any equivalence table can be used independently of whether the event AB v appeal to be judged
Reproduced in: https: //www.jianshu.com/p/febc7f5b0bcb