Conditional probability: P (x| Y
Joint probability: P (X, Y)
Edge probability: P (X), P (Y).
Joint probability = conditional probability * Edge probability
The inverse problem is usually solved with conditional probabilities.
- Inverse problem refers to the problem that the cause should be reversed from the result;
- A positive problem is the introduction of results from a cause.
- The inverse problems are common:
- Communication: According to the received signal containing noise y presumably send a signal x;
- Speech recognition: Based on the audio waveform data identified by Mioko, Y guesses the voice information x;
- Text recognition: Based on the image read by the scanner y guess the text x written by the user;
- Automatic message filtering: Based on the received message text y guess the type of the message x (whether it is advertising, etc.)
- The relationship between x, Y is expressed by the random variable x, Y.
- The Bayesian formula discusses the following types of problems:
- Consistent all P (cause) and P (Result | reason)
- Ask P (cause | result)
where P (cause) is called a priori probability, p (cause | result) is called posterior probability, and the distribution of response is called prior distribution and posterior distribution.
- If there are multiple random variables in the problem, we first look at whether there is a real association between these random variables:
Nature of Satisfaction:
- If x is not related to Y, it is meaningless to push y by X.
- "Independent" differs from "Uniform distribution": P (y=1| x=**) = P (y=2| x=**) = P (y=3| x=**) = .... (does not satisfy independence)
- "Independent" differs from "Independent distribution": P (x=1) = P (y=1), p (x=2) = P (y=2), p (x=3) = P (y=3), ...
- "Independent" differs from "mutex": independence does not mean that the "event x=1 and Y=1 do not occur simultaneously", whereas the mutex means that x and Y are not independent random variables.
- Independence means that x is not associated with Y, and we cannot judge the value of x based on Y.
- Conditional probabilities are independent of condition: P (x| Y) = P (x|-y)
- Add or remove conditions do not affect: P (x| Y) = P (X)
- The joint probability is the product of the edge probability: P (x, Y) = P (x) *p (y)
The cause of Bayesian (probability theory analysis)