i.i.d. assumption, iid independent and identically distributed Independent means one event’s outcome doesn’t provide any information about another event. Identical means that if a subset of data is sampled from different parts of the dataset, the distribution is the same (identical parameters)
Reverse of
Markov Chain sequence data.
Random Variable s, when there are multiple, are mutually independent and all have the same
Probability Distribution The n samples your observed are considered as random variables.
Identical distributed i f f P ( X ≤ x ) = P ( Y ≤ x ) ∀ x ∈ I , I ∈ R iff \text{ } P(X\le x) = P(Y\le x) \forall x \in I, I\in R i ff P ( X ≤ x ) = P ( Y ≤ x ) ∀ x ∈ I , I ∈ R Independently distributed i f f P ( X ) = x ∩ Y = y ) = P ( X = x ) P ( Y = y ) ∀ x , y ∈ I , I ∈ R iff \text{ } P(X)=x \cap Y = y) = P(X=x)P(Y=y) \forall x , y\in I, I\in R i ff P ( X ) = x ∩ Y = y ) = P ( X = x ) P ( Y = y ) ∀ x , y ∈ I , I ∈ R
Clarifications on I.I.D. assumption in machine learning
In this question, it was stated that the assumption of i.i.d. for data comes in the form of
$$(X_i,y_i)∼P(X,y),∀i=1,...,N \\(X_i,y_i) \;independent\; of \;(X_j,y_j),\;∀i≠j∈{1,...,N}
$$
I am clear w...
https://stats.stackexchange.com/questions/546518/clarifications-on-i-i-d-assumption-in-machine-learning
