Maybe it is my communications background, it took me long time to really “understand” why we need MCMC. Consider a really simple inference problem of trying to recover state from data , in Bayesian inference, we try to compute the posterior distribution In all textbooks, it will just explain that the denominator is hard to…
I like to view Markov chain as simply state transition model. Let’s consider finite number of states to make thing simple. Time homogeneous: simply mean that the state transition matrix does not change over time Irreducible: I hate this term as I tend to forget what it really means. Model is irreducible if one can…
I usually remember what Frobenius norm is. That is, the sum of square of all elements in a matrix. And I sometimes remember what nuclear norm is. That is, the sum of singular values of a matrix. But I forgot what trace norm is when I came across it again today. Actually all of them…
Came across Kelly criterion with 李永樂老師’s video. The proof is indeed rather elementary. However, it also puzzled me when I tried to derive it myself. It seems that the argument is completely okay. Hopefully, someone can correct me. Update: This is a good lesson learned. Yes. Have to be really careful in terms of expectation….
This is the third post of my data privacy series. Please refer to the first post for the definition of differential privacy and the second post for privacy mechanism. Robustness of differential privacy versus processing If a mechanism is -differential private to begin with, then further operation on is still -differential private. Proof: Let’s assume…
This is the second post of my data privacy series. You may want to also check out this post for an introduction to data privacy and differential privacy. 🙂 For convenient, let’s repeat the definition of differential privacy from the previous post. Definition: -Differential Privacy The query is -differentially private if and only if for…
A group $latex G$ in the context of math is a simple algebraic structure with a product operation $latex *$. Naturally, the operator won’t be of much use if the structure is not closed under the operation. Namely, we would like to have $latex a * b$ also in $latex G$ if both elements $latex…