I finally figured out how to use KaTex last night and posted a something on the gradient of logistic regression to test things out. So now I’ve decided to maintain this list of mathematical words/jargons that I come across quite frequently in my field and everytime have to check wikipedia to refresh my memory. I hope this will make it easier for me to remember them.
Subadditive: A subadditive function is a function \(f:A \rightarrow B\) , having a domain A and an ordered codomain B that are both closed under addition, with the following property,
\[\forall x,y \in A, f(x+y) \leq f(x) + f(y)\]Submodular: Let \(N\) be a finite ground set and \(f : 2^{N} \to R\). Then \(f\) is submodular if \(\forall A,B \subseteq N\),
\[f(A) + f(B) \geq f(A \cup B) + f(A \cap B)\]Hamming Distance: In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different
Log Determinant of SPD Matrix Usually in computation packages the determinant of the covariance matrix throws NaNs . But it turns out that log of the determinant might still be finite. Therefore,
L = tf.tf.cholesky(cov)
log_det_cov = 2*reduce_sum(tf.log(tf.matrix_diag(L)))