MULTIDIMENSIONAL DYNAMIC RISK MEASURE VIA CONDITIONAL g -EXPECTATION

The dynamic ‘expectation–conditional maximization either’ algorithm

The ‘expectation–conditional maximization either’ (ECME) algorithm has proven to be an effective way of accelerating the expectation–maximization algorithm for many problems. Recognizing the limitation of using prefixed acceleration subspaces in the ECME algorithm, we propose a dynamic ECME (DECME) algorithm which allows the acceleration subspaces to be chosen dynamically. The simplest DECME im...

Derandomizing via the Method of Conditional Expectation

Suppose we want to derandomize A—that is, give a deterministic variant of A which succeeds with probabilty 1 on every input. Sometimes we can do this using the method of conditional expectation. We can think of A as a binary tree which, given x, branches on the sampled value of each random bit Ri in turn. Paths in this tree correspond to different possible random strings R1, . . . , Rm that cou...

CONDITIONAL EXPECTATION IN THE KOPKA'S D-POSETS

The notion of a $D$-poset was introduced in a connection withquantum mechanical models. In this paper, we introduce theconditional expectation of  random variables on theK^{o}pka's $D$-Poset and prove the basic properties ofconditional expectation on this  structure.

Conditional Expectation

Let μ and λ be two positive bounded measures on the same meaurable space (Ω,F). We call μ and λ equivalent, and write μ ≡ λ, if they have the same null sets— so, if they were probability measures, the notion of “a.s.” would be the same for both. More generally, we call λ absolutely continuous (AC) w.r.t. μ, and write λ μ, if μ(A) = 0 implies λ(A) = 0, i.e., if every μ-null set is also λ-null. W...

Conditional expectation