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About 4,805 papers for “Conditional expectation”

Conditional Expectation

Jean‐Pierre Florens, Vêlayoudom Marimoutou, Anne Péguin-Feissolle · Cambridge University Press eBooks · 2007

Cited by 0

Conditional Expectation

Arup Bose, Arijit Chakrabarty, Rajat Subhra Hazra · Texts and readings in mathematics · 2024

Cited by 0

Conditional Expectation

Paul E. Pfeiffer · Birkhäuser Boston eBooks · 1979

In order to introduce and develop the second concept of conditional independence, we need to examine the concept of conditional expectation. The usual introductory treatment of conditional expectation is intuitive, straightforward, but severely limited in scope. More general treatments tend to assume familiarity with advanced notions of measurability and abstract integration theory. We seek to bridge the gap and make the appropriate aspects of a general treatment more readily accessible.

Cited by 0

Conditional expectation

Wiley series in probability and statistics · 2017

In this chapter, the authors introduce the general concept of a conditional expectation given a σ-algebra 𝒸. The concepts of a conditional expectation value and a conditional probability are defined more generally, using the factorization of a conditional expectation. The authors also define the general concept of a regression as a factorization g of a conditional expectation E(Y | X) = g(X), provided that X is real-valued. Furthermore, they define an (X=x)-conditional expectation value E(Y | X=x) as a value g(x) of the factorization g. This means that E(Y | X=x) is defined even if P(X=x) = 0. However, E(Y | X=x) is not uniquely defined. Nevertheless, they can formulate propositions about the conditional expectation values E(Y | X=x) for PX-almost all values x of X. Finally, they introduce the concept of mean independence and study its relationship to stochastic independence and uncorrelatedness.

Cited by 0

Conditional Expectation Propagation

Zheng Wang, Shandian Zhe · arXiv (Cornell University) · 2019

Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propagation provides a good solution, it has to run numerical optimizations to find Laplace approximations in every update, which is still quite inefficient. To overcome these practical barriers, we propose conditional expectation propagation (CEP) that performs conditional moment matching given the variables outside each message, and then takes expectation w.r.t the approximate posterior of these variables. The conditional moments are often analytical and much easier to derive. In the most general case, we can use (fully) factorized messages to represent the conditional moments by quadrature formulas. We then compute the expectation of the conditional moments via Taylor approximations when necessary. In this way, our algorithm can always conduct efficient, analytical fixed point iterations. Experiments on several popular models for which standard EP is available or unavailable demonstrate the advantages of CEP in both inference quality and computational efficiency.

Cited by 1Open access