Latent variable conditional models, including the latent conditional random fields as a special case, are popular models for many natural language processing and vision processing tasks. The computational complexity of the exact decoding/inference in latent conditional random fields is unclear. In this paper, we try to clarify the computational complexity of the exact decoding. We analyze the c...

We study conditional probability from the perspective of complexity theory of functions and operators in analysis, building on work by Ko (1983), Friedman (1984), and Kawamura and Cook (2010). For some random variable X in {0, 1}N whose distribution is continuous and polynomial-time computable, and some polynomial-time computable function f : {0, 1}N → [0, 1] for which the random variable f(X) ...

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.

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained frommany clusters. As the variable selection procedure, we here use the Akaike Information Criterion, AIC. In the context of the mixed linear models, two kinds of AIC have been proposed: marginal AIC...

This paper considers the problem of optimal estimation of a random variable X based on an observation denoted by a random vector Y. A mild restriction on the regular conditional distribution function of X given o(Y) is presented which ensures that E[Q,(X-g(Y))] is minimized for any cost function Q, that is nonnegative, even, and convex. Further, we show that given any real valued Bore1 measurab...

Abstract: In this paper, we obtain certain expressions and recurrence relations for two general classes of distributions based on some conditional expectations of k-th lower record values. We consider the necessary and sufficient conditions such that these conditional expectations hold for some distribution functions. Furthermore, an expression of conditional expectation of other general class ...

A causal graph G(V, E) specifies causal relationships among the random variables representing the vertices of the graph V . The relationships are specified by the directed edges E ; an edge Vi ! Vj implies that Vi 2 V is a direct parental cause for the effect Vj 2 V . With some abuse of notation, we will denote the random variable associated with a node V 2 V by V itself. We will denote the par...