Material similarity of scaled models

Scaled random segmental models

We present the concept of a scaled random segmental model, which aims to overcome the modeling problem created by the fact that segment realizations of the same phonetic unit di er in length. In the scaled model the variance of the random mean trajectory is inversely proportional to the segment length. The scaled model enables a Baum-Welch type parameter reestimation, unlike the previously sugg...

Scaled Models for Nucleation ∗ Barbara

Similarity Component Analysis: Supplementary Material

k=1 q1−s k r s k log θk (S1) where p(s) = Pr(s1, . . . , sK|u,v, s) = ∏K k=1 Pr(sk|u,v, s). pk = P (sk = 1|u,v) is given by eq. (2). qk = P (sk = 1|u,v, s = 0) and rk = P (sk = 1|u,v, s = 1) are given by eq. (7). Note that the last equation uses the fact that Ep(s)(sk) = q 1−s k r s k. The third term Ep(s)[s log(1− ∏K k=1 θ 1(sk=1) k )] is not tractable; variational methods can be used, as desc...

A generative theory of similarity: supplementary material

Featural Model Suppose that s and s are two objects represented as binary feature vectors. Let n be the number of features possessed by one or both of the objects, and let the domain D be the set of all n-place binary vectors. A generative process over D is specified by a n-place vector θ, where θi is the probability that an object has value 1 on feature i. We place independent beta priors on e...

Scaled marginal models for multiple continuous outcomes.

In studies that involve multivariate outcomes it is often of interest to test for a common exposure effect. For example, our research is motivated by a study of neurocognitive performance in a cohort of HIV-infected women. The goal is to determine whether highly active antiretroviral therapy affects different aspects of neurocognitive functioning to the same degree and if so, to test for the tr...