In this paper, we present an overview of generalized expectation criteria (GE), a simple, robust, scalable method for semi-supervised training using weakly-labeled data. GE fits model parameters by favoring models that match certain expectation constraints, such as marginal label distributions, on the unlabeled data. This paper shows how to apply generalized expectation criteria to two classes ...

The Expectation Maximization (EM) algorithm [1, 2] is one of the most widely used algorithms in statistics. Suppose we are given some observed data X and a model family parametrized by θ, and would like to find the θ which maximizes p(X |θ), i.e. the maximum likelihood estimator. The basic idea of EM is actually quite simple: when direct maximization of p(X |θ) is complicated we can augment the...

The Expectation Maximisation (EM) algorithm is a procedure that iteratively optimises parameters of a given model, to maximise the likelihood of observing a given (training) dataset. Assuming that our framework has unobserved data, X, observed data, Y , parameters Θ, and a likelihood function L(X,Y,Θ) = P(X,Y |Θ), we can derive the steps of the algorithm as follows: 1. Choose initial parameters...

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...

Aiming at the actuality that the research about costumer service recovery prediction structure is relatively deficient under the background of China culture, based on literature analysis, profound interview, opening investigation and expectation research, we adopt exploratory factor analysis method and confirmatory factor analysis method to develop and validate the scale used to measure custome...

Parameter estimation in dynamic systems finds applications in various disciplines, including system biology. The well-known expectation-maximization (EM) algorithm is a popular method and has been widely used to solve system identification and parameter estimation problems. However, the conventional EM algorithm cannot exploit the sparsity. On the other hand, in gene regulatory network inferenc...

In this paper, we study the linear fractional transportation problem with uncertain arameters. After recalling some definitions, concepts and theorems in uncertainty theory we present three approaches for solving this problem. First we consider the expected value of the objective function together with the expectation of satisfying constraints. Optimizing the expected value of the objective fun...

Analysis of spatio-temporal point patterns plays an important role in several disciplines, yet inference in these systems remains computationally challenging due to the high resolution modelling generally required by large data sets and the analytically intractable likelihood function. Here, we exploit the sparsity structure of a fully-discretised log-Gaussian Cox process model by using expecta...

SUMMARY The Expectation-Maximization (EM) algorithm is a powerful computational technique for locating maxima of functions. It is widely used in statistics for maximum likelihood or maximum a posteriori estimation in incomplete data models. In certain situations however, this method is not applicable because the expectation step cannot be performed in closed{form. To deal with these problems, a...

the position of financial organization would be increasingly decisive in the next decade in view of the frightening competition. with the increasing number of businesses and growing competitions today, each organization wants to be the customer’s first choice and try to satisfy them for getting loyalty for their future endurance in the market.  however, it is open to ask whether the organizatio...