Continuing the work of Hiriart-Urruty and Phelps, we discuss (in both locally convex spaces and Banach spaces) the formulas for the conjugates and subdifferentials of the precomposition of a convex function by a continuous linear mapping and the marginal function of a convex function by a continuous linear mapping. We exhibit a certain (incomplete) duality between the operations of precompositi...

In this paper we address the problem of using region-based approximations to find the optimal points of a given function. Our approach combines the use of Kikuchi approximations with the application of generalized belief propagation (GBP) using maximization instead of marginalization. The relationship between the fixed points of maximum GBP and the free energy is elucidated. A straightforward c...

We consider the problem of covariance matrix estimation in the presence of latent variables. Under suitable conditions, it is possible to learn the marginal covariance matrix of the observed variables via a tractable convex program, where the concentration matrix of the observed variables is decomposed into a sparse matrix (representing the graphical structure of the observed variables) and a l...

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce t...

Under the Kyoto Protocol the European Union agreed to reduce emissions of greenhouse gases by 8 percent. The Burden-Sharing Agreement (BSA) redistributes the reduction target among the member states. The purpose of this paper is to evaluate the BSA. To determine if cost efficiency was considered, marginal abatement costs (MACs) are first calculated based on an estimation of the directional outp...

The 20 century was characterized by a special improvement in health. The aim of the World Health Organization policy of EQUITY IN HEALTH was to enable equal accessibility and high quality of health care for all citizens. However, some social groups remained more or less outside social systems including the healthcare system due to the social marginalization defined as an impact on health that w...

We study optimal methods for Alternative Dispute Resolution (ADR), a technique to achieve settlement and avoid costly adversarial hearings. Participation is voluntary. Disputants are privately informed about their marginal cost of evidence provision. If ADR fails engender settlement, the disputants can use information obtained during determine what provide in an hearing. Optimal induces asymmet...

Any regular Gaussian probability distribution that can be represented by an AMP chain graph (CG) can be expressed as a system of linear equations with correlated errors whose structure depends on the CG. However, the CG represents the errors implicitly, as no nodes in the CG correspond to the errors. We propose in this paper to add some deterministic nodes to the CG in order to represent the er...

U rban poverty has long been a concern of urban and development debates, and has been an important focus in social science research. Informal settlement in Mashhad city is highlighted because of its wide spreading and severity. This study aimed to determine the causes of urban poverty in informal settlement regions. The data were collected from household level questionnaire in 2016 a...