Probabilistic techniques are central to data analysis, but different approaches can be difficult to apply, combine, and compare. This paper introduces composable generative population models (CGPMs), a computational abstraction that extends directed graphical models and can be used to describe and compose a broad class of probabilistic data analysis techniques. Examples include hierarchical Bay...

The paper studies a robust mixed integer program with single unrestricted continuous variable. purpose of the is polyhedral study solution set using submodularity. A submodular function diminishing returns property, and little work has been studied on utilization submodularity in optimization problems considering data uncertainty. In this paper, we propose valid inequalities Valid for are defin...

Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these may require the optimization probability values subject to constraints among distributions random variables. Here, we introduce a new class probabilistic logic programs, namely Optimizable Programs, and provide algorithm find best assignment probabilities variables, such t...

Probabilistic calibration is the task of producing reliable estimates of the conditional class probability P (class|observation) from the outputs of numerical classifiers. A recent comparative study [1] revealed that Isotonic Regression [2] and Platt Calibration [3] are most effective probabilistic calibration technique for a wide range of classifiers. This paper will demonstrate that these met...

In the past few years there has been a lot of work lying at the intersection of probability theory, logic programming and machine learning [14, 18, 13, 9, 6, 1, 11]. This work is known under the names of statistical relational learning [7, 5], probabilistic logic learning [4], or probabilistic inductive logic programming. Whereas most of the existing works have started from a probabilistic lear...

Probabilistic inductive logic programming, sometimes also called statistical relational learning, addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with first order logic representations and machine learning. A rich variety of different formalisms and learning techniques have been developed. In the present paper, we start from inductiv...