Gaussian Logic for Predictive Classification

Kuželka, Ondřej; Szabóová, Andrea; Holec, Matĕj; Železný, Filip

doi:10.1007/978-3-642-23783-6_18

Cited by 7 publications

(5 citation statements)

References 21 publications

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“…The TreeLiker tool can be configured to utilize a block-wise construction of tree-like relational features (RelF) [14], a hierarchical feature construction (HiFi) [13], or a Gaussian Logic-based algorithm (Poly) [11] for classification. These three algorithms can also be run in a grounding-counting setting (GC) considering the number of examples covered by a generated feature during learning.…”

Section: Discussionmentioning

confidence: 99%

SML-Bench – A benchmarking framework for structured machine learning

Westphal¹,

Bühmann²,

Bin³

et al. 2019

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The availability of structured data has increased significantly over the past decade and several approaches to learn from structured data have been proposed. These logic-based, inductive learning methods are often conceptually similar, which would allow a comparison among them even if they stem from different research communities. However, so far no efforts were made to define an environment for running learning tasks on a variety of tools, covering multiple knowledge representation languages. With SML-Bench, we propose a benchmarking framework to run inductive learning tools from the ILP and semantic web communities on a selection of learning problems. In this paper, we present the foundations of SML-Bench, discuss the systematic selection of benchmarking datasets and learning problems, and showcase an actual benchmark run on the currently supported tools.

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Section: Discussionmentioning

confidence: 99%

SML-Bench – A benchmarking framework for structured machine learning

Westphal¹,

Bühmann²,

Bin³

et al. 2019

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show abstract

“…In Probabilistic Soft Logic [4], arbitrarily complex similarity measures between objects are combined with logic constraints, again using T-norms for the continuous relaxation of Boolean operators. In Gaussian Logic [5], numeric variables are modeled with multivariate Gaussian distributions. Their parameters are tied according to logic formulae defined over these variables, and combined with weighted first order formulae modeling the discrete part of the domain (as in standard MLNs).…”

Section: Related Workmentioning

confidence: 99%

“…Since ψ can be expressed in terms of Satisfiability Modulo Linear Arithmetic, the latter minimization problem can be readily cast as an OMT problem. Translating back to the example, maximizing the compatibility function f boils down to: argmax w ψ(I, O) = argmax (−dx 2 , −dy 2 )w = argmin (dx 2 , dy 2 )w (5) which is exactly the cost minimization problem in Equation 1.…”

Section: Touching Blocksmentioning

confidence: 99%

“…There is relatively little previous work on hybrid SRL methods. A number of approaches [3,4,5,6] focused on the feature representation perspective, in order to extend statistical relational learning algorithms to deal with continuous features as inputs. On the other hand, performing inference over joint continuous-discrete relational domains is still a challenge.…”

Section: Introductionmentioning

confidence: 99%

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Structured learning modulo theories

Teso¹,

Sebastiani²,

Passerini³

2017

Artificial Intelligence

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Modelling problems containing a mixture of Boolean and numerical variables is a long-standing interest of Artificial Intelligence. However, performing inference and learning in hybrid domains is a particularly daunting task. The ability to model this kind of domains is crucial in "learning to design" tasks, that is, learning applications where the goal is to learn from examples how to perform automatic de novo design of novel objects. In this paper we present Structured Learning Modulo Theories, a max-margin approach for learning in hybrid domains based on Satisfiability Modulo Theories, which allows to combine Boolean reasoning and optimization over continuous linear arithmetical constraints. The main idea is to leverage a state-of-the-art generalized Satisfiability Modulo Theory solver for implementing the inference and separation oracles of Structured Output SVMs. We validate our method on artificial and real world scenarios.

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“…There are a number of applications involving both Boolean and numerical constraints, such as environment learning for robot planning [5] and the modeling of gene expression data [14]. Here we describe two of them, to illustrate the flexibility and expressive power of LMT.…”

Section: Applicationsmentioning

confidence: 99%

Hybrid SRL with Optimization Modulo Theories

Teso¹,

Sebastiani²,

Passerini³

2014

Preprint

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Generally speaking, the goal of constructive learning could be seen as, given an example set of structured objects, to generate novel objects with similar properties. From a statistical-relational learning (SRL) viewpoint, the task can be interpreted as a constraint satisfaction problem, i.e. the generated objects must obey a set of soft constraints, whose weights are estimated from the data. Traditional SRL approaches rely on (finite) First-Order Logic (FOL) as a description language, and on MAX-SAT solvers to perform inference. Alas, FOL is unsuited for constructive problems where the objects contain a mixture of Boolean and numerical variables. It is in fact difficult to implement, e.g. linear arithmetic constraints within the language of FOL. In this paper we propose a novel class of hybrid SRL methods that rely on Satisfiability Modulo Theories, an alternative class of formal languages that allow to describe, and reason over, mixed Boolean-numerical objects and constraints. The resulting methods, which we call Learning Modulo Theories, are formulated within the structured output SVM framework, and employ a weighted SMT solver as an optimization oracle to perform efficient inference and discriminative max margin weight learning. We also present a few examples of constructive learning applications enabled by our method.

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Gaussian Logic for Predictive Classification

Cited by 7 publications

References 21 publications

SML-Bench – A benchmarking framework for structured machine learning

SML-Bench – A benchmarking framework for structured machine learning

Structured learning modulo theories

Hybrid SRL with Optimization Modulo Theories

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