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Combinatorial Exploration is a new domain-agnostic algorithmic framework to automatically and rigorously study the structure of combinatorial objects and derive their counting sequences and generating functions. We describe how it works and…

The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…

Data Structures and Algorithms · Computer Science 2011-12-23 Philippe Duchon

In this paper, we give a general framework for the Boltzmann generation of colored objects belonging to combinatorial constructible classes. We propose an intuitive notion called profiled objects which allows the sampling of size-colored…

Discrete Mathematics · Computer Science 2009-11-17 Olivier Bodini , Alice Jacquot

Randomly generating structured objects is important in testing and optimizing functional programs, whereas generating random $'l$-terms is more specifically needed for testing and optimizing compilers. For that a tool called QuickCheck has…

Data Structures and Algorithms · Computer Science 2014-04-29 Pierre Lescanne

Boltzmann samplers, introduced by Duchon et al. in 2001, make it possible to uniformly draw approximate size objects from any class which can be specified through the symbolic method. This, through by evaluating the associated generating…

Discrete Mathematics · Computer Science 2014-11-14 Olivier Bodini , Jérémie Lumbroso , Nicolas Rolin

Model combination, often regarded as a key sub-field of ensemble learning, has been widely used in both academic research and industry applications. To facilitate this process, we propose and implement an easy-to-use Python toolkit, combo,…

Machine Learning · Computer Science 2020-09-22 Yue Zhao , Xuejian Wang , Cheng Cheng , Xueying Ding

A natural approach to software quality assurance consists in writing unit tests securing programmer-declared code invariants. Throughout the literature a great body of work has been devoted to tools and techniques automating this…

Logic in Computer Science · Computer Science 2017-09-14 Maciej Bendkowski , Katarzyna Grygiel , Paul Tarau

Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…

Data Structures and Algorithms · Computer Science 2023-04-11 Megan Bernstein , Matthew Fahrbach , Dana Randall

Combinatorial experiments involve synthesis of sample libraries with lateral composition gradients requiring spatially-resolved characterization of structure and properties. Due to maturation of combinatorial methods and their successful…

We present a famework for the automatic compilation of multi-parametric Boltzmann samplers for algebraic data types in Haskell. Our framework uses Template Haskell to synthesise efficient, entropy-optimal samplers generating random…

Software Engineering · Computer Science 2022-08-02 Maciej Bendkowski

We present Ecole, a new library to simplify machine learning research for combinatorial optimization. Ecole exposes several key decision tasks arising in general-purpose combinatorial optimization solvers as control problems over Markov…

Machine Learning · Computer Science 2020-11-26 Antoine Prouvost , Justin Dumouchelle , Lara Scavuzzo , Maxime Gasse , Didier Chételat , Andrea Lodi

Meta-learning (a.k.a. learning to learn) has recently emerged as a promising paradigm for a variety of applications. There are now many meta-learning methods, each focusing on different modeling aspects of base and meta learners, but all…

Machine Learning · Computer Science 2020-09-29 Yaohua Liu , Risheng Liu

Complementary-label learning (CLL) is a weakly supervised learning paradigm for multiclass classification, where only complementary labels -- indicating classes an instance does not belong to -- are provided to the learning algorithm.…

Machine Learning · Computer Science 2024-11-20 Nai-Xuan Ye , Tan-Ha Mai , Hsiu-Hsuan Wang , Wei-I Lin , Hsuan-Tien Lin

In this paper we describe Ecole (Extensible Combinatorial Optimization Learning Environments), a library to facilitate integration of machine learning in combinatorial optimization solvers. It exposes sequential decision making that must be…

Machine Learning · Computer Science 2021-04-08 Antoine Prouvost , Justin Dumouchelle , Maxime Gasse , Didier Chételat , Andrea Lodi

We study the problem of using low computational cost to automate the choices of learners and hyperparameters for an ad-hoc training dataset and error metric, by conducting trials of different configurations on the given training data. We…

Machine Learning · Computer Science 2021-05-20 Chi Wang , Qingyun Wu , Markus Weimer , Erkang Zhu

We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n…

Discrete Mathematics · Computer Science 2011-03-29 Manuel Bodirsky , Éric Fusy , Mihyun Kang , Stefan Vigerske

Combinatorial optimization augmented machine learning (COAML) has recently emerged as a powerful paradigm for integrating predictive models with combinatorial decision-making. By embedding combinatorial optimization oracles into learning…

Machine Learning · Computer Science 2026-01-16 Maximilian Schiffer , Heiko Hoppe , Yue Su , Louis Bouvier , Axel Parmentier

This paper introduces the first, open source software library for Constraint Consistent Learning (CCL). It implements a family of data-driven methods that are capable of (i) learning state-independent and -dependent constraints, (ii)…

Robotics · Computer Science 2020-02-19 Yuchen Zhao , Jeevan Manavalan , Prabhakar Ray , Hsiu-Chin Lin , Matthew Howard

In this paper, we introduce CDL, a software library designed for the analysis of permutations and linear orders subject to various structural restrictions. Prominent examples of these restrictions include pattern avoidance, a topic of…

Mathematical Software · Computer Science 2025-12-04 Bei Zhou , Klas Markstrōm , Søren Riis

Vision benefits from grouping pixels into objects and understanding their spatial relationships, both laterally and in depth. We capture this with a scene representation comprising an occlusion-ordered stack of "object layers," each…

Computer Vision and Pattern Recognition · Computer Science 2025-08-13 Aneel Damaraju , Dean Hazineh , Todd Zickler
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