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Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery

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Stefano Ermon, Ronan Le Bras, Santosh K. Suram, John M. Gregoire, Carla Gomes, Bart Selman, Robert B. van Dover

Artificial Intelligence · Submitted 27 Nov 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions.

how it is stated · asserted 1.00 read the record →

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arXiv ID1411.7441 (version 1)
Pith IDM3MS3CJE, Pith's permanent record of this paper and its review
CitationBart Selman, Carla Gomes, John M. Gregoire, Robert B. van Dover, Ronan Le Bras, Santosh K. Suram, Stefano Ermon. "Pattern Decomposition with Complex Combinatorial Constraints: Application to Materials Discovery." arXiv:1411.7441 (2014). https://pith.science/paper/M3MS3CJE
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,301 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.06 · human participants 0.03 · controlled comparison 0.49 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.94 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. background 1.00 0.04 0.02 asserted 1.00
s1 Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. contribution 0.97 0.79 0.06 asserted 0.98
s2 In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. method 0.73 0.95 0.04 asserted 0.99
s3 Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. result 1.00 0.96 0.77 asserted 1.00
s4 We also show the effectiveness of our approach for enforcing background knowledge on other application domains. result 0.91 0.92 0.09 asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.83.

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not examined
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  • references and citing sentences
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not run
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  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Identifying important components or factors in large amounts of noisy data is a key problem in machine learning and data mining. Motivated by a pattern decomposition problem in materials discovery, aimed at discovering new materials for renewable energy, e.g. for fuel and solar cells, we introduce CombiFD, a framework for factor based pattern decomposition that allows the incorporation of a-priori knowledge as constraints, including complex combinatorial constraints. In addition, we propose a new pattern decomposition algorithm, called AMIQO, based on solving a sequence of (mixed-integer) quadratic programs. Our approach considerably outperforms the state of the art on the materials discovery problem, scaling to larger datasets and recovering more precise and physically meaningful decompositions. We also show the effectiveness of our approach for enforcing background knowledge on other application domains.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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