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Daniel N. Rockmore

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7 papers
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7

AILAW Journal 2020 Journal Article

Modeling law search as prediction

  • Faraz Dadgostari
  • Mauricio Guim
  • Peter A. Beling
  • Michael A. Livermore
  • Daniel N. Rockmore

Abstract Law search is fundamental to legal reasoning and its articulation is an important challenge and open problem in the ongoing efforts to investigate legal reasoning as a formal process. This Article formulates a mathematical model that frames the behavioral and cognitive framework of law search as a sequential decision process. The model has two components: first, a model of the legal corpus as a search space and second, a model of the search process (or search strategy ) that is compatible with that environment. The search space has the structure of a “multi-network”—an interleaved structure of distinct networks—developed in earlier work. In this Article, we develop and formally describe three related models of the search process. We then implement these models on a subset of the corpus of U.S. Supreme Court opinions and assess their performance against two benchmark prediction tasks. The first is to predict the citations in a document from its semantic content. The second is to predict the search results generated by human users. For both benchmarks, all search models outperform a null model with the learning-based model outperforming the other approaches. Our results indicate that through additional work and refinement, there may be the potential for machine law search to achieve human or near-human levels of performance.

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TCS Journal 2008 Journal Article

A fast Hermite transform

  • Gregory Leibon
  • Daniel N. Rockmore
  • Wooram Park
  • Robert Taintor
  • Gregory S. Chirikjian

We present algorithms for fast and stable approximation of the Hermite transform of a compactly supported function on the real line, attainable via an application of a fast algebraic algorithm for computing sums associated with a three-term relation. Trade-offs between approximation in bandlimit (in the Hermite sense), and size of the support region are addressed. Numerical experiments are presented that show the feasibility and utility of our approach. Generalizations to any family of orthogonal polynomials are outlined. Applications to various problems in tomographic reconstruction, including the determination of protein structure, are discussed.

Details DOI
v2026.09.13