The discovery of structural form
The discovery of structural form
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DOI：
10.1073/pnas.0802631105
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发表时间：
2008-08-05
影响因子：
11.1
通讯作者：
Tenenbaum, Joshua B.
中科院分区：
文献类型：
--
作者：
Kemp, Charles;Tenenbaum, Joshua B.
无论是作为科学数据分析的工具，还是作为人类学习的模型，在数据中发现结构的算法都变得越来越重要，但它们受到一个严重的限制。科学家们在观测数据中发现了定性的新结构形式：例如，林奈认识到生物物种的等级组织，门捷列夫认识到化学元素的周期结构。类似的洞察力在认知发展中起着关键作用：儿童发现，对象类别标签可以被组织成等级，友谊网络被组织成派系，比较关系(例如，“大于”或“好于”)尊重传递性秩序。然而，标准算法只能学习必须预先指定的单一形式的结构：例如，用于分层聚类的算法创建树结构，而用于降维的算法创建低维空间。在这里，我们提出了一个计算模型，它学习许多不同形式的结构，并发现哪种形式最适合给定的数据集。该模型在表示树、线性顺序、多维空间、环、优势等级、集团和其他形式的图文法空间上进行概率推理，并成功地发现了各种物理、生物和社会领域的底层结构。我们的方法使结构学习方法更接近人类的能力，并可能导致对认知发展的更深层次的计算理解。
Algorithms for finding structure in data have become increasingly important both as tools for scientific data analysis and as models of human learning, yet they suffer from a critical limitation. Scientists discover qualitatively new forms of structure in observed data: For instance, Linnaeus recognized the hierarchical organization of biological species, and Mendeleev recognized the periodic structure of the chemical elements. Analogous insights play a pivotal role in cognitive development: Children discover that object category labels can be organized into hierarchies, friendship networks are organized into cliques, and comparative relations (e.g., "bigger than" or "better than") respect a transitive order. Standard algorithms, however, can only learn structures of a single form that must be specified in advance: For instance, algorithms for hierarchical clustering create tree structures, whereas algorithms for dimensionality-reduction create low-dimensional spaces. Here, we present a computational model that learns structures of many different forms and that discovers which form is best for a given dataset. The model makes probabilistic inferences over a space of graph grammars representing trees, linear orders, multidimensional spaces, rings, dominance hierarchies, cliques, and other forms and successfully discovers the underlying structure of a variety of physical, biological, and social domains. Our approach brings structure learning methods closer to human abilities and may lead to a deeper computational understanding of cognitive development.