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Discrete Stochastic Search and Its Application to Feature-Selection for Deep Relational Machines

机译：离散随机搜索及其在深度关系机特征选择中的应用

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We use a model for discrete stochastic search in which one or more objects ("targets") are to be found by a search over n locations ("boxes"), where n is infinitely large. Each box has some probability that it contains a target, resulting in a distribution H over boxes. We model the search for the targets as a stochastic procedure that draws boxes using some distribution S. We derive first a general expression on the expected number of misses E[Z] made by the search procedure in terms of H and S. We then obtain an expression for an optimal distribution 5* to minimise E[Z]. This results in a relation between: the entropy of H and the KL-divergence between H and S*. This result induces a 2-partitions over the boxes consisting of those boxes with H probability greater than ~1/_n and the rest. We use this result to devise a stochastic search procedure for the practical situation when H is unknown. We present results from simulations that agree with theoretical predictions; and demonstrate that the expected misses by the optimal seeker decreases as the entropy of H decreases, with a maximum obtained for uniform H. Finally, we demonstrate applications of this stochastic search procedure with a coarse assumption about H. The theoretical results and the procedure are applicable to stochastic search over any aspect of machine learning that involves a discrete search-space: for example, choice over features, structures or discretized parameter-selection. In this work, the procedure is used to select features for Deep Relational Machines (DRMs) which are Deep Neural Networks (DNNs) defined in terms of domain-specific knowledge and built with features selected from large, potentially infinite-attribute space. Empirical results obtained across over 70 real-world datasets show that using the stochastic search procedure results in significantly better performances than the state-of-the-art.
机译：我们使用一种用于离散随机搜索的模型，其中通过对n个位置（“框”）进行搜索来找到一个或多个对象（“目标”），其中n无限大。每个盒子都有一定的概率包含目标，从而导致盒子上的分布H。我们将搜索目标建模为使用某些分布S绘制框的随机过程。首先，根据H和S推导由搜索过程产生的未命中预期数目E [Z]的一般表达式。然后，我们获得最佳分布5 *以最小化E [Z]的表达式。这导致：H的熵与H和S *之间的KL发散之间的关系。该结果在由H概率大于〜1 / _n的那些盒子和其余盒子组成的盒子上引起2个分区。我们使用此结果为H未知的实际情况设计随机搜索程序。我们提供了与理论预测相符的模拟结果;并证明随着H熵的减小，最优搜索器的预期缺失减少，对于均匀H而言获得最大值。最后，我们证明了这种随机搜索过程在H的粗略假设下的应用。理论结果和过程是适用于涉及离散搜索空间的机器学习任何方面的随机搜索：例如，对特征，结构的选择或离散化的参数选择。在这项工作中，该过程用于选择深层关系机器（DRM）的功能，这些特征是根据特定领域知识定义的深层神经网络（DNN），并使用从可能具有无限大属性的巨大空间中选择的特征来构建。从70多个现实世界数据集中获得的经验结果表明，使用随机搜索过程所得到的性能要比最新技术好得多。

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