We consider the task of feature selection for reconstruction which consists in choosing a small subset of features from which whole data instances can be reconstructed. This is of particular importance in several contexts involving for example costly physical measurements, sensor placement or information compression. To break the intrinsic combinatorial nature of this problem, we formulate the task as optimizing a binary mask distribution enabling an accurate reconstruction. We then face two main challenges. One concerns differentiability issues due to the binary distribution. The second one corresponds to the elimination of redundant information by selecting variables in a correlated fashion which requires modeling the covariance of the binary distribution. We address both issues by introducing a relaxation of the problem via a novel reparameterization of the logitNormal distribution. We demonstrate that the proposed method provides an effective exploration scheme and leads to efficient feature selection for reconstruction through evaluation on several high dimensional image benchmarks. We show that the method leverages the intrinsic geometry of the data, facilitating reconstruction.

中文翻译：

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可微特征选择，一种重新参数化方法

我们考虑用于重建的特征选择任务，该任务包括选择可以重建整个数据实例的一小部分特征。这在涉及昂贵的物理测量、传感器放置或信息压缩等多种情况下尤为重要。为了打破这个问题的内在组合性质，我们将任务制定为优化二进制掩码分布，从而实现准确的重建。然后我们面临两个主要挑战。一个关注由于二进制分布引起的可微性问题。第二个对应于通过以相关方式选择变量来消除冗余信息，这需要对二元分布的协方差进行建模。我们通过对 logitNormal 分布进行新的重新参数化来引入问题的松弛来解决这两个问题。我们证明了所提出的方法提供了一种有效的探索方案，并通过对几个高维图像基准的评估来为重建提供有效的特征选择。我们表明该方法利用数据的内在几何形状，促进重建。