IEEE Trans Pattern Anal Mach Intell. 2020 Jul;42(7):1713-1728. doi: 10.1109/TPAMI.2019.2901688. Epub 2019 Feb 26.
Many vision-based applications rely on logistic regression for embedding classification within a probabilistic context, such as recognition in images and videos or identifying disease-specific image phenotypes from neuroimages. Logistic regression, however, often performs poorly when trained on data that is noisy, has irrelevant features, or when the samples are distributed across the classes in an imbalanced setting; a common occurrence in visual recognition tasks. To deal with those issues, researchers generally rely on ad-hoc regularization techniques or model a subset of these issues. We instead propose a mathematically sound logistic regression model that selects a subset of (relevant) features and (informative and balanced) set of samples during the training process. The model does so by applying cardinality constraints (via l-'norm' sparsity) on the features and samples. l defines sparsity in mathematical settings but in practice has mostly been approximated (e.g., via l or its variations) for computational simplicity. We prove that a local minimum to the non-convex optimization problems induced by cardinality constraints can be computed by combining block coordinate descent with penalty decomposition. On synthetic, image recognition, and neuroimaging datasets, we show that the accuracy of the method is higher than alternative methods and classifiers commonly used in the literature.
许多基于视觉的应用程序都依赖逻辑回归来在概率环境中嵌入分类，例如在图像和视频中进行识别，或从神经影像中识别特定疾病的图像表型。然而，当在噪声数据、不相关特征或样本在不平衡设置中分布在各个类别上的情况下进行训练时，逻辑回归的性能往往不佳；这种情况在视觉识别任务中很常见。为了解决这些问题，研究人员通常依赖于特定的正则化技术或仅对这些问题的一部分进行建模。相比之下，我们提出了一种数学上合理的逻辑回归模型，该模型可以在训练过程中选择特征和样本的子集。该模型通过对特征和样本应用基数约束（通过 l-范数稀疏性）来实现这一点。l 在数学环境中定义了稀疏性，但在实践中，为了计算简便，主要是通过 l 或其变体来近似。我们证明了通过结合块坐标下降和惩罚分解，可以计算出由基数约束引起的非凸优化问题的局部极小值。在合成数据集、图像识别数据集和神经影像数据集上的实验表明，与文献中常用的替代方法和分类器相比，该方法的准确性更高。
