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Image classification is widely used to build predictive models for breast cancer diagnosis. Most existing approaches overwhelmingly rely on deep convolutional networks to build such diagnosis pipelines. These model architectures, although remarkable in performance, are black-box systems that provide minimal insight into the inner logic behind their predictions. This is a major drawback as the explainability of prediction is vital for applications such as cancer diagnosis. In this paper, we address this issue by proposing an explainable machine learning pipeline for breast cancer diagnosis based on ultrasound images. We extract first- and second-order texture features of the ultrasound images and use them to build a probabilistic ensemble of decision tree classifiers. Each decision tree learns to classify the input ultrasound image by learning a set of robust decision thresholds for texture features of the image. The decision path of the model predictions can then be interpreted by decomposing the learned decision trees. Our results show that our proposed framework achieves high predictive performance while being explainable.