Localizing Anomalies via Multiscale Score Matching Analysis

Anomaly detection and localization in medical imaging remain critical challenges in healthcare. This paper introduces Spatial-MSMA (Multiscale Score Matching Analysis), a novel unsupervised method for anomaly localization in volumetric brain MRIs. Building upon the MSMA framework, our approach incorporates spatial information and conditional likelihoods to enhance anomaly detection capabilities. We employ a flexible normalizing flow model conditioned on patch positions and global image features to estimate patch-wise anomaly scores. The method is evaluated on a dataset of 1,650 T1- and T2-weighted brain MRIs from typically developing children, with simulated lesions added to the test set. Spatial-MSMA significantly outperforms existing methods, including reconstruction-based, generative-based, and interpretation-based approaches, in lesion detection and segmentation tasks. Our model achieves superior performance in both distance-based metrics (99th percentile Hausdorff Distance: $7.05 \pm 0.61$, Mean Surface Distance: $2.10 \pm 0.43$) and component-wise metrics (True Positive Rate: $0.83 \pm 0.01$, Positive Predictive Value: $0.96 \pm 0.01$). These results demonstrate Spatial-MSMA's potential for accurate and interpretable anomaly localization in medical imaging, with implications for improved diagnosis and treatment planning in clinical settings. Our code is available at~\url{https://github.com/ahsanMah/sade/}.

Anomaly Detection via Gumbel Noise Score Matching

We propose Gumbel Noise Score Matching (GNSM), a novel unsupervised method to detect anomalies in categorical data. GNSM accomplishes this by estimating the scores, i.e. the gradients of log likelihoods w.r.t.~inputs, of continuously relaxed categorical distributions. We test our method on a suite of anomaly detection tabular datasets. GNSM achieves a consistently high performance across all experiments. We further demonstrate the flexibility of GNSM by applying it to image data where the model is tasked to detect poor segmentation predictions. Images ranked anomalous by GNSM show clear segmentation failures, with the outputs of GNSM strongly correlating with segmentation metrics computed on ground-truth. We outline the score matching training objective utilized by GNSM and provide an open-source implementation of our work.

Multiscale Score Matching for Out-of-Distribution Detection

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.