Anand Joshi

Haleh Akrami, Omar Zamzam, Anand Joshi et al.

Quantile Regression (QR) can be used to estimate aleatoric uncertainty in deep neural networks and can generate prediction intervals. Quantifying uncertainty is particularly important in critical applications such as clinical diagnosis, where a realistic assessment of uncertainty is essential in determining disease status and planning the appropriate treatment. The most common application of quantile regression models is in cases where the parametric likelihood cannot be specified. Although quantile regression is quite robust to outlier response observations, it can be sensitive to outlier covariate observations (features). Outlier features can compromise the performance of deep learning regression problems such as style translation, image reconstruction, and deep anomaly detection, potentially leading to misleading conclusions. To address this problem, we propose a robust solution for quantile regression that incorporates concepts from robust divergence. We compare the performance of our proposed method with (i) least trimmed quantile regression and (ii) robust regression based on the regularization of case-specific parameters in a simple real dataset in the presence of outlier. These methods have not been applied in a deep learning framework. We also demonstrate the applicability of the proposed method by applying it to a medical imaging translation task using diffusion models.

Omar Zamzam, Haleh Akrami, Anand Joshi et al.

Brain lesions are abnormalities or injuries in brain tissue that are often detectable using magnetic resonance imaging (MRI), which reveals structural changes in the affected areas. This broad definition of brain lesions includes areas of the brain that are irreversibly damaged, as well as areas of brain tissue that are deformed as a result of lesion growth or swelling. Despite the importance of differentiating between damaged and deformed tissue, existing lesion segmentation methods overlook this distinction, labeling both of them as a single anomaly. In this work, we introduce a diffusion model-based framework for analyzing and reversing the brain lesion process. Our pipeline first segments abnormal regions in the brain, then estimates and reverses tissue deformations by restoring displaced tissue to its original position, isolating the core lesion area representing the initial damage. Finally, we inpaint the core lesion area to arrive at an estimation of the pre-lesion healthy brain. This proposed framework reverses a forward lesion growth process model that is well-established in biomechanical studies that model brain lesions. Our results demonstrate improved accuracy in lesion segmentation, characterization, and brain labeling compared to traditional methods, offering a robust tool for clinical and research applications in brain lesion analysis. Since pre-lesion healthy versions of abnormal brains are not available in any public dataset for validation of the reverse process, we simulate a forward model to synthesize multiple lesioned brain images.

Haleh Akrami, Anand Joshi, Sergul Aydore et al.

Despite impressive state-of-the-art performance on a wide variety of machine learning tasks, deep learning methods can produce over-confident predictions, particularly with limited training data. Therefore, quantifying uncertainty is particularly important in critical applications such as lesion detection and clinical diagnosis, where a realistic assessment of uncertainty is essential in determining surgical margins, disease status and appropriate treatment. In this work, we propose a novel approach that uses quantile regression for quantifying aleatoric uncertainty in both supervised and unsupervised lesion detection problems. The resulting confidence intervals can be used for lesion detection and segmentation. In the unsupervised setting, we combine quantile regression with the Variational AutoEncoder (VAE). Here we address the problem of quantifying uncertainty in the images that are reconstructed by the VAE as the basis for principled outlier or lesion detection. The VAE models the output as a conditionally independent Gaussian characterized by its mean and variance. Unfortunately, joint optimization of both mean and variance in the VAE leads to the well-known problem of shrinkage or underestimation of variance. Here we describe an alternative Quantile-Regression VAE (QR-VAE) that avoids this variance shrinkage problem by directly estimating conditional quantiles for the input image. Using the estimated quantiles, we compute the conditional mean and variance for the input image from which we then detect outliers by thresholding at a false-discovery-rate corrected p-value. In the supervised setting, we develop binary quantile regression (BQR) for the supervised lesion segmentation task. We show how BQR can be used to capture uncertainty in lesion boundaries in a manner that characterizes expert disagreement.