Consistent and Asymptotically Unbiased Estimation of Proper Calibration Errors

Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration error and refinement -- utilizing a Bregman divergence. While uncertainty calibration has gained significant attention, current literature lacks a general estimator for these quantities with known statistical properties. To address this gap, we propose a method that allows consistent, and asymptotically unbiased estimation of all proper calibration errors and refinement terms. In particular, we introduce Kullback--Leibler calibration error, induced by the commonly used cross-entropy loss. As part of our results, we prove the relation between refinement and f-divergences, which implies information monotonicity in neural networks, regardless of which proper scoring rule is optimized. Our experiments validate empirically the claimed properties of the proposed estimator and suggest that the selection of a post-hoc calibration method should be determined by the particular calibration error of interest.

Beyond Classification: Definition and Density-based Estimation of Calibration in Object Detection

Despite their impressive predictive performance in various computer vision tasks, deep neural networks (DNNs) tend to make overly confident predictions, which hinders their widespread use in safety-critical applications. While there have been recent attempts to calibrate DNNs, most of these efforts have primarily been focused on classification tasks, thus neglecting DNN-based object detectors. Although several recent works addressed calibration for object detection and proposed differentiable penalties, none of them are consistent estimators of established concepts in calibration. In this work, we tackle the challenge of defining and estimating calibration error specifically for this task. In particular, we adapt the definition of classification calibration error to handle the nuances associated with object detection, and predictions in structured output spaces more generally. Furthermore, we propose a consistent and differentiable estimator of the detection calibration error, utilizing kernel density estimation. Our experiments demonstrate the effectiveness of our estimator against competing train-time and post-hoc calibration methods, while maintaining similar detection performance.

End-To-End Prediction of Knee Osteoarthritis Progression With Multi-Modal Transformers

Knee Osteoarthritis (KOA) is a highly prevalent chronic musculoskeletal condition with no currently available treatment. The manifestation of KOA is heterogeneous and prediction of its progression is challenging. Current literature suggests that the use of multi-modal data and advanced modeling methods, such as the ones based on Deep Learning, has promise in tackling this challenge. To date, however, the evidence on the efficacy of this approach is limited. In this study, we leveraged recent advances in Deep Learning and, using a Transformer approach, developed a unified framework for the multi-modal fusion of knee imaging data. Subsequently, we analyzed its performance across a range of scenarios by investigating multiple progression horizons -- from short-term to long-term. We report our findings using a large cohort (n=2421-3967) derived from the Osteoarthritis Initiative dataset. We show that structural knee MRI allows identifying radiographic KOA progressors on par with multi-modal fusion approaches, achieving an area under the ROC curve (ROC AUC) of 0.70-0.76 and Average Precision (AP) of 0.15-0.54 in 2-8 year horizons. Progression within 1 year was better predicted with a multi-modal method using X-ray, structural, and compositional MR images -- ROC AUC of 0.76(0.04), AP of 0.13(0.04) -- or via clinical data. Our follow-up analysis generally shows that prediction from the imaging data is more accurate for post-traumatic subjects, and we further investigate which subject subgroups may benefit the most. The present study provides novel insights into multi-modal imaging of KOA and brings a unified data-driven framework for studying its progression in an end-to-end manner, providing new tools for the design of more efficient clinical trials. The source code of our framework and the pre-trained models are made publicly available.

Understanding metric-related pitfalls in image analysis validation

Validation metrics are key for the reliable tracking of scientific progress and for bridging the current chasm between artificial intelligence (AI) research and its translation into practice. However, increasing evidence shows that particularly in image analysis, metrics are often chosen inadequately in relation to the underlying research problem. This could be attributed to a lack of accessibility of metric-related knowledge: While taking into account the individual strengths, weaknesses, and limitations of validation metrics is a critical prerequisite to making educated choices, the relevant knowledge is currently scattered and poorly accessible to individual researchers. Based on a multi-stage Delphi process conducted by a multidisciplinary expert consortium as well as extensive community feedback, the present work provides the first reliable and comprehensive common point of access to information on pitfalls related to validation metrics in image analysis. Focusing on biomedical image analysis but with the potential of transfer to other fields, the addressed pitfalls generalize across application domains and are categorized according to a newly created, domain-agnostic taxonomy. To facilitate comprehension, illustrations and specific examples accompany each pitfall. As a structured body of information accessible to researchers of all levels of expertise, this work enhances global comprehension of a key topic in image analysis validation.

A Stronger Baseline For Automatic Pfirrmann Grading Of Lumbar Spine MRI Using Deep Learning

This paper addresses the challenge of grading visual features in lumbar spine MRI using Deep Learning. Such a method is essential for the automatic quantification of structural changes in the spine, which is valuable for understanding low back pain. Multiple recent studies investigated different architecture designs, and the most recent success has been attributed to the use of transformer architectures. In this work, we argue that with a well-tuned three-stage pipeline comprising semantic segmentation, localization, and classification, convolutional networks outperform the state-of-the-art approaches. We conducted an ablation study of the existing methods in a population cohort, and report performance generalization across various subgroups. Our code is publicly available to advance research on disc degeneration and low back pain.

Clinically-Inspired Multi-Agent Transformers for Disease Trajectory Forecasting from Multimodal Data

Deep neural networks are often applied to medical images to automate the problem of medical diagnosis. However, a more clinically relevant question that practitioners usually face is how to predict the future trajectory of a disease. Current methods for prognosis or disease trajectory forecasting often require domain knowledge and are complicated to apply. In this paper, we formulate the prognosis prediction problem as a one-to-many prediction problem. Inspired by a clinical decision-making process with two agents -- a radiologist and a general practitioner -- we predict prognosis with two transformer-based components that share information with each other. The first transformer in this framework aims to analyze the imaging data, and the second one leverages its internal states as inputs, also fusing them with auxiliary clinical data. The temporal nature of the problem is modeled within the transformer states, allowing us to treat the forecasting problem as a multi-task classification, for which we propose a novel loss. We show the effectiveness of our approach in predicting the development of structural knee osteoarthritis changes and forecasting Alzheimer's disease clinical status directly from raw multi-modal data. The proposed method outperforms multiple state-of-the-art baselines with respect to performance and calibration, both of which are needed for real-world applications. An open-source implementation of our method is made publicly available at \url{https://github.com/Oulu-IMEDS/CLIMATv2}.

On confidence intervals for precision matrices and the eigendecomposition of covariance matrices

The eigendecomposition of a matrix is the central procedure in probabilistic models based on matrix factorization, for instance principal component analysis and topic models. Quantifying the uncertainty of such a decomposition based on a finite sample estimate is essential to reasoning under uncertainty when employing such models. This paper tackles the challenge of computing confidence bounds on the individual entries of eigenvectors of a covariance matrix of fixed dimension. Moreover, we derive a method to bound the entries of the inverse covariance matrix, the so-called precision matrix. The assumptions behind our method are minimal and require that the covariance matrix exists, and its empirical estimator converges to the true covariance. We make use of the theory of U-statistics to bound the $L_2$ perturbation of the empirical covariance matrix. From this result, we obtain bounds on the eigenvectors using Weyl's theorem and the eigenvalue-eigenvector identity and we derive confidence intervals on the entries of the precision matrix using matrix inversion perturbation bounds. As an application of these results, we demonstrate a new statistical test, which allows us to test for non-zero values of the precision matrix. We compare this test to the well-known Fisher-z test for partial correlations, and demonstrate the soundness and scalability of the proposed statistical test, as well as its application to real-world data from medical and physics domains.

AdaTriplet: Adaptive Gradient Triplet Loss with Automatic Margin Learning for Forensic Medical Image Matching

This paper tackles the challenge of forensic medical image matching (FMIM) using deep neural networks (DNNs). FMIM is a particular case of content-based image retrieval (CBIR). The main challenge in FMIM compared to the general case of CBIR, is that the subject to whom a query image belongs may be affected by aging and progressive degenerative disorders, making it difficult to match data on a subject level. CBIR with DNNs is generally solved by minimizing a ranking loss, such as Triplet loss (TL), computed on image representations extracted by a DNN from the original data. TL, in particular, operates on triplets: anchor, positive (similar to anchor) and negative (dissimilar to anchor). Although TL has been shown to perform well in many CBIR tasks, it still has limitations, which we identify and analyze in this work. In this paper, we introduce (i) the AdaTriplet loss -- an extension of TL whose gradients adapt to different difficulty levels of negative samples, and (ii) the AutoMargin method -- a technique to adjust hyperparameters of margin-based losses such as TL and our proposed loss dynamically. Our results are evaluated on two large-scale benchmarks for FMIM based on the Osteoarthritis Initiative and Chest X-ray-14 datasets. The codes allowing replication of this study have been made publicly available at \url{https://github.com/Oulu-IMEDS/AdaTriplet}.

Predicting Knee Osteoarthritis Progression from Structural MRI using Deep Learning

Accurate prediction of knee osteoarthritis (KOA) progression from structural MRI has a potential to enhance disease understanding and support clinical trials. Prior art focused on manually designed imaging biomarkers, which may not fully exploit all disease-related information present in MRI scan. In contrast, our method learns relevant representations from raw data end-to-end using Deep Learning, and uses them for progression prediction. The method employs a 2D CNN to process the data slice-wise and aggregate the extracted features using a Transformer. Evaluated on a large cohort (n=4,866), the proposed method outperforms conventional 2D and 3D CNN-based models and achieves average precision of $0.58\pm0.03$ and ROC AUC of $0.78\pm0.01$. This paper sets a baseline on end-to-end KOA progression prediction from structural MRI. Our code is publicly available at https://github.com/MIPT-Oulu/OAProgressionMR.