Conformal prediction provides a powerful framework for constructing distribution-free prediction regions with finite-sample coverage guarantees. While extensively studied in univariate settings, its extension to multi-output problems presents additional challenges, including complex output dependencies and high computational costs, and remains relatively underexplored. In this work, we present a unified comparative study of nine conformal methods with different multivariate base models for constructing multivariate prediction regions within the same framework. This study highlights their key properties while also exploring the connections between them. Additionally, we introduce two novel classes of conformity scores for multi-output regression that generalize their univariate counterparts. These scores ensure asymptotic conditional coverage while maintaining exact finite-sample marginal coverage. One class is compatible with any generative model, offering broad applicability, while the other is computationally efficient, leveraging the properties of invertible generative models. Finally, we conduct a comprehensive empirical evaluation across 13 tabular datasets, comparing all the multi-output conformal methods explored in this work. To ensure a fair and consistent comparison, all methods are implemented within a unified code base.

Abstract Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for constructing conformal prediction regions that are valid for both univariate and multivariate time series. JANET generalises the inductive conformal framework and efficiently produces joint prediction regions with controlled K-familywise error rates, enabling flexible adaptation to specific application needs. Our empirical evaluation demonstrates JANET’s superior performance in multi-step prediction tasks across diverse time series datasets, highlighting its potential for reliable and interpretable uncertainty quantification in sequential data.

Lymphadenectomy generally accompanies various oncology surgeries to remove infected cancer cells. However, there are two limitations in robot-assisted lymphadenectomy: 1) lymph nodes are not visible during operation since they are hidden by the superficial fat layer; 2) intra-operative bleeding may occur during lymph node removal caused by collisions between surgical instruments and delicate blood vessels (arteries or veins) near the lymph nodes. Therefore, we propose a framework integrating augmented reality and virtual fixtures to address these limitations. Augmented reality intra-operatively visualizes the hidden lymph nodes by projecting the corresponding 3D pre-operative model, and virtual fixtures are used to provide force feedback to surgeons to avoid possible collisions when they operate the surgical instruments to resect the lymph nodes surrounding the blood vessel. Ten human subjects were invited to perform an emulated lymphadenectomy based on the da Vinci robot in a dry lab. Experimental results demonstrated that the proposed framework can keep localizing the hidden lymph nodes, and reduce the number of collisions (21% and 48% reduction rates using two different force models compared to the standard setup, respectively) between the instruments and the delicate blood vessel during lymph node resection. It shows the potential to enhance the safety of robot-assisted lymphadenectomy.

Robot-assisted surgery is rapidly developing in the medical field, and the integration of augmented reality shows the potential to improve the operation performance of surgeons by providing more visual information. In this paper, we proposed a markerless augmented reality framework to enhance safety by avoiding intra-operative bleeding, which is a high risk caused by collision between surgical instruments and delicate blood vessels (arteries or veins). Advanced stereo reconstruction and segmentation networks are compared to find the best combination to reconstruct the intra-operative blood vessel in 3D space for registration with the pre-operative model, and the minimum distance detection between the instruments and the blood vessel is implemented. A robot-assisted lymphadenectomy is emulated on the da Vinci Research Kit in a dry lab, and ten human subjects perform this operation to explore the usability of the proposed framework. The result shows that the augmented reality framework can help the users to avoid the dangerous collision between the instruments and the delicate blood vessel while not introducing an extra load. It provides a flexible framework that integrates augmented reality into the medical robotic platform to enhance safety during surgery.