Heng Yang

Inductive Conformal Prediction (ICP) provides a practical and effective approach for equipping deep learning models with uncertainty estimates in the form of set-valued predictions which are guaranteed to contain the ground truth with high probability. Despite the appeal of this coverage guarantee, these sets may not be efficient: the size and contents of the prediction sets are not directly controlled, and instead depend on the underlying model and choice of score function. To remedy this, recent work has proposed learning model and score function parameters using data to directly optimize the efficiency of the ICP prediction sets. While appealing, the generalization theory for such an approach is lacking: direct optimization of empirical efficiency may yield prediction sets that are either no longer efficient on test data, or no longer obtain the required coverage on test data. In this work, we use PAC-Bayes theory to obtain generalization bounds on both the coverage and the efficiency of set-valued predictors which can be directly optimized to maximize efficiency while satisfying a desired test coverage. In contrast to prior work, our framework allows us to utilize the entire calibration dataset to learn the parameters of the model and score function, instead of requiring a separate hold-out set for obtaining test-time coverage guarantees. We leverage these theoretical results to provide a practical algorithm for using calibration data to simultaneously fine-tune the parameters of a model and score function while guaranteeing test-time coverage and efficiency of the resulting prediction sets. We evaluate the approach on regression and classification tasks, and outperform baselines calibrated using a Hoeffding bound-based PAC guarantee on ICP, especially in the low-data regime.

We consider a category-level perception problem, where one is given 3D sensor data picturing an object of a given category (e.g. a car), and has to reconstruct the pose and shape of the object despite intra-class variability (i.e. different car models have different shapes). We consider an active shape model, where -- for an object category -- we are given a library of potential CAD models describing objects in that category, and we adopt a standard formulation where pose and shape estimation are formulated as a non-convex optimization. Our first contribution is to provide the first certifiably optimal solver for pose and shape estimation. In particular, we show that rotation estimation can be decoupled from the estimation of the object translation and shape, and we demonstrate that (i) the optimal object rotation can be computed via a tight (small-size) semidefinite relaxation, and (ii) the translation and shape parameters can be computed in closed-form given the rotation. Our second contribution is to add an outlier rejection layer to our solver, hence making it robust to a large number of misdetections. Towards this goal, we wrap our optimal solver in a robust estimation scheme based on graduated non-convexity. To further enhance robustness to outliers, we also develop the first graph-theoretic formulation to prune outliers in category-level perception, which removes outliers via convex hull and maximum clique computations; the resulting approach is robust to 70%-90% outliers. Our third contribution is an extensive experimental evaluation. Besides providing an ablation study on a simulated dataset and on the PASCAL3D+ dataset, we combine our solver with a deep-learned keypoint detector, and show that the resulting approach improves over the state of the art in vehicle pose estimation in the ApolloScape datasets.

Background: The conventional treatments for non-acute subdural hematoma (SDH) are facing the challenge of high hematoma recurrence and progression. A novel treatment of middle meningeal artery (MMA) embolization showed the potential role in decreasing the recurrence and progression rate of SDH compared to conventional treatments in multiple cohort studies. A randomized controlled trial is warranted to determine the effectiveness and safety of MMA embolization for non-acute hematoma and whether MMA embolization is superior to conventional treatments to lower the symptomatic recurrence and progression rate of non-acute SDH. Methods: This is an investigator-initiated, multi-center, prospective, open-label parallel group trial with blinded outcome assessment (PROBE design) assessing superiority of MMA embolization compared to conventional treatments. A total of 722 patients are planned to be randomized 1:1 to receive MMA embolization (intervention) or conventional treatments (control). The primary outcome is the symptomatic SDH recurrence/progression rate within 90 ± 14 days post-randomization. Discussion: This trial will clarify whether MMA embolization could reduce the recurrence or progression rate of symptomatic non-acute SDH compared to conventional treatment. Trial registration: ClinicalTrials.gov. Identifier: NCT04700345, Registered on 7 January 2021.

We study the problem of aligning two sets of 3D geometric primitives given known correspondences. Our first contribution is to show that this primitive alignment framework unifies five perception problems including point cloud registration, primitive (mesh) registration, category-level 3D registration, absolution pose estimation (APE), and category-level APE. Our second contribution is to propose DynAMical Pose estimation (DAMP), the first general and practical algorithm to solve primitive alignment problem by simulating rigid body dynamics arising from virtual springs and damping, where the springs span the shortest distances between corresponding primitives. We evaluate DAMP in simulated and real datasets across all five problems, and demonstrate (i) DAMP always converges to the globally optimal solution in the first three problems with 3D-3D correspondences; (ii) although DAMP sometimes converges to suboptimal solutions in the last two problems with 2D-3D correspondences, using a scheme for escaping local minima, DAMP always succeeds. Our third contribution is to demystify the surprising empirical performance of DAMP and formally prove a global convergence result in the case of point cloud registration by charactering local stability of the equilibrium points of the underlying dynamical system.

The protein structure initiatives have increased the number of experimentally determined protein tertiary structures, providing tremendous opportunities for detailed comparative analysis of proteins. Although protein structures provide the most exquisite type of molecular information that can yield mechanistic insights into how proteins function, there are still many protein structures with undetermined or poorly defined functions. Functional annotation from protein 3-D structures has attracted many researchers, with most approaches relying on structural superposition against well-characterized proteins. 3-D structure superposition is a complex and computationally demanding problem; forcing most available approaches to only consider backbone atoms for simplicity and efficiency. In this study, we propose protein surface as a more powerful representation of proteins than the traditional backbone or atomic representations. In order to efficiently analyze protein surfaces, we introduce a novel approach to reduce the 3-D surface to a 2-D image map and utilize image registration algorithms to compare these feature-rich images. Whereas the dimension reduction inherently captures the 3-D geometry of the surface patches, we enrich the image map with additional features known to be important for defining molecular activity of the proteins, such as curvature, electrostatic potential, hydrophobicity, and residue conservation. Comparison of these enriched surface maps using image registration methods allows us to find similar surface patches shared between proteins. While the computational challenges remain to scale our approach to study comparisons in the entire set of available protein structures, our novel approach provides unique advantages compared to other structure comparison methods. We show that our method is able to detect local similarities even when proteins lack a global structure similarity. We also demonstrate the utility of the image maps and their comparisons in functional annotation, and drug target prediction tasks.

We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our first contribution is to formulate geometric perception as an optimization problem that jointly optimizes the feature descriptor and the geometric models given a large corpus of visual measurements (e.g., images, point clouds). Under this optimization formulation, we show that two important streams of research in vision, namely robust model fitting and deep feature learning, correspond to optimizing one block of the unknown variables while fixing the other block. This analysis naturally leads to our second contribution -- the SGP algorithm that performs alternating minimization to solve the joint optimization. SGP iteratively executes two meta-algorithms: a teacher that performs robust model fitting given learned features to generate geometric pseudo-labels, and a student that performs deep feature learning under noisy supervision of the pseudo-labels. As a third contribution, we apply SGP to two perception problems on large-scale real datasets, namely relative camera pose estimation on MegaDepth and point cloud registration on 3DMatch. We demonstrate that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.