Fast Projection onto the Capped Simplex withApplications to Sparse Regression in Bioinformatics

We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a much lower computational cost compared with the existing sorting-based methods proposed in the literature. We provide a theory for partial explanation and justification of the method. We demonstrate that the proposed algorithm can produce a solution of the projection problem with high precision on large scale datasets, and the algorithm is able to significantly outperform the state-of-the-art methods in terms of runtime (about 6-8 times faster than a commercial software with respect to CPU time for input vector with 1 million variables or more). We further illustrate the effectiveness of the proposed algorithm on solving sparse regression in a bioinformatics problem. Empirical results on the GWAS dataset (with 1,500,000 single-nucleotide polymorphisms) show that, when using the proposed method to accelerate the Projected Quasi-Newton (PQN) method, the accelerated PQN algorithm is able to handle huge-scale regression problem and it is more efficient (about 3-6 times faster) than the current state-of-the-art methods.

Dynamic Event Camera Calibration

Camera calibration is an important prerequisite towards the solution of 3D computer vision problems. Traditional methods rely on static images of a calibration pattern. This raises interesting challenges towards the practical usage of event cameras, which notably require image change to produce sufficient measurements. The current standard for event camera calibration therefore consists of using flashing patterns. They have the advantage of simultaneously triggering events in all reprojected pattern feature locations, but it is difficult to construct or use such patterns in the field. We present the first dynamic event camera calibration algorithm. It calibrates directly from events captured during relative motion between camera and calibration pattern. The method is propelled by a novel feature extraction mechanism for calibration patterns, and leverages existing calibration tools before optimizing all parameters through a multi-segment continuous-time formulation. As demonstrated through our results on real data, the obtained calibration method is highly convenient and reliably calibrates from data sequences spanning less than 10 seconds.

Know Thyself: Transferable Visuomotor Control Through Robot-Awareness

Training visuomotor robot controllers from scratch on a new robot typically requires generating large amounts of robot-specific data. Could we leverage data previously collected on another robot to reduce or even completely remove this need for robot-specific data? We propose a "robot-aware" solution paradigm that exploits readily available robot "self-knowledge" such as proprioception, kinematics, and camera calibration to achieve this. First, we learn modular dynamics models that pair a transferable, robot-agnostic world dynamics module with a robot-specific, analytical robot dynamics module. Next, we set up visual planning costs that draw a distinction between the robot self and the world. Our experiments on tabletop manipulation tasks in simulation and on real robots demonstrate that these plug-in improvements dramatically boost the transferability of visuomotor controllers, even permitting zero-shot transfer onto new robots for the very first time. Project website: https://hueds.github.io/rac/

Visual Odometry with an Event Camera Using Continuous Ray Warping and Volumetric Contrast Maximization

We present a new solution to tracking and mapping with an event camera. The motion of the camera contains both rotation and translation, and the displacements happen in an arbitrarily structured environment. As a result, the image matching may no longer be represented by a low-dimensional homographic warping, thus complicating an application of the commonly used Image of Warped Events (IWE). We introduce a new solution to this problem by performing contrast maximization in 3D. The 3D location of the rays cast for each event is smoothly varied as a function of a continuous-time motion parametrization, and the optimal parameters are found by maximizing the contrast in a volumetric ray density field. Our method thus performs joint optimization over motion and structure. The practical validity of our approach is supported by an application to AGV motion estimation and 3D reconstruction with a single vehicle-mounted event camera. The method approaches the performance obtained with regular cameras, and eventually outperforms in challenging visual conditions.

A Prospective Observational Study to Investigate Performance of a Chest X-ray Artificial Intelligence Diagnostic Support Tool Across 12 U.S. Hospitals

Importance: An artificial intelligence (AI)-based model to predict COVID-19 likelihood from chest x-ray (CXR) findings can serve as an important adjunct to accelerate immediate clinical decision making and improve clinical decision making. Despite significant efforts, many limitations and biases exist in previously developed AI diagnostic models for COVID-19. Utilizing a large set of local and international CXR images, we developed an AI model with high performance on temporal and external validation. Conclusions and Relevance: AI-based diagnostic tools may serve as an adjunct, but not replacement, for clinical decision support of COVID-19 diagnosis, which largely hinges on exposure history, signs, and symptoms. While AI-based tools have not yet reached full diagnostic potential in COVID-19, they may still offer valuable information to clinicians taken into consideration along with clinical signs and symptoms.

Improving the Transient Times for Distributed Stochastic Gradient Methods

We consider the distributed optimization problem where $n$ agents each possessing a local cost function, collaboratively minimize the average of the $n$ cost functions over a connected network. Assuming stochastic gradient information is available, we study a distributed stochastic gradient algorithm, called exact diffusion with adaptive stepsizes (EDAS) adapted from the Exact Diffusion method and NIDS and perform a non-asymptotic convergence analysis. We not only show that EDAS asymptotically achieves the same network independent convergence rate as centralized stochastic gradient descent (SGD) for minimizing strongly convex and smooth objective functions, but also characterize the transient time needed for the algorithm to approach the asymptotic convergence rate, which behaves as $K_T=\mathcal{O}\left(\frac{n}{1-\lambda_2}\right)$, where $1-\lambda_2$ stands for the spectral gap of the mixing matrix. To the best of our knowledge, EDAS achieves the shortest transient time when the average of the $n$ cost functions is strongly convex and each cost function is smooth. Numerical simulations further corroborate and strengthen the obtained theoretical results.

Fusing RGBD Tracking and Segmentation Tree Sampling for Multi-Hypothesis Volumetric Segmentation

Despite rapid progress in scene segmentation in recent years, 3D segmentation methods are still limited when there is severe occlusion. The key challenge is estimating the segment boundaries of (partially) occluded objects, which are inherently ambiguous when considering only a single frame. In this work, we propose Multihypothesis Segmentation Tracking (MST), a novel method for volumetric segmentation in changing scenes, which allows scene ambiguity to be tracked and our estimates to be adjusted over time as we interact with the scene. Two main innovations allow us to tackle this difficult problem: 1) A novel way to sample possible segmentations from a segmentation tree; and 2) A novel approach to fusing tracking results with multiple segmentation estimates. These methods allow MST to track the segmentation state over time and incorporate new information, such as new objects being revealed. We evaluate our method on several cluttered tabletop environments in simulation and reality. Our results show that MST outperforms baselines in all tested scenes.