Accelerating Incremental Gradient Optimization with Curvature Information

This paper studies an acceleration technique for incremental aggregated gradient ({\sf IAG}) method through the use of \emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of interest arise in large-scale learning applications. Our technique utilizes a curvature-aided gradient tracking step to produce accurate gradient estimates incrementally using Hessian information. We propose and analyze two methods utilizing the new technique, the curvature-aided IAG ({\sf CIAG}) method and the accelerated CIAG ({\sf A-CIAG}) method, which are analogous to gradient method and Nesterov's accelerated gradient method, respectively. Setting $\kappa$ to be the condition number of the objective function, we prove the $R$ linear convergence rates of $1 - \frac{4c_0 \kappa}{(\kappa+1)^2}$ for the {\sf CIAG} method, and $1 - \sqrt{\frac{c_1}{2\kappa}}$ for the {\sf A-CIAG} method, where $c_0,c_1 \leq 1$ are constants inversely proportional to the distance between the initial point and the optimal solution. When the initial iterate is close to the optimal solution, the $R$ linear convergence rates match with the gradient and accelerated gradient method, albeit {\sf CIAG} and {\sf A-CIAG} operate in an incremental setting with strictly lower computation complexity. Numerical experiments confirm our findings. The source codes used for this paper can be found on \url{http://github.com/hoitowai/ciag/}.Comment: 22 pages, 3 figures, 3 tables. Accepted by Computational Optimization and Applications, to appea

Tracking the gradients using the Hessian: A new look at variance reducing stochastic methods

Our goal is to improve variance reducing stochastic methods through better control variates. We first propose a modification of SVRG which uses the Hessian to track gradients over time, rather than to recondition, increasing the correlation of the control variates and leading to faster theoretical convergence close to the optimum. We then propose accurate and computationally efficient approximations to the Hessian, both using a diagonal and a low-rank matrix. Finally, we demonstrate the effectiveness of our method on a wide range of problems.Comment: 17 pages, 2 figures, 1 tabl

Long Distance GNSS-Denied Visual Inertial Navigation for Autonomous Fixed Wing Unmanned Air Vehicles: SO(3) Manifold Filter based on Virtual Vision Sensor

This article proposes a visual inertial navigation algorithm intended to diminish the horizontal position drift experienced by autonomous fixed wing UAVs (Unmanned Air Vehicles) in the absence of GNSS (Global Navigation Satellite System) signals. In addition to accelerometers, gyroscopes, and magnetometers, the proposed navigation filter relies on the accurate incremental displacement outputs generated by a VO (Visual Odometry) system, denoted here as a Virtual Vision Sensor or VVS, which relies on images of the Earth surface taken by an onboard camera and is itself assisted by the filter inertial estimations. Although not a full replacement for a GNSS receiver since its position observations are relative instead of absolute, the proposed system enables major reductions in the GNSS-Denied attitude and position estimation errors. In order to minimize the accumulation of errors in the absence of absolute observations, the filter is implemented in the manifold of rigid body rotations or SO (3). Stochastic high fidelity simulations of two representative scenarios involving the loss of GNSS signals are employed to evaluate the results. The authors release the C++ implementation of both the visual inertial navigation filter and the high fidelity simulation as open-source software.Comment: 27 pages, 14 figures. arXiv admin note: substantial text overlap with arXiv:2205.1324

Enhancing endoscopic navigation and polyp detection using artificial intelligence

Colorectal cancer (CRC) is one most common and deadly forms of cancer. It has a very high mortality rate if the disease advances to late stages however early diagnosis and treatment can be curative is hence essential to enhancing disease management. Colonoscopy is considered the gold standard for CRC screening and early therapeutic treatment. The effectiveness of colonoscopy is highly dependent on the operator’s skill, as a high level of hand-eye coordination is required to control the endoscope and fully examine the colon wall. Because of this, detection rates can vary between different gastroenterologists and technology have been proposed as solutions to assist disease detection and standardise detection rates. This thesis focuses on developing artificial intelligence algorithms to assist gastroenterologists during colonoscopy with the potential to ensure a baseline standard of quality in CRC screening. To achieve such assistance, the technical contributions develop deep learning methods and architectures for automated endoscopic image analysis to address both the detection of lesions in the endoscopic image and the 3D mapping of the endoluminal environment. The proposed detection models can run in real-time and assist visualization of different polyp types. Meanwhile the 3D reconstruction and mapping models developed are the basis for ensuring that the entire colon has been examined appropriately and to support quantitative measurement of polyp sizes using the image during a procedure. Results and validation studies presented within the thesis demonstrate how the developed algorithms perform on both general scenes and on clinical data. The feasibility of clinical translation is demonstrated for all of the models on endoscopic data from human participants during CRC screening examinations