MLFeb 5, 2025
Gradient Descent Algorithm in Hilbert Spaces under Stationary Markov Chains with $φ$- and $β$-MixingPriyanka Roy, Susanne Saminger-Platz
In this paper, we study a strictly stationary Markov chain gradient descent algorithm operating in general Hilbert spaces. Our analysis focuses on the mixing coefficients of the underlying process, specifically the $φ$- and $β$-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds on the convergence behavior of the algorithm based on the exponential as well as the polynomial decay of the mixing coefficients.
MLJul 8, 2025
Online Regularized Learning Algorithms in RKHS with $β$- and $φ$-Mixing SequencesPriyanka Roy, Susanne Saminger-Platz
In this paper, we study an online regularized learning algorithm in a reproducing kernel Hilbert spaces (RKHS) based on a class of dependent processes. We choose such a process where the degree of dependence is measured by mixing coefficients. As a representative example, we analyze a strictly stationary Markov chain, where the dependence structure is characterized by the \(φ\)- and \(β\)-mixing coefficients. Under these assumptions, we derive probabilistic upper bounds as well as convergence rates for both the exponential and polynomial decay of the mixing coefficients.
CVDec 17, 2018
OCTID: Optical Coherence Tomography Image DatabasePeyman Gholami, Priyanka Roy, Mohana Kuppuswamy Parthasarathy et al.
Optical coherence tomography (OCT) is a non-invasive imaging modality which is widely used in clinical ophthalmology. OCT images are capable of visualizing deep retinal layers which is crucial for early diagnosis of retinal diseases. In this paper, we describe a comprehensive open-access database containing more than 500 highresolution images categorized into different pathological conditions. The image classes include Normal (NO), Macular Hole (MH), Age-related Macular Degeneration (AMD), Central Serous Retinopathy (CSR), and Diabetic Retinopathy (DR). The images were obtained from a raster scan protocol with a 2mm scan length and 512x1024 pixel resolution. We have also included 25 normal OCT images with their corresponding ground truth delineations which can be used for an accurate evaluation of OCT image segmentation. In addition, we have provided a user-friendly GUI which can be used by clinicians for manual (and semi-automated) segmentation.