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Georgios Vasileios Karanikolas

Bio: Georgios Vasileios Karanikolas is an academic researcher from University of Minnesota. The author has contributed to research in topics: Gaussian process & Dimensionality reduction. The author has an hindex of 5, co-authored 9 publications receiving 219 citations.

Papers
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Journal ArticleDOI
25 Apr 2018
TL;DR: The main goal of this paper is to outline overarching advances, and develop a principled framework to capture nonlinearities through kernels, which are judiciously chosen from a preselected dictionary to optimally fit the data.
Abstract: Identifying graph topologies as well as processes evolving over graphs emerge in various applications involving gene-regulatory, brain, power, and social networks, to name a few. Key graph-aware learning tasks include regression, classification, subspace clustering, anomaly identification, interpolation, extrapolation, and dimensionality reduction. Scalable approaches to deal with such high-dimensional tasks experience a paradigm shift to address the unique modeling and computational challenges associated with data-driven sciences. Albeit simple and tractable, linear time-invariant models are limited since they are incapable of handling generally evolving topologies, as well as nonlinear and dynamic dependencies between nodal processes. To this end, the main goal of this paper is to outline overarching advances, and develop a principled framework to capture nonlinearities through kernels, which are judiciously chosen from a preselected dictionary to optimally fit the data. The framework encompasses and leverages (non) linear counterparts of partial correlation and partial Granger causality, as well as (non)linear structural equations and vector autoregressions, along with attributes such as low rank, sparsity, and smoothness to capture even directional dependencies with abrupt change points, as well as time-evolving processes over possibly time-evolving topologies. The overarching approach inherits the versatility and generality of kernel-based methods, and lends itself to batch and computationally affordable online learning algorithms, which include novel Kalman filters over graphs. Real data experiments highlight the impact of the nonlinear and dynamic models on consumer and financial networks, as well as gene-regulatory and functional connectivity brain networks, where connectivity patterns revealed exhibit discernible differences relative to existing approaches.

187 citations

Proceedings ArticleDOI
20 Mar 2016
TL;DR: A kernel-based nonlinear connectivity model based on which it obtains topology revealing PCs is proposed, and a data-driven approach is advocated to learn the combination of multiple kernel functions that optimizes the data fit.
Abstract: Partial correlations (PCs) of functional magnetic resonance imaging (fMRI) time series play a principal role in revealing connectivity of brain networks. To explore nonlinear behavior of the blood-oxygen-level dependent signal, the present work postulates a kernel-based nonlinear connectivity model based on which it obtains topology revealing PCs. Instead of relying on a single predefined kernel, a data-driven approach is advocated to learn the combination of multiple kernel functions that optimizes the data fit. Synthetically generated data based on both a dynamic causal and a linear model are used to validate the proposed approach in resting-state fMRI scenarios, highlighting the gains in edge detection performance when compared with the popular linear PC method. Tests on real fMRI data demonstrate that connectivity patterns revealed by linear and nonlinear models are different.

49 citations

Proceedings Article
03 Jun 2020
TL;DR: An online interactive ensemble (OI-E) GP framework is developed to jointly learn the sought function, and for the first time select interactively the EGP kernel on-the-fly.
Abstract: Combining benefits of kernels with Bayesian models, Gaussian process (GP) based approaches have well-documented merits not only in learning over a rich class of nonlinear functions, but also quantifying the associated uncertainty. While most GP approaches rely on a single preselected prior, the present work employs a weighted ensemble of GP priors, each having a unique covariance (kernel) belonging to a prescribed kernel dictionary – which leads to a richer space of learning functions. Leveraging kernel approximants formed by spectral features for scalability, an online interactive ensemble (OI-E) GP framework is developed to jointly learn the sought function, and for the first time select interactively the EGP kernel on-the-fly. Performance of OI-EGP is benchmarked by the best fixed function estimator via regret analysis. Furthermore, the novel OI-EGP is adapted to accommodate dynamic learning functions. Synthetic and real data tests demonstrate the e↵ectiveness of the proposed schemes.

25 citations

Proceedings ArticleDOI
15 Apr 2018
TL;DR: A multi-task deep neural network (DNN) architecture that can employ any FCN as a building block, allows for leveraging shared features between different tasks, and can be efficiently trained end-to-end is proposed.
Abstract: Segmentation of ventricles from cardiac magnetic resonance (MR) images is a key step to obtaining clinical parameters useful for prognosis of cardiac pathologies. To improve upon the performance of existing fully convolutional network (FCN) based automatic right ventricle (RV) segmentation approaches, a multi-task deep neural network (DNN) architecture is proposed. The multi-task model can employ any FCN as a building block, allows for leveraging shared features between different tasks, and can be efficiently trained end-to-end. Specifically, a multi-task U-net is developed and implemented using the Tensorflow framework. Numerical tests on real datasets showcase the merits of the proposed approach and in particular its ability to offer improved segmentation performance for small-size RVs.

20 citations

Proceedings ArticleDOI
01 Mar 2017
TL;DR: This work advocates a multi-kernel based nonlinear model for obtaining the effective connectivity between brain regions, by wedding the merits of partial correlation in undirected topology identification with the ability of partial Granger causality (PGC) to estimate edge directionality.
Abstract: Granger causality based approaches are popular in unveiling directed interactions among brain regions. The present work advocates a multi-kernel based nonlinear model for obtaining the effective connectivity between brain regions, by wedding the merits of partial correlation in undirected topology identification with the ability of partial Granger causality (PGC) to estimate edge directionality. The premise is that existing linear PGC approaches may be inadequate for capturing certain dependencies, whereas available nonlinear connectivity models lack data adaptability that multi-kernel learning methods can offer. The proposed approach is tested on both synthetic and real resting-state fMRI data, with the former illustrating the gains in directed edge presence detection performance, as compared to existing PGC methods, and with the latter highlighting differences in the estimated test statistics.

7 citations


Cited by
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Journal ArticleDOI
TL;DR: This study reviews recent advances in UQ methods used in deep learning and investigates the application of these methods in reinforcement learning (RL), and outlines a few important applications of UZ methods.
Abstract: Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian approximation and ensemble learning techniques are two most widely-used UQ methods in the literature. In this regard, researchers have proposed different UQ methods and examined their performance in a variety of applications such as computer vision (e.g., self-driving cars and object detection), image processing (e.g., image restoration), medical image analysis (e.g., medical image classification and segmentation), natural language processing (e.g., text classification, social media texts and recidivism risk-scoring), bioinformatics, etc. This study reviews recent advances in UQ methods used in deep learning. Moreover, we also investigate the application of these methods in reinforcement learning (RL). Then, we outline a few important applications of UQ methods. Finally, we briefly highlight the fundamental research challenges faced by UQ methods and discuss the future research directions in this field.

809 citations

Journal ArticleDOI
TL;DR: Models of Network Growth All networks, whether they are social, technological, or biological, are the result of a growth process, and many continue to grow for prolonged periods of time, continually modifying their connectivity structure throughout their entire existence.
Abstract: Models of Network Growth All networks, whether they are social, technological, or biological, are the result of a growth process. Many of these networks continue to grow for prolonged periods of time, continually modifying their connectivity structure throughout their entire existence. For example, the World Wide Web has grown from a small number of cross-linked documents in the early 1 990s to an estimated 30 billion indexed web pages in 2009.3 The extraordinary growth of the Web continues unabated and has occurred without any top-down design, yet the topology of its hyperlink structure exhibits characteristic statistical patterns (Pastor-Satorras and Vespig­ nani, 2004). Other technological networks such as the power grid, global transportation networks, or mobile communication networks continue to grow and evolve, each displaying characteristic patterns of expansion and elaboration. Growth and change in social and organizational

691 citations

Journal ArticleDOI
TL;DR: Graph signal processing (GSP) has been widely used to infer the underlying graph topology as discussed by the authors, where correlation analysis takes center stage along with its connections to covariance selection and high dimensional regression for learning Gaussian graphical models.
Abstract: Network topology inference is a significant problem in network science. Most graph signal processing (GSP) efforts to date assume that the underlying network is known and then analyze how the graph?s algebraic and spectral characteristics impact the properties of the graph signals of interest. Such an assumption is often untenable beyond applications dealing with, e.g., directly observable social and infrastructure networks; and typically adopted graph construction schemes are largely informal, distinctly lacking an element of validation. This article offers an overview of graph-learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology. Fairly mature statistical approaches are surveyed first, where correlation analysis takes center stage along with its connections to covariance selection and high-dimensional regression for learning Gaussian graphical models. Recent GSP-based network inference frameworks are also described, which postulate that the network exists as a latent underlying structure and that observations are generated as a result of a network process defined in such a graph. A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks and nonlinear models of pairwise interaction, as well as extensions to directed (di) graphs and their relation to causal inference. All in all, this article introduces readers to challenges and opportunities for SP research in emerging topic areas at the crossroads of modeling, prediction, and control of complex behavior arising in networked systems that evolve over time.

269 citations

Journal ArticleDOI
TL;DR: In this paper, the authors survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective.
Abstract: The construction of a meaningful graph topology plays a crucial role in the effective representation, processing, analysis and visualization of structured data. When a natural choice of the graph is not readily available from the data sets, it is thus desirable to infer or learn a graph topology from the data. In this tutorial overview, we survey solutions to the problem of graph learning, including classical viewpoints from statistics and physics, and more recent approaches that adopt a graph signal processing (GSP) perspective. We further emphasize the conceptual similarities and differences between classical and GSP-based graph inference methods, and highlight the potential advantage of the latter in a number of theoretical and practical scenarios. We conclude with several open issues and challenges that are keys to the design of future signal processing and machine learning algorithms for learning graphs from data.

261 citations

Journal ArticleDOI
TL;DR: In this article, a review of deep learning-based segmentation methods for cardiac image segmentation is provided, which covers common imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound.
Abstract: Deep learning has become the most widely used approach for cardiac image segmentation in recent years. In this paper, we provide a review of over 100 cardiac image segmentation papers using deep learning, which covers common imaging modalities including magnetic resonance imaging (MRI), computed tomography (CT), and ultrasound (US) and major anatomical structures of interest (ventricles, atria and vessels). In addition, a summary of publicly available cardiac image datasets and code repositories are included to provide a base for encouraging reproducible research. Finally, we discuss the challenges and limitations with current deep learning-based approaches (scarcity of labels, model generalizability across different domains, interpretability) and suggest potential directions for future research.

254 citations