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11	An Evaluation of Approaches for Generative Adversarial Network Overfitting Detection Tung Tien Vu (12091421) 20 November 2023 (has links) <p dir="ltr">Generating images from training samples solves the challenge of imbalanced data. It provides the necessary data to run machine learning algorithms for image classification, anomaly detection, and pattern recognition tasks. In medical settings, having imbalanced data results in higher false negatives due to a lack of positive samples. Generative Adversarial Networks (GANs) have been widely adopted for image generation. GANs allow models to train without computing intractable probability while producing high-quality images. However, evaluating GANs has been challenging for the researchers due to a need for an objective function. Most studies assess the quality of generated images and the variety of classes those images cover. Overfitting of training images, however, has received less attention from researchers. When the generated images are mere copies of the training data, GAN models will overfit and will not generalize well. This study examines the ability to detect overfitting of popular metrics: Maximum Mean Discrepancy (MMD) and Fréchet Inception Distance (FID). We investigate the metrics on two types of data: handwritten digits and chest x-ray images using Analysis of Variance (ANOVA) models.</p> Deep learning Statistical data science generative adversarial network (GANs) chest X-ray datasets frechet inception distance maximum mean discrepancy (MMD)
12	Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces Hofmann, B., Scherzer, O. 30 October 1998 (has links) (PDF) The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results. nonlinear operator equations ill-posedness Frechet derivative source conditions stability estimates ill-posedness measurres a posteriori estimates MSC 65J15 MSC 65J20 MSC 47H15 MSC 47H17 ddc:510
13	On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces Hofmann, B. 30 October 1998 (has links) (PDF) In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed. Nonlinear inverse problems oerator equations ill-posedness stability estimates local ill-posedness Frechet derivative linearized problem compact operators integral equations parameter identification MSC 65J20 MSC 47H15 MSC 65J10 MSC 65J15 MSC 65R30 MSC 45G10 ddc:510
14	Local Ill-Posedness and Source Conditions of Operator Equations in Hilbert Spaces Hofmann, B., Scherzer, O. 30 October 1998 (has links) The characterization of the local ill-posedness and the local degree of nonlinearity are of particular importance for the stable solution of nonlinear ill-posed problems. We present assertions concerning the interdependence between the ill-posedness of the nonlinear problem and its linearization. Moreover, we show that the concept of the degree of nonlinearity com bined with source conditions can be used to characterize the local ill-posedness and to derive a posteriori estimates for nonlinear ill-posed problems. A posteriori estimates are widely used in finite element and multigrid methods for the solution of nonlinear partial differential equations, but these techniques are in general not applicable to inverse an ill-posed problems. Additionally we show for the well-known Landweber method and the iteratively regularized Gauss-Newton method that they satisfy a posteriori estimates under source conditions; this can be used to prove convergence rates results. info:eu-repo/classification/ddc/510 ddc:510
15	On Ill-Posedness and Local Ill-Posedness of Operator Equations in Hilbert Spaces: On Ill-Posedness and Local Ill-Posedness of OperatorEquations in Hilbert Spaces Hofmann, B. 30 October 1998 (has links) In this paper, we study ill-posedness concepts of nonlinear and linear inverse problems in a Hilbert space setting. We define local ill-posedness of a nonlinear operator equation $F(x) = y_0$ in a solution point $x_0$ and the interplay between the nonlinear problem and its linearization using the Frechet derivative $F\acent(x_0)$ . To find an appropriate ill-posedness concept for the linarized equation we define intrinsic ill-posedness for linear operator equations $Ax = y$ and compare this approach with the ill-posedness definitions due to Hadamard and Nashed. info:eu-repo/classification/ddc/510 ddc:510 Nonlinear inverse problems oerator equations ill-posedness stability estimates local ill-posedness Frechet derivative linearized problem compact operators integral equations parameter identification MSC 65J20 MSC 47H15 MSC 65J10 MSC 65J15 MSC 65R30 MSC 45G10

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