Estimation of F-region plasma density and virtual height of the F-region in ionograms using deep learning

Speaker: Juha Vierinen, UiT Space Physics Group

Juha Vierinen, associate professor at the UiT Space Physics Group, gave a lunch talk on deep learning-based analysis of ionograms. The goal is to automatically estimate the plasma density and virtual height of the F-region, which would enable large scale statistical analysis of ionogram imagery.

A study of generative adversarial networks to improve classification of microscopic foraminifera

Speaker: Eirik Agnalt Østmo

Foraminifera are single-celled organisms with shells that live in the marine environment and can be found abundantly as fossils in e.g. sediment cores. The assemblages of different species and their numbers serves as an important source of data for marine, geological, climate and environmental research.

In this week's internal talk Eirik presents the work from his master's thesis where he attempted to use generative adversarial networks (GANs) to model microscope images of foraminifera and generate synthetic foraminifera images. The synthetic images was used in addition to the original images to attempt to improve a deep learning-based classification model that had previously been proposed (Johansen and Sørensen, 2020).

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The Approximation Power of Deep Neural Networks: Theory and Applications

Speaker: Gitta Kutynoik, Technische Universität Berlin

Despite the outstanding success of deep neural networks in real-world applications, most of the related research is empirically driven and a mathematical foundation is almost completely missing. The main goal of a neural network is to approximate a function, which for instance encodes a classification task. Thus, one theoretical approach to derive a fundamental understanding of deep neural networks focusses on their approximation abilities.

In this talk we will provide an introduction into this research area. After a general overview of mathematics of deep neural networks, we will discuss theoretical results which prove that not only do (memory-optimal) neural networks have as much approximation power as classical systems such as wavelets or shearlets, but they are also able to beat the curse of dimensionality. On the numerical side, we will then show that superior performance can typically be achieved by combining deep neural networks with classical approaches from approximation theory.

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Applied Harmonic Analysis meets Sparse Regularization of Inverse Problems

Speaker: Gitta Kutynoik, Technische Universität Berlin

Sparse regularization of inverse problems has already shown its effectiveness both theoretically and practically. The area of applied harmonic analysis offers a variety of systems such as wavelet systems which provide sparse approximations within certain model situations which then allows to apply this general approach provided that the solution belongs to this model class. However, many important problem classes in the multivariate situation are governed by anisotropic structures such as singularities concentrated on lower dimensional embedded manifolds, for instance, edges in images or shear layers in solutions of transport dominated equations. Since it was shown that the (isotropic) wavelet systems are not capable of sparsely approximating such anisotropic features, the need arose to introduce appropriate anisotropic representation systems. Among various suggestions, shearlets are the most widely used today. Main reasons for this are their optimal sparse approximation properties within a suitable model situation in combination with their unified treatment of the continuum and digital realm, leading to faithful implementations.

In this talk, we will first provide an introduction to sparse regularization of inverse problems, followed by an introduction to the area of applied harmonic analysis, in particular, discussing the anisotropic representation system of shearlets and presenting the main theoretical results. We will then analyze the effectiveness of using shearlets for sparse regularization of exemplary inverse problems both theoretically and numerically.

Conformal predictions

Speaker: Henrik Boström

Conformal prediction is a relatively new framework in which the predictive models output sets of predictions with a bound on the error rate, i.e., in a classification context, the probability of excluding the correct class label is lower than a predefined significance level. An investigation of the use of decision trees within the conformal prediction framework is presented, with the overall purpose to determine the effect of different algorithmic choices, including split criterion, pruning scheme and way to calculate the probability estimates. Since the error rate is bounded by the framework, the most important property of conformal predictors is efficiency, which concerns minimizing the number of elements in the output prediction sets. Results from one of the largest empirical investigations to date within the conformal prediction framework are presented, showing that in order to optimize efficiency, the decision trees should be induced using no pruning and with smoothed probability estimates. The choice of split criterion to use for the actual induction of the trees did not turn out to have any major impact on the efficiency. Finally, the experimentation also showed that when using decision trees, standard inductive conformal prediction was as efficient as the recently suggested method cross-conformal prediction. This is an encouraging results since cross-conformal prediction uses several decision trees, thus sacrificing the interpretability of a single decision tree.

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