RNDr. Jan Kalina, Ph.D.

Recent research on reliability in the context of deep learning has shown that there is no unique understanding of reliability assessment for training of deep networks, i.e. there is no unity as to which steps should be performed to accompany the training. Statistical approaches to the newly arising field of diagnostics for deep learning start from the simplest ideas such as verification of the trained network on out-of-distribution data [5]. More powerful approaches include verifying the influence of adversarial examples in the data [1], evaluation of uncertainty within deep learning algorithms [3], or computational methods for error propagation throughout the network [2]. One of rare theoretical approaches standing on probabilistic reasoning is the hypothesis test of reliability for a multi-class classifier [4]. The thesis will propose novel tools for assessing reliability of trained deep networks. Theoretical investigations will evaluate the influence of possible errors (uncertainty, measurement errors, or outlying measurements) on the results of a trained deep network. Another aim is to derive diagnostic tools for checking the probability assumptions for deep networks. The tools used here may include bootstrapping and nonparametric combinations of tests.

• [1] Alshemali B., Kalita J. (2020). Improving the reliability of deep neural networks in NLP: A review. Knowledge-based systems 191, 105210.
• [2] Bosio A., Bernardi P., Ruospo A., Sanchez E. (2019). A reliability analysis of a deep neural network. IEEE Latin American Test Symposium LATS 2019, 1-6.
• [3] Caldeira J., Nord B. (2021). Deeply uncertain: Comparing methods of uncertainty quantification in deep learning algorithms. Machine Learning: Science and Technology 2, 015002.
• [4] Gweon H. (2022). A power-controlled reliability assessment for multi-class probabilistic classifiers. Advances in Data Analysis and Classification. Online first.
• [5] Martensson G., Ferreira D., Granberg T., Cavallin L., Oppedal K. et al. (2020). The reliability of a deep learning model in clinical out-of-distribution MRI data: A multicohort study. Medical Image Analysis 66, 101714.

Linear discriminant analysis (LDA) represent a well known statistical classification method. Its various regularized versions are available for high-dimensional data with the number of variables exceeding (perhaps largely) the number of data samples. Recent proposal include regularized robust versions of LDA that are resistant to the presence of outlying values in the data. These consider robust estimates of the mean and of the covariance matrix. The aim of the work will be to propose and investigated novel versions of robust regularized LDA and to perform extensive simulations to study their performance. These will be based on new robust estimates of the covariance matrix: One idea is to exploit the novel MRWCD estimator (minimum regularized weighted covariance determinant) [1]. Another idea is to exploit the estimator based on numerical linear algebra manipulations, particularly on the minimum product of a small number of the largest eigenvalues of the covariance matrix [2].

• [1] Kalina J., Tichavský J. (2022): The minimum weighted covariance determinant estimator for high-dimensional data. Advances in Data Analysis and Classification 16, 977-999.
• [2] Kalina J. (2020): The minimum weighted covariance determinant estimator revisited. Communications in Statistics Simulation and Computation 51, 3888-3900.