Transfer Learning is an area of statistics and machine learning research that seeks answers to the following question: how do we build successful learning algorithms when the data available for training our model is qualitatively different from the data we hope the model will perform well on? In this thesis, we focus on a specific area of Transfer Learning called label shift, also known as quantification. In quantification, the aforementioned discrepancy is isolated to a shift in the distribution of the response variable. In such a setting, accurately inferring the response variable's new distribution is both an important estimation task in its own right and a crucial step for ensuring that the learning algorithm can adapt to the new data. We make two contributions to this field. First, we present a new procedure called SELSE which estimates the shift in the response variable's distribution. Second, we prove that SELSE is semiparametric efficient among a large family of quantification algorithms, i.e., SELSE's normalized error has the smallest possible asymptotic variance matrix compared to any other algorithm in that family. This family includes nearly all existing algorithms, including ACC/PACC quantifiers and maximum likelihood based quantifiers such as EMQ and MLLS. Empirical experiments reveal that SELSE is competitive with, and in many cases outperforms, existing state-of-the-art quantification methods, and that this improvement is especially large when the number of test samples is far greater than the number of train samples.

We consider the problem of data classification where the training set consists of just a few data points. We explore this phenomenon mathematically and reveal key relationships between the geometry of an AI model's feature space, the structure of the underlying data distributions, and the model's generalisation capabilities. The main thrust of our analysis is to reveal the influence on the model's generalisation capabilities of nonlinear feature transformations mapping the original data into high, and possibly infinite, dimensional spaces.

EEG-based tinnitus classification is a valuable tool for tinnitus diagnosis, research, and treatments. Most current works are limited to a single dataset where data patterns are similar. But EEG signals are highly non-stationary, resulting in model's poor generalization to new users, sessions or datasets. Thus, designing a model that can generalize to new datasets is beneficial and indispensable. To mitigate distribution discrepancy across datasets, we propose to achieve Disentangled and Side-aware Unsupervised Domain Adaptation (DSUDA) for cross-dataset tinnitus diagnosis. A disentangled auto-encoder is developed to decouple class-irrelevant information from the EEG signals to improve the classifying ability. The side-aware unsupervised domain adaptation module adapts the class-irrelevant information as domain variance to a new dataset and excludes the variance to obtain the class-distill features for the new dataset classification. It also align signals of left and right ears to overcome inherent EEG pattern difference. We compare DSUDA with state-of-the-art methods, and our model achieves significant improvements over competitors regarding comprehensive evaluation criteria. The results demonstrate our model can successfully generalize to a new dataset and effectively diagnose tinnitus.

Graph classification is an important area in both modern research and industry. Multiple applications, especially in chemistry and novel drug discovery, encourage rapid development of machine learning models in this area. To keep up with the pace of new research, proper experimental design, fair evaluation, and independent benchmarks are essential. Design of strong baselines is an indispensable element of such works. In this thesis, we explore multiple approaches to graph classification. We focus on Graph Neural Networks (GNNs), which emerged as a de facto standard deep learning technique for graph representation learning. Classical approaches, such as graph descriptors and molecular fingerprints, are also addressed. We design fair evaluation experimental protocol and choose proper datasets collection. This allows us to perform numerous experiments and rigorously analyze modern approaches. We arrive to many conclusions, which shed new light on performance and quality of novel algorithms. We investigate application of Jumping Knowledge GNN architecture to graph classification, which proves to be an efficient tool for improving base graph neural network architectures. Multiple improvements to baseline models are also proposed and experimentally verified, which constitutes an important contribution to the field of fair model comparison.

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise. For a robust recovery against noise and the choice of hyper-parameters, we introduce two new mechanisms, narrow-fit and trimming, for the coefficient support and value recovery, respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming of the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to $100\%$ noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

Semiconductor lasers have been rapidly evolving to meet the demands of next-generation optical networks. This imposes much more stringent requirements on the laser reliability, which are dominated by degradation mechanisms (e.g., sudden degradation) limiting the semiconductor laser lifetime. Physics-based approaches are often used to characterize the degradation behavior analytically, yet explicit domain knowledge and accurate mathematical models are required. Building such models can be very challenging due to a lack of a full understanding of the complex physical processes inducing the degradation under various operating conditions. To overcome the aforementioned limitations, we propose a new data-driven approach, extracting useful insights from the operational monitored data to predict the degradation trend without requiring any specific knowledge or using any physical model. The proposed approach is based on an unsupervised technique, a conditional variational autoencoder, and validated using vertical-cavity surface-emitting laser (VCSEL) and tunable edge emitting laser reliability data. The experimental results confirm that our model (i) achieves a good degradation prediction and generalization performance by yielding an F1 score of 95.3%, (ii) outperforms several baseline ML based anomaly detection techniques, and (iii) helps to shorten the aging tests by early predicting the failed devices before the end of the test and thereby saving costs

Purpose: Hard-to-interpret Black-box Machine Learning (ML) were often used for early Alzheimer's Disease (AD) detection. Methods: To interpret eXtreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Machine (SVM) black-box models a workflow based on Shapley values was developed. All models were trained on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset and evaluated for an independent ADNI test set, as well as the external Australian Imaging and Lifestyle flagship study of Ageing (AIBL), and Open Access Series of Imaging Studies (OASIS) datasets. Shapley values were compared to intuitively interpretable Decision Trees (DTs), and Logistic Regression (LR), as well as natural and permutation feature importances. To avoid the reduction of the explanation validity caused by correlated features, forward selection and aspect consolidation were implemented. Results: Some black-box models outperformed DTs and LR. The forward-selected features correspond to brain areas previously associated with AD. Shapley values identified biologically plausible associations with moderate to strong correlations with feature importances. The most important RF features to predict AD conversion were the volume of the amygdalae, and a cognitive test score. Good cognitive test performances and large brain volumes decreased the AD risk. The models trained using cognitive test scores significantly outperformed brain volumetric models ($p<0.05$). Cognitive Normal (CN) vs. AD models were successfully transferred to external datasets. Conclusion: In comparison to previous work, improved performances for ADNI and AIBL were achieved for CN vs. Mild Cognitive Impairment (MCI) classification using brain volumes. The Shapley values and the feature importances showed moderate to strong correlations.

Skeleton-based Motion Capture (MoCap) systems have been widely used in the game and film industry for mimicking complex human actions for a long time. MoCap data has also proved its effectiveness in human activity recognition tasks. However, it is a quite challenging task for smaller datasets. The lack of such data for industrial activities further adds to the difficulties. In this work, we have proposed an ensemble-based machine learning methodology that is targeted to work better on MoCap datasets. The experiments have been performed on the MoCap data given in the Bento Packaging Activity Recognition Challenge 2021. Bento is a Japanese word that resembles lunch-box. Upon processing the raw MoCap data at first, we have achieved an astonishing accuracy of 98% on 10-fold Cross-Validation and 82% on Leave-One-Out-Cross-Validation by using the proposed ensemble model.

Learning curves provide insight into the dependence of a learner's generalization performance on the training set size. This important tool can be used for model selection, to predict the effect of more training data, and to reduce the computational complexity of model training and hyperparameter tuning. This review recounts the origins of the term, provides a formal definition of the learning curve, and briefly covers basics such as its estimation. Our main contribution is a comprehensive overview of the literature regarding the shape of learning curves. We discuss empirical and theoretical evidence that supports well-behaved curves that often have the shape of a power law or an exponential. We consider the learning curves of Gaussian processes, the complex shapes they can display, and the factors influencing them. We draw specific attention to examples of learning curves that are ill-behaved, showing worse learning performance with more training data. To wrap up, we point out various open problems that warrant deeper empirical and theoretical investigation. All in all, our review underscores that learning curves are surprisingly diverse and no universal model can be identified.

The use of supervised Machine Learning (ML) to enhance Intrusion Detection Systems has been the subject of significant research. Supervised ML is based upon learning by example, demanding significant volumes of representative instances for effective training and the need to re-train the model for every unseen cyber-attack class. However, retraining the models in-situ renders the network susceptible to attacks owing to the time-window required to acquire a sufficient volume of data. Although anomaly detection systems provide a coarse-grained defence against unseen attacks, these approaches are significantly less accurate and suffer from high false-positive rates. Here, a complementary approach referred to as 'One-Shot Learning', whereby a limited number of examples of a new attack-class is used to identify a new attack-class (out of many) is detailed. The model grants a new cyber-attack classification without retraining. A Siamese Network is trained to differentiate between classes based on pairs similarities, rather than features, allowing to identify new and previously unseen attacks. The performance of a pre-trained model to classify attack-classes based only on one example is evaluated using three datasets. Results confirm the adaptability of the model in classifying unseen attacks and the trade-off between performance and the need for distinctive class representation.