Robust contrastive learning and nonlinear ICA in the presence of outliers

Peer reviewe

Universal hidden monotonic trend estimation with contrastive learning

In this paper, we describe a universal method for extracting the underlying monotonic trend factor from time series data. We propose an approach related to the Mann-Kendall test, a standard monotonic trend detection method and call it contrastive trend estimation (CTE). We show that the CTE method identifies any hidden trend underlying temporal data while avoiding the standard assumptions used for monotonic trend identification. In particular, CTE can take any type of temporal data (vector, images, graphs, time series, etc.) as input. We finally illustrate the interest of our CTE method through several experiments on different types of data and problems

Independent Component Analysis for Binary Data

Independent Component Analysis (ICA) aims to separate the observed signals into their underlying independent components responsible for generating the observations. Most research in ICA has focused on continuous signals, while the methodology for binary and discrete signals is less developed. Yet, binary observations are equally present in various fields and applications, such as causal discovery, signal processing, and bioinformatics. In the last decade, Boolean OR and XOR mixtures have been shown to be identifiable by ICA, but such models suffer from limited expressivity, calling for new methods to solve the problem. In this thesis, "Independent Component Analysis for Binary Data", we estimate the mixing matrix of ICA from binary observations and an additionally observed auxiliary variable by employing a linear model inspired by the Identifiable Variational Autoencoder (iVAE), which exploits the non-stationarity of the data. The model is optimized with a gradient-based algorithm that uses second-order optimization with limited memory, resulting in a training time in the order of seconds for the particular study cases. We investigate which conditions can lead to the reconstruction of the mixing matrix, concluding that the method is able to identify the mixing matrix when the number of observed variables is greater than the number of sources. In such cases, the linear binary iVAE can reconstruct the mixing matrix up to order and scale indeterminacies, which are considered in the evaluation with the Mean Cosine Similarity Score. Furthermore, the model can reconstruct the mixing matrix even under a limited sample size. Therefore, this work demonstrates the potential for applications in real-world data and also offers a possibility to study and formalize identifiability in future work. In summary, the most important contributions of this thesis are the empirical study of the conditions that enable the mixing matrix reconstruction using the binary iVAE, and the empirical results on the performance and efficiency of the model. The latter was achieved through a new combination of existing methods, including modifications and simplifications of a linear binary iVAE model and the optimization of such a model under limited computational resources

Cluster Exploration using Informative Manifold Projections

Dimensionality reduction (DR) is one of the key tools for the visual exploration of high-dimensional data and uncovering its cluster structure in two- or three-dimensional spaces. The vast majority of DR methods in the literature do not take into account any prior knowledge a practitioner may have regarding the dataset under consideration. We propose a novel method to generate informative embeddings which not only factor out the structure associated with different kinds of prior knowledge but also aim to reveal any remaining underlying structure. To achieve this, we employ a linear combination of two objectives: firstly, contrastive PCA that discounts the structure associated with the prior information, and secondly, kurtosis projection pursuit which ensures meaningful data separation in the obtained embeddings. We formulate this task as a manifold optimization problem and validate it empirically across a variety of datasets considering three distinct types of prior knowledge. Lastly, we provide an automated framework to perform iterative visual exploration of high-dimensional data

Reconstruction Error and Principal Component Based Anomaly Detection in Hyperspectral imagery

The rapid expansion of remote sensing and information collection capabilities demands methods to highlight interesting or anomalous patterns within an overabundance of data. This research addresses this issue for hyperspectral imagery (HSI). Two new reconstruction based HSI anomaly detectors are outlined: one using principal component analysis (PCA), and the other a form of non-linear PCA called logistic principal component analysis. Two very effective, yet relatively simple, modifications to the autonomous global anomaly detector are also presented, improving algorithm performance and enabling receiver operating characteristic analysis. A novel technique for HSI anomaly detection dubbed multiple PCA is introduced and found to perform as well or better than existing detectors on HYDICE data while using only linear deterministic methods. Finally, a response surface based optimization is performed on algorithm parameters such as to affect consistent desired algorithm performance

Interpretable brain age prediction using linear latent variable models of functional connectivity

Neuroimaging-driven prediction of brain age, defined as the predicted biological age of a subject using only brain imaging data, is an exciting avenue of research. In this work we seek to build models of brain age based on functional connectivity while prioritizing model interpretability and understanding. This way, the models serve to both provide accurate estimates of brain age as well as allow us to investigate changes in functional connectivity which occur during the ageing process. The methods proposed in this work consist of a two-step procedure: first, linear latent variable models, such as PCA and its extensions, are employed to learn reproducible functional connectivity networks present across a cohort of subjects. The activity within each network is subsequently employed as a feature in a linear regression model to predict brain age. The proposed framework is employed on the data from the CamCAN repository and the inferred brain age models are further demonstrated to generalize using data from two open-access repositories: the Human Connectome Project and the ATR Wide-Age-Range.Peer reviewe

Selected Inductive Biases in Neural Networks To Generalize Beyond the Training Domain

Die künstlichen neuronalen Netze des computergesteuerten Sehens können mit den vielf\"altigen Fähigkeiten des menschlichen Sehens noch lange nicht mithalten. Im Gegensatz zum Menschen können künstliche neuronale Netze durch kaum wahrnehmbare Störungen durcheinandergebracht werden, es mangelt ihnen an Generalisierungsfähigkeiten über ihre Trainingsdaten hinaus und sie benötigen meist noch enorme Datenmengen für das Erlernen neuer Aufgaben. Somit sind auf neuronalen Netzen basierende Anwendungen häufig auf kleine Bereiche oder kontrollierte Umgebungen beschränkt und lassen sich schlecht auf andere Aufgaben übertragen. In dieser Dissertation, werden vier Veröffentlichungen besprochen, die sich mit diesen Einschränkungen auseinandersetzen und Algorithmen im Bereich des visuellen Repräsentationslernens weiterentwickeln. In der ersten Veröffentlichung befassen wir uns mit dem Erlernen der unabhängigen Faktoren, die zum Beispiel eine Szenerie beschreiben. Im Gegensatz zu vorherigen Arbeiten in diesem Forschungsfeld verwenden wir hierbei jedoch weniger künstliche, sondern natürlichere Datensätze. Dabei beobachten wir, dass die zeitlichen Änderungen von Szenerien beschreibenden, natürlichen Faktoren (z.B. die Positionen von Personen in einer Fußgängerzone) einer verallgemeinerten Laplace-Verteilung folgen. Wir nutzen die verallgemeinerte Laplace-Verteilung als schwaches Lernsignal, um neuronale Netze für mathematisch beweisbares Repräsentationslernen unabhängiger Faktoren zu trainieren. Wir erzielen in den disentanglement_lib Wettbewerbsdatensätzen vergleichbare oder bessere Ergebnisse als vorherige Arbeiten – dies gilt auch für die von uns beigesteuerten Datensätze, welche natürliche Faktoren beinhalten. Die zweite Veröffentlichung untersucht, ob verschiedene neuronale Netze bereits beobachtete, eine Szenerie beschreibende Faktoren generalisieren können. In den meisten bisherigen Generalisierungswettbewerben werden erst während der Testphase neue Störungsfaktoren hinzugefügt - wir hingegen garantieren, dass die für die Testphase relevanten Variationsfaktoren bereits während der Trainingsphase teilweise vorkommen. Wir stellen fest, dass die getesteten neuronalen Netze meist Schwierigkeiten haben, die beschreibenden Faktoren zu generalisieren. Anstatt die richtigen Werte der Faktoren zu bestimmen, neigen die Netze dazu, Werte in zuvor beobachteten Bereichen vorherzusagen. Dieses Verhalten ist bei allen untersuchten neuronalen Netzen recht ähnlich. Trotz ihrer begrenzten Generalisierungsfähigkeiten, können die Modelle jedoch modular sein: Obwohl sich einige Faktoren während der Trainingsphase in einem zuvor ungesehenen Wertebereich befinden, können andere Faktoren aus einem bereits bekannten Wertebereich größtenteils dennoch korrekt bestimmt werden. Die dritte Veröffentlichung präsentiert ein adversielles Trainingsverfahren für neuronale Netze. Das Verfahren ist inspiriert durch lokale Korrelationsstrukturen häufiger Bildartefakte, die z.B. durch Regen, Unschärfe oder Rauschen entstehen können. Im Klassifizierungswettbewerb ImageNet-C zeigen wir, dass mit unserer Methode trainierte Netzwerke weniger anfällig für häufige Störungen sind als einige, die mit bestehenden Methoden trainiert wurden. Schließlich stellt die vierte Veröffentlichung einen generativen Ansatz vor, der bestehende Ansätze gemäß mehrerer Robustheitsmetriken beim MNIST Ziffernklassifizierungswettbewerb übertrifft. Perzeptiv scheint unser generatives Modell im Vergleich zu früheren Ansätzen stärker auf das menschliche Sehen abgestimmt zu sein, da Bilder von Ziffern, die für unser generatives Modell mehrdeutig sind, auch für den Menschen mehrdeutig erscheinen können. Diese Arbeit liefert also Möglichkeiten zur Verbesserung der adversiellen Robustheit und der Störungstoleranz sowie Erweiterungen im Bereich des visuellen Repräsentationslernens. Somit nähern wir uns im Bereich des maschinellen Lernens weiter der Vielfalt menschlicher Fähigkeiten an.Artificial neural networks in computer vision have yet to approach the broad performance of human vision. Unlike humans, artificial networks can be derailed by almost imperceptible perturbations, lack strong generalization capabilities beyond the training data and still mostly require enormous amounts of data to learn novel tasks. Thus, current applications based on neural networks are often limited to a narrow range of controlled environments and do not transfer well across tasks. This thesis presents four publications that address these limitations and advance visual representation learning algorithms. In the first publication, we aim to push the field of disentangled representation learning towards more realistic settings. We observe that natural factors of variation describing scenes, e.g., the position of pedestrians, have temporally sparse transitions in videos. We leverage this sparseness as a weak form of learning signal to train neural networks for provable disentangled visual representation learning. We achieve competitive results on the disentanglement_lib benchmark datasets and our own contributed datasets, which include natural transitions. The second publication investigates whether various visual representation learning approaches generalize along partially observed factors of variation. In contrast to prior robustness benchmarks that add unseen types of perturbations during test time, we compose, interpolate, or extrapolate the factors observed during training. We find that the tested models mostly struggle to generalize to our proposed benchmark. Instead of predicting the correct factors, models tend to predict values in previously observed ranges. This behavior is quite common across models. Despite their limited out-of-distribution performances, the models can be fairly modular as, even though some factors are out-of-distribution, other in-distribution factors are still mostly inferred correctly. The third publication presents an adversarial noise training method for neural networks inspired by the local correlation structure of common corruptions caused by rain, blur, or noise. On the ImageNet-C classification benchmark, we show that networks trained with our method are less susceptible to common corruptions than those trained with existing methods. Finally, the fourth publication introduces a generative approach that outperforms existing approaches according to multiple robustness metrics on the MNIST digit classification benchmark. Perceptually, our generative model is more aligned with human vision compared to previous approaches, as images of digits at our model's decision boundary can also appear ambiguous to humans. In a nutshell, this work investigates ways of improving adversarial and corruption robustness, and disentanglement in visual representation learning algorithms. Thus, we alleviate some limitations in machine learning and narrow the gap towards human capabilities