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Modern machine learning methods including deep learning have achieved great success in predictive accuracy for supervised learning tasks, but may still fall short in giving useful estimates of their predictive {\em uncertainty}. Quantifying…

It has been demonstrated many times that the behavior of the human visual system is connected to the statistics of natural images. Since machine learning relies on the statistics of training data as well, the above connection has…

Although stochastic approximation learning methods have been widely used in the machine learning literature for over 50 years, formal theoretical analyses of specific machine learning algorithms are less common because stochastic…

Autism Spectrum Disorder (ASD) is one neuro developmental disorder that is now widespread in the world. ASD persists throughout the life of an individual, impacting the way they behave and communicate, resulting to notable deficits…

It is often observed that the probabilistic predictions given by a machine learning model can disagree with averaged actual outcomes on specific subsets of data, which is also known as the issue of miscalibration. It is responsible for the…

While machine-generated texts (MGTs) offer great convenience, they also pose risks such as disinformation and phishing, highlighting the need for reliable detection. Metric-based methods, which extract statistically distinguishable features…

Fine-tuning is a common practice in deep learning, achieving excellent generalization results on downstream tasks using relatively little training data. Although widely used in practice, it is lacking strong theoretical understanding. We…

When humans interact with intelligent systems, their causal responsibility for outcomes becomes equivocal. We analyze the descriptive abilities of a newly developed responsibility quantification model (ResQu) to predict actual human…

Additional training of a deep learning model can cause negative effects on the results, turning an initially positive sample into a negative one (degradation). Such degradation is possible in real-world use cases due to the diversity of…

We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector…

Machine learning has emerged as a promising paradigm for enabling connected, automated vehicles to autonomously cruise the streets and react to unexpected situations. A key challenge, however, is to collect and select real-time and reliable…

When the distribution of the data used to train a classifier differs from that of the test data, i.e., under dataset shift, well-established routines for calibrating the decision scores of the classifier, estimating the proportion of…

The measurement precision of modern quantum simulators is intrinsically constrained by the limited set of measurements that can be efficiently implemented on hardware. This fundamental limitation is particularly severe for quantum…

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

Diagnostic testing provides a unique setting for studying and developing tools in classification theory. In such contexts, the concept of prevalence, i.e. the number of individuals with a given condition, is fundamental, both as an inherent…

Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…

A key factor for ensuring safety in Autonomous Vehicles (AVs) is to avoid any abnormal behaviors under undesirable and unpredicted circumstances. As AVs increasingly rely on Deep Neural Networks (DNNs) to perform safety-critical tasks,…

Machine learning models deployed in real-world applications are often evaluated with precision-based metrics such as F1-score or AUC-PR (Area Under the Curve of Precision Recall). Heavily dependent on the class prior, such metrics make it…

It is generally well understood that predictive classification and compression are intrinsically related concepts in information theory. Indeed, many deep learning methods are explained as learning a kind of compression, and that better…

Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective…