Uncertainty Quantification: Classical and Quantum Approaches for Limited Labelled-Datasets

Kurzfassung

Deep learning (DL) models are extensively used to analyze small- and large-scale datasets due to their scalability and their computational efficiency compared with conventional statistical approaches such as Bayesian analysis. However, they are not capable of learning informative information from small-scale datasets and explaining their predictions; namely, their outputs, given small-scale datasets as input, are not trustworthy and reliable which can be measured by using uncertainty quantification. In fact, DL models are often considered as uninterpretable black boxes with unknown uncertainties, and they even suffer learning on small-scale datasets. In contrast, Bayesian analysis is a gold standard technique for uncertainty quantification in order to obtain trustworthy and reliable predictions generated by models fitted small-scale datasets (observations) due to its high computational cost on processing large-scale datasets. Hence, DL models integrated with Bayesian analysis, that is, Bayesian Neural Networks (BNNs), are slowly gaining a great interest, since they can be trained on both small-and large-scale datasets and allow make their outputs interpretable by yielding trustworthy and reliable uncertainties. However, BNN inference on large-scale datasets persists high computational cost even on supercomputers, and commonly used methodologies to overcome this challenge are Monte Carlo Markov Chain (MCMC) and variational inference (VI) approaches. Moreover, the VI approach, returning approximate samples, can be scaled on big datasets in contrast to the exact sampling MCMC. Therefore, this study assesses and examines quantum VI paradigm for processing BNN inference to improve its sampling power. More importantly, the quantum VI method promises quantum advantage over its classical counterpart, since it can be executed on near- and long-term quantum computers, representing classically intractable probability distributions but hard-to-sample it on a conventional computer in the context of computational complexity hierarchy conjectures.