In recent years we have observed a convergence of the fields of robotics and machine learning initiated by technological advances bringing AI closer to the physical world. A prerequisite, however, for successful applications is to formulate reliable and precise offline algorithms, requiring minimal tuning, fast and adaptive online algorithms and finally effective ways of rectifying corrupt demonstrations. In this work we aim to address some of those challenges. We begin by employing two offline algorithms for the purpose of Learning by Demonstration (LbD). A Bayesian non-parametric approach, able to infer the optimal model size without compromising the model's descriptive power and a Quantum Statistical extension to the mixture model able to achieve high precision for a given model size. We explore the efficacy of those algorithms in several one- and multi-shot LbD application achieving very promising results in terms of speed and and accuracy. Acknowledging that more realistic robotic applications also require more adaptive algorithmic approaches, we then introduce an online learning algorithm for quantum mixtures based on the online EM. The method exhibits high stability and precision, outperforming well-established online algorithms, as demonstrated for several regression benchmark datasets and a multi-shot trajectory LbD case study. Finally, aiming to account for data corruption due to sensor failures or occlusions, we propose a model for automatically rectifying damaged sequences in an unsupervised manner. In our approach we take into account the sequential nature of the data, the redundancy manifesting itself among repetitions of the same task and the potential of knowledge transfer across different tasks. We have devised a temporal factor model, with each factor modelling a single basic pattern in time and collectively forming a dictionary of fundamental trajectories shared across sequences. We have evaluated our method in a number of real-life datasets.