Optimal transport (OT) theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools is sensitive to outliers or it can perform poorly when the underlying model has heavy-tails. To cope with these issues, we introduce a new class of procedures. (i) We consider a robust version of the primal OT problem (ROBOT) and show that it defines the {robust Wasserstein distance}, $W^{(\lambda)}$, which depends on a tuning parameter $\lambda > 0$. (ii) We illustrate the link between $W_1$ and $W^{(\lambda)}$ and study its key measure theoretic aspects. (iii) We derive some concentration inequalities for $W^{(\lambda)}$. (iii) We use $W^{(\lambda)}$ to define minimum distance estimators, we provide their statistical guarantees and we illustrate how to apply concentration inequalities for the selection of $\lambda$. (v) We derive the {dual} form of the ROBOT and illustrate its applicability to machine learning problems (generative adversarial networks and domain adaptation). Numerical exercises provide evidence of the benefits yielded by our methods.

The most successful artificial intelligence (AI) systems will be those comprising an emotional intelligence almost indistinguishable from human-to-human interaction, according to Bronwyn van der Merwe, group director at Fjord Australia and New Zealand -- Accenture Interactive's design and innovation arm. While the concept of AI is not new, in 2017 van der Merwe expects emotional intelligence to emerge as the driving force behind what she called the next generation in AI, as humans will be drawn to human-like interaction. As businesses continue to experiment with the Internet of Things, interesting use cases are emerging. Here are some of the most common ways IoT is deployed in the enterprise. Speaking with ZDNet, van der Merwe explained that building on the first phase of AI technology, emotional intelligence enhances AI's ability to understand emotional input, and continually adapt to and learn from information to provide human-like responses in real time.