Modern datasets, from areas such as neuroimaging and geostatistics, often come in the form of a random sample of tensor-valued data which can be understood as noisy observations of an underlying smooth multidimensional random function. Many of the traditional techniques from functional data analysis are plagued by the curse of dimensionality and quickly become intractable as the dimension of the domain increases. In this paper, we propose a framework for learning multidimensional continuous representations from a random sample of tensors that is immune to several manifestations of the curse. These representations are defined to be multiplicatively separable and adapted to the data according to an $L^{2}$ optimality criteria, analogous to a multidimensional functional principal components analysis. We show that the resulting estimation problem can be solved efficiently by the tensor decomposition of a carefully defined reduction transformation of the observed data. The incorporation of both regularization and dimensionality reduction is discussed. The advantages of the proposed method over competing methods are demonstrated in a simulation study. We conclude with a real data application in neuroimaging.

Assume we have a person, call center agent, who has a list of questions and answers. If anyone calls him and asks a question, this person goes through the list and answers the question, just like our bot above. So, this person is a little silly, he does not remember the previous questions. But… we have other agents out there, and they all are allowed to redirect the customer to each other. Ok, now if the user calls the Agent 1 and says he needs car insurance, Agent 1 says "ok, sure" and redirects the user to the Agent 2, whose name is "car".

There's a Robotic Bartender at CES and Its Name is Somabar Of all the of the cool details in the Star Trek universe, our favorite is easily the replicator--a microwave-sized cutout in the wall that can create any dish, snack, or drink with a simple command. We may be a long way off from enjoying replicated meals, but at CES this year we had the chance to drink a margarita mixed by what might be the next-best thing. Somabar is a robotic bartender that was initially funded on Kickstarter last year. Since then, the device has been through several iterations (the one I used on the trade show floor being the most recent). It's roughly the size of a mini-fridge, but the rows of cylindrical booze/mixer pods lining its side make it look like something out of Blade Runner.