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"Global history faces two seemingly opposite challenges for an inter-dependent, over-heating planet. If we are going to muster meaningful narratives about the togetherness of strangers near and far, we are going to have to be more global and get more serious about engaging other languages and other ways of telling history. Historians and their reader-citizens are also going to have to re-signify the place of local attachments and meanings. Going deeper into the stories of Others afar and Strangers at home means dispensing with the idea that global integration was like an electric circuit, bringing light to the connected. Becoming inter-dependent is not just messier than drawing a wiring diagram. It means reckoning with dimensions of networks and circuits that global historians - and possibly all narratives of cosmopolitan convergence - leave out of the story: lighting up corners of the earth leaves others in the dark.  The story of the globalists illuminates some at the expense of others, the left behind, the ones who cannot move, and those who become immobilised because the light no longer shines on them."

Optimization is a key tool in machine learning, where the goal is to achieve the best possible objective function value in a minimum amount of time. Obtaining any form of global guarantees can usually be done with convex objective functions, or with special cases such as risk minimization with one-hidden over-parameterized layer neural networks (see the June post). In this post, I will consider low-dimensional problems (imagine 10 or 20), with no constraint on running time (thus get ready for some running-times that are exponential in dimension!).

You probably interact with fifty to a hundred machine learning products every day, from your social media feeds and YouTube recommendations to your email spam filter and the updates that the New York Times, CNN, or Fox News decide to push, not to mention the hidden models that place ads on the websites you visit, and that redesign your 'experience' on the fly. Not all models are created equal, however: they operate on different principles, and impact us as individuals and communities in different ways. They differ fundamentally from each other along dimensions such as alignment of incentives between stakeholders, "creep factor", and the nature of how their feedback loops ope !L

The analysis of questionnaires often involves representing the high-dimensional responses in a low-dimensional space (e.g., PCA, MCA, or t-SNE). However questionnaire data often contains categorical variables and common statistical model assumptions rarely hold. Here we present a non-parametric approach based on Fisher Information which obtains a low-dimensional embedding of a statistical manifold (SM). The SM has deep connections with parametric statistical models and the theory of phase transitions in statistical physics. Firstly we simulate questionnaire responses based on a non-linear SM and validate our method compared to other methods. Secondly we apply our method to two empirical datasets containing largely categorical variables: an anthropological survey of rice farmers in Bali and a cohort study on health inequality in Amsterdam. Compare to previous analysis and known anthropological knowledge we conclude that our method best discriminates between different behaviours, paving the way to dimension reduction as effective as for continuous data.