Training Gaussian Mixture Models at Scale via Coresets

How can we train a statistical mixture model on a massive data set? In this work we show how to construct coresets for mixtures of Gaussians. A coreset is a weighted subset of the data, which guarantees that models fitting the coreset also provide a good fit for the original data set. We show that, perhaps surprisingly, Gaussian mixtures admit coresets of size polynomial in dimension and the number of mixture components, while being independent of the data set size. Hence, one can harness computationally intensive algorithms to compute a good approximation on a significantly smaller data set. More importantly, such coresets can be efficiently constructed both in distributed and streaming settings and do not impose restrictions on the data generating process. Our results rely on a novel reduction of statistical estimation to problems in computational geometry and new combinatorial complexity results for mixtures of Gaussians. Empirical evaluation on several real-world datasets suggests that our coreset-based approach enables significant reduction in training-time with negligible approximation error

Hate-baiting: The radical right and ‘fifth column discourse’ in European and American democracies today

Modern politics relies enormously upon shaping ‘the message’ toward targeted constituencies. Whether it’s Labour’s ‘Controls on Immigration’ or the Tories’ ‘blue-collar cabinet’ on either side of the recent 2015 General Election in Britain, reaching beyond a core ‘base’ of activists is now widely recognised as a key ingredient to political success. Whilst being ‘on message’ can be seen to be problematic for all political movements and organisations, it has special challenges for radical right movements. This short article presents a survey of some of the issues at play in terms of the post-war radical right, before focussing on two ‘doublespeak’ tactics – namely ‘metonymy’ and ‘inversion’ – as they are exemplified in the LaRouche organisation, deriving its name from the American political activist Lyndon LaRouche. There are a number of aspects are touched upon in this context, although discussion will be largely placed upon ‘coded’ anti-Semitic rhetoric since 1945, as well as postwar denial of the Holocaust. This overview argues, above all, that the variegated forces of ethno-nationalism have found novel and innovative ways to adapt in, and to, the 21st century. Indeed, the modes of expression employed in the process of re-framing radical right politics – often leading to the development of public messages that differ markedly to ‘backstage’ ideas – is an increasingly important area for scholarly enquiry

Social Media and the Cordon Sanitaire: Populist politics, the online space, and a relationship that just isn’t there:Language and Politics

© John Benjamins Publishing Company. Much research has sought to map the spread of extreme and populist political ideologies across Western Europe. Despite this, it often fails to explain how these ideologies move from the political fringes to positions of influence, subverting the traditional cordon sanitaire around extreme views. As a result of recent successes by populist actors, a more nuanced understanding of this process is required. This paper posits an explanation for this success, suggesting that the growing pluralisation of the online media environment and the impact of social media content sharing are key to understanding how fringe political actors avoid both overt and implicit barriers to popularising extreme positions. Using data from the British Election Study, this paper offers a quantitative test of this approach, finding an inconsistent relationship between social media use and extreme political opinions. Potential explanations for this are discussed alongside possible directions for future research