George Papandreou

Tamir Hazan

Daniel Tarlow

A description of perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees. In nearly all machine learning, decisions must be made given current knowledge. Surprisingly, making what is believed to be the best decision is not always the best strategy, even when learning in a supervised learning setting. An emerging body of work on learning under different rules applies perturbations to decision and learning procedures. These methods provide simple and highly efficient learning rules with improved theoretical guarantees. This book describes perturbation-based methods developed in machine learning to augment novel optimization methods with strong statistical guarantees, offering readers a state-of-the-art overview. Chapters address recent modeling ideas that have arisen within the perturbations framework, including Perturb & MAP, herding, and the use of neural networks to map generic noise to distribution over highly structured data. They describe new learning procedures for perturbation models, including an improved EM algorithm and a learning algorithm that aims to match moments of model samples to moments of data. They discuss understanding the relation of perturbation models to their traditional counterparts, with one chapter showing that the perturbations viewpoint can lead to new algorithms in the traditional setting. And they consider perturbation-based regularization in neural networks, offering a more complete understanding of dropout and studying perturbations in the context of deep neural networks.

Perturbations, Optimization, and Statistics

Paul Krugman

Newt Gingrich

Arthur Laffer

As middle-class incomes stagnate in advanced economies while the rich experience record income gains, the eleventh semi-annual Munk Debate pits wealth redistribution supporters Paul Krugman and George Papandreou against Newt Gingrich and Arthur Laffer to debate taxation — should the rich pay more? For some the answer is obvious: redistribute the wealth of the top income earners who have enjoyed, for almost a generation, the lion’s share of all income gains. Imposing higher taxes on the wealthy is the best way for countries such as Canada to reinvest in their social safety nets, education, and infrastructure while protecting the middle class. Others argue that anemic economic growth, not income inequality, is the real problem facing advanced countries. In a globalized economy, raising taxes on society’s wealth creators leads to capital flight, falling government revenues, and less money for the poor. These same voices contend that lowering taxes on everyone stimulates innovation and investment, fuelling future prosperity. In this edition of the Munk Debates — Canada’s premier international debate series — Nobel Prize–winning economist Paul Krugman and former Prime Minster of Greece George Papandreou square off against former Speaker of the U.S. House of Representatives Newt Gingrich and famed economist Arthur Laffer to debate if the rich should bear the brunt of higher taxes. For the first time ever, this stimulating debate, which will take place in front of a sold-out audience, will be available in print. With advanced countries facing overextended social services, crumbling infrastructure, and sluggish economic growth, the Munk Debate on economic inequality tackles the essential public policy issue: Should we tax the rich more?

George Papandreou

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