In this work we derive a variant of the classic Glivenko-Cantelli Theorem, which asserts uniform convergence of the empirical Cumulative Distribution Function (CDF) to the CDF of the underlying distribution. Our variant allows for tighter convergence bounds for extreme values of the CDF. We apply our bound in the context of revenue learning, which is a well-studied problem in economics and algorithmic game theory. We derive sample-complexity bounds on the uniform convergence rate of the empirical revenues to the true revenues, assuming a bound on the k'th moment of the valuations, for any (possibly fractional) k 1. For uniform convergence in the limit, we give a complete characterization and a zero-one law: if the first moment of the valuations is finite, then uniform convergence almost surely occurs; conversely, if the first moment is infinite, then uniform convergence almost never occurs.
Catastrophic forgetting is a problem of neural networks that loses the information of the first task after training the second task. Here, we propose a method, i.e. incremental moment matching (IMM), to resolve this problem. IMM incrementally matches the moment of the posterior distribution of the neural network which is trained on the first and the second task, respectively. To make the search space of posterior parameter smooth, the IMM procedure is complemented by various transfer learning techniques including weight transfer, L2-norm of the old and the new parameter, and a variant of dropout with the old parameter. We analyze our approach on a variety of datasets including the MNIST, CIFAR-10, Caltech-UCSD-Birds, and Lifelog datasets.
One in four colleagues regularly cut corners, says new study Men are more likely to skip tasks than their female counterparts Younger males are the most likely contenders to be'lazy' employees However, the study notes that people may skip tasks with noble intentions such as getting the job done in the time available Younger males are the most likely contenders to be'lazy' employees New research claims that as many as one in four colleagues regularly skip tasks that are part of their job. Are YOU suffering from information overload? The power of positive thinking: Optimism can fend off... Relationship troubles? Don't tell your mates: Confiding in... Days really ARE dragging, say scientists - and in 200... Are YOU suffering from information overload? The power of positive thinking: Optimism can fend off... Relationship troubles?
Watch the moment Mark Selby beat Ronnie O'Sullivan 10-7 in a thrilling final to win the UK Championship for the second time. Highlights: Selby beats O'Sullivan in final thriller'No thoughts' - Mourinho won't comment on referee O'Sullivan makes 134 break in final fightback'It's a nice story, it's a pity we were on wrong side' Selby beats O'Sullivan in superb UK Championship final - video & report
Jamiaca's Elaine Thompson talks to BBC Sport about her 100m and 200m wins at the Rio Olympic Games and describes what it means to be the'Sprint Queen' of athletics. Win was'really hard work' - Klopp On the move: Which players could leave in January? Coach of the Year Eddie Van Hoof's life in gymnastics