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Highly overparametrized neural networks can display curiously strong generalization performance - a phenomenon that has recently garnered a wealth of theoretical and empirical research in order to better understand it. In contrast to most previous work, which typically considers the performance as a function of the model size, in this paper we empirically study the generalization performance as the size of the training set varies over multiple orders of magnitude. These systematic experiments lead to some interesting and potentially very useful observations; perhaps most notably that training on smaller subsets of the data can lead to more reliable model selection decisions whilst simultaneously enjoying smaller computational costs. Our experiments furthermore allow us to estimate Minimum Description Lengths for common datasets given modern neural network architectures, thereby paving the way for principled model selection taking into account Occams-razor.
Bin Packing problems have been widely studied because of their broad applications in different domains. Known as a set of NP-hard problems, they have different vari- ations and many heuristics have been proposed for obtaining approximate solutions. S
We are surrounded by huge amounts of large-scale high dimensional data. It is desirable to reduce the dimensionality of data for many learning tasks due to the curse of dimensionality. Feature selection has shown its effectiveness in many application
Most of existing clustering algorithms are proposed without considering the selection bias in data. In many real applications, however, one cannot guarantee the data is unbiased. Selection bias might bring the unexpected correlation between features
In Big data era, information integration often requires abundant data extracted from massive data sources. Due to a large number of data sources, data source selection plays a crucial role in information integration, since it is costly and even impos
When applying Value at Risk (VaR) procedures to specific positions or portfolios, we often focus on developing procedures only for the specific assets in the portfolio. However, since this small portfolio risk analysis ignores information from assets