排序是计算机内经常进行的一种操作,其目的是将一组“无序”的记录序列调整为“有序”的记录序列。分内部排序和外部排序。若整个排序过程不需要访问外存便能完成,则称此类排序问题为内部排序。反之,若参加排序的记录数量很大,整个序列的排序过程不可能在内存中完成,则称此类排序问题为外部排序。内部排序的过程是一个逐步扩大记录的有序序列长度的过程。

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https://arxiv.org/abs/2002.12312

在这篇论文中,我们讨论了协同过滤和排名的一些最新进展。第一章简要介绍了协同过滤与排名的历史与现状;第二章首先讨论了图信息的点态协同过滤问题,以及我们提出的新方法如何对深度图信息进行编码,这有助于现有的四种图信息协同过滤算法;第三章介绍了协同排序的配对方法,以及如何将算法加速到接近线性的时间复杂度;第4章是关于新的列表方法的协作排名,以及如何更好的选择列表方法的损失显式和隐式反馈超过点和两两损失;第5章是关于我们提出的新的正则化技术——随机共享嵌入(SSE),以及它在6个不同的任务(包括推荐和自然语言处理)中的理论有效性和经验有效性;第6章是我们如何在SSE的帮助下,为最先进的序列推荐模型引入个性化,这对于防止我们的个性化模型对训练数据的过度拟合起到了重要的作用;第7章,我们总结了目前所取得的成果,并展望了未来的发展方向;第八章是所有章节的附录。

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We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove that it encompasses several important subclasses, such as functions of bounded submodularity ratio, $\alpha$-augmentable functions, and weighted rank functions of an independence system of bounded rank quotient - as well as additional objective functions for which the greedy algorithm yields an approximation. For this general class of functions, we show a tight bound of $\frac{\alpha}{\gamma}\cdot\frac{\mathrm{e}^\alpha}{\mathrm{e}^\alpha-1}$ on the approximation ratio of the greedy algorithm that tightly interpolates between bounds from the literature for functions of bounded submodularity ratio and for $\alpha$-augmentable functions. In paritcular, as a by-product, we close a gap left in [Math.Prog., 2020] by obtaining a tight lower bound for $\alpha$-augmentable functions for all $\alpha\geq1$. For weighted rank functions of independence systems, our tight bound becomes $\frac{\alpha}{\gamma}$, which recovers the known bound of $1/q$ for independence systems of rank quotient at least $q$.

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We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove that it encompasses several important subclasses, such as functions of bounded submodularity ratio, $\alpha$-augmentable functions, and weighted rank functions of an independence system of bounded rank quotient - as well as additional objective functions for which the greedy algorithm yields an approximation. For this general class of functions, we show a tight bound of $\frac{\alpha}{\gamma}\cdot\frac{\mathrm{e}^\alpha}{\mathrm{e}^\alpha-1}$ on the approximation ratio of the greedy algorithm that tightly interpolates between bounds from the literature for functions of bounded submodularity ratio and for $\alpha$-augmentable functions. In paritcular, as a by-product, we close a gap left in [Math.Prog., 2020] by obtaining a tight lower bound for $\alpha$-augmentable functions for all $\alpha\geq1$. For weighted rank functions of independence systems, our tight bound becomes $\frac{\alpha}{\gamma}$, which recovers the known bound of $1/q$ for independence systems of rank quotient at least $q$.

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