arXiv 1607.045792016-07cs.LGmath.OCstat.ML

基于对偶嵌入的条件分布学习

Learning from Conditional Distributions via Dual Embeddings

Georgia Institute of Technology（佐治亚理工学院）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）

Bo Dai, Niao He, Yunpeng Pan, Byron Boots, Le Song

备注：: 24 pages, 11 figures

摘要：

许多机器学习任务，如强化学习中的不变性学习和策略评估，可以被描述为从条件分布学习的问题。在这样的问题中，每个样本$x$本身与由样本$\{z_i\}_{i=1}^M$表示的条件分布$p(z|x)$相关联，并且目标是学习将这些条件分布链接到目标值$y$的函数$f$。当我们只有有限的样本或在极端情况下每个条件分布只有一个样本时，这些学习问题变得非常具有挑战性。常用的方法要么假设$z$独立于$x$，要么需要来自每个条件分布的压倒性的大样本。为了解决这些挑战，我们提出了一种新的方法，它采用了一个新的最小-最大重新制定的学习条件分布问题。通过这种新的重新表述，我们只需要处理联合分发$p(z,x)$。我们还设计了一个有效的学习算法，Embedding-SGD，并建立了理论样本复杂度的问题。最后，我们在合成和真实世界数据集上的数值实验表明，该方法可以显着改善现有的算法。

英文摘要：

Many machine learning tasks, such as learning with invariance and policy evaluation in reinforcement learning, can be characterized as problems of learning from conditional distributions. In such problems, each sample $x$ itself is associated with a conditional distribution $p(z|x)$ represented by samples $\{z_i\}_{i=1}^M$, and the goal is to learn a function $f$ that links these conditional distributions to target values $y$. These learning problems become very challenging when we only have limited samples or in the extreme case only one sample from each conditional distribution. Commonly used approaches either assume that $z$ is independent of $x$, or require an overwhelmingly large samples from each conditional distribution. To address these challenges, we propose a novel approach which employs a new min-max reformulation of the learning from conditional distribution problem. With such new reformulation, we only need to deal with the joint distribution $p(z,x)$. We also design an efficient learning algorithm, Embedding-SGD, and establish theoretical sample complexity for such problems. Finally, our numerical experiments on both synthetic and real-world datasets show that the proposed approach can significantly improve over the existing algorithms.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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