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摘要翻译：
广义线性模型（GLMs）和单指标模型（SIMs）提供了线性回归的强有力的推广，其中目标变量被假定为线性预测器的一维函数（可能未知）。一般来说，这些问题需要非凸估计过程，在实践中，迭代局部搜索启发式算法经常被使用。Kalai和Sastry(2009)最近提供了第一个可证明的学习SIMs和GLMs的有效方法，假设数据实际上是在GLM下产生的，并且是在一定的单调性和Lipschitz约束下产生的。然而，为了获得可证明的性能，该方法要求每次迭代都有一个新的样本。在本文中，我们提供了学习GLMs和SIMs的算法，这些算法在计算和统计上都是有效的。我们还提供了一个实证研究，证明了它们在实践中的可行性。
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英文标题：
《Efficient Learning of Generalized Linear and Single Index Models with
Isotonic Regression》
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作者：
Sham Kakade and Adam Tauman Kalai and Varun Kanade and Ohad Shamir
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最新提交年份：
2011
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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一级分类：Computer Science 计算机科学
二级分类：Machine Learning 机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Statistics 统计学
二级分类：Machine Learning 机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
Generalized Linear Models (GLMs) and Single Index Models (SIMs) provide powerful generalizations of linear regression, where the target variable is assumed to be a (possibly unknown) 1-dimensional function of a linear predictor. In general, these problems entail non-convex estimation procedures, and, in practice, iterative local search heuristics are often used. Kalai and Sastry (2009) recently provided the first provably efficient method for learning SIMs and GLMs, under the assumptions that the data are in fact generated under a GLM and under certain monotonicity and Lipschitz constraints. However, to obtain provable performance, the method requires a fresh sample every iteration. In this paper, we provide algorithms for learning GLMs and SIMs, which are both computationally and statistically efficient. We also provide an empirical study, demonstrating their feasibility in practice.
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PDF链接：
https://arxiv.org/pdf/1104.2018
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