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arXiv cs/0502074cs.LGcs.CC
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计算模式识别的样本复杂度

On sample complexity for computational pattern recognition

Daniil Ryabko

摘要:

在模式识别问题的统计设置中,近似未知标记函数所需的示例数量在目标学习类的VC维中是线性的。在这项工作中,我们考虑的问题是否存在这样的界限,如果我们限制我们的注意力可计算的模式识别方法,假设未知的标签功能也是可计算的。我们发现,在这种情况下,一个可计算的方法来近似的标签功能所需的例子的数量不仅不是线性的,但增长速度(在VC维的类)比任何可计算的功能。预测器或目标函数没有时间或空间限制;我们考虑的唯一资源是训练样本。模式识别的任务被认为是与另一个学习问题--数据压缩--相结合的。数据压缩任务的不可能结果允许我们估计模式识别的样本复杂度。

英文摘要:

In statistical setting of the pattern recognition problem the number of examples required to approximate an unknown labelling function is linear in the VC dimension of the target learning class. In this work we consider the question whether such bounds exist if we restrict our attention to computable pattern recognition methods, assuming that the unknown labelling function is also computable. We find that in this case the number of examples required for a computable method to approximate the labelling function not only is not linear, but grows faster (in the VC dimension of the class) than any computable function. No time or space constraints are put on the predictors or target functions; the only resource we consider is the training examples. The task of pattern recognition is considered in conjunction with another learning problem -- data compression. An impossibility result for the task of data compression allows us to estimate the sample complexity for pattern recognition.

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