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首页> 外文期刊>Machine Learning >Improved MCMC sampling methods for estimating weighted sums in Winnow with application to DNF learning
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Improved MCMC sampling methods for estimating weighted sums in Winnow with application to DNF learning

机译：改进的MCMC采样方法，用于估计Winnow中的加权和，并将其应用于DNF学习

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摘要

A Markov chain Monte Carlo method has previously been introduced to estimate weighted sums in multiplicative weight update algorithms when the number of inputs is exponential. However, the original algorithm still required extensive simulation of the Markov chain in order to get accurate estimates of the weighted sums. We propose an optimized version of the original algorithm that produces exactly the same classifications while often using fewer Markov chain simulations. We also apply three other sampling techniques and empirically compare them with the original Metropolis sampler to determine how effective each is in drawing good samples in the least amount of time, in terms of accuracy of weighted sum estimates and in terms of Winnow's prediction accuracy. We found that two other samplers (Gibbs and Metropolized Gibbs) were slightly better than Metropolis in their estimates of the weighted sums. For prediction errors, there is little difference between any pair of MCMC techniques we tested. Also, on the data sets we tested, we discovered that all approximations of Winnow have no disadvantage when compared to brute force Winnow (where weighted sums are exactly computed), so generalization accuracy is not compromised by our approximation. This is true even when very small sample sizes and mixing times are used.
机译：当输入数量为指数时，先前已引入马尔可夫链蒙特卡罗方法来估计乘法加权更新算法中的加权和。然而，原始算法仍然需要对马尔可夫链进行广泛的仿真，以便获得加权和的准确估计。我们提出了原始算法的优化版本，该算法可产生完全相同的分类，同时通常使用较少的马尔可夫链模拟。我们还应用了其他三种采样技术，并与原始的Metropolis采样器进行了经验比较，以确定每种方法在最短时间内提取加权样本的有效性，无论是加权总和估计的准确性还是Winnow的预测准确性。我们发现另外两个采样器（Gibbs和Metropolized Gibbs）在加权总和的估计上稍好于Metropolis。对于预测误差，我们测试的任何一对MCMC技术之间几乎没有差异。此外，在我们测试的数据集上，我们发现与强力Winnow（精确计算加权总和）相比，Winnow的所有近似值都没有缺点，因此近似值不会影响泛化精度。即使使用很小的样品量和混合时间也是如此。

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