Random Features for Large-Scale Kernel Machines · CiteArk

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Random Features for Large-Scale Kernel Machines

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作者：Ali Rahimi、Benjamin Recht

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On Adult classification, Fourier+LS trained fastest and had 14.9% test error. CVM had the lowest printed error, 14.8%, but required 73 minutes; Binning+LS had the highest printed error of the four entries.整组结论：等待复现0/8 项指标获得支持 · 0 项已有评估8项测量结果展开结果表

实验方案已生成，还没有运行记录

测量结果

已评估 0/8 项

获得支持 0有争议或冲突 0尚未评估 8

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	14.9%	—	尚未评估
	9 seconds	—	尚未评估
	15.3%	—	尚未评估
	1.5 minutes	—	尚未评估
	14.8%	—	尚未评估
	73 minutes	—	尚未评估
	15.1%	—	尚未评估
	7 minutes	—	尚未评估

打开 Claim 详情

On Census regression, Fourier features with least squares reported the lowest normalized RMS test error and the shortest training time among the four table entries.整组结论：等待复现0/8 项指标获得支持 · 0 项已有评估8项测量结果展开结果表

实验方案已生成，还没有运行记录

测量结果

已评估 0/8 项

获得支持 0有争议或冲突 0尚未评估 8

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	5%	—	尚未评估
	36 seconds	—	尚未评估
	7.5%	—	尚未评估
	19 minutes	—	尚未评估
	8.8%	—	尚未评估
	7.5 minutes	—	尚未评估
	9%	—	尚未评估
	13 minutes	—	尚未评估

打开 Claim 详情

On Forest Cover classification, Binning+LS matched libSVM's printed 2.2% test error, slightly improved on CVM's 2.3%, and trained in 25 minutes versus 7.5 hours for CVM and 44 hours for libSVM. Fourier+LS was slower than binning and had much higher error, 11.6%.整组结论：等待复现0/8 项指标获得支持 · 0 项已有评估8项测量结果展开结果表

实验方案已生成，还没有运行记录

测量结果

已评估 0/8 项

获得支持 0有争议或冲突 0尚未评估 8

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	11.6%	—	尚未评估
	71 minutes	—	尚未评估
	2.2%	—	尚未评估
	25 minutes	—	尚未评估
	2.3%	—	尚未评估
	7.5 hours	—	尚未评估
	2.2%	—	尚未评估
	44 hours	—	尚未评估

打开 Claim 详情

The authors caution that KDDCUP99 is inherently oversampled: using only 50 randomly sampled training examples, either an SVM or least squares with random features consistently produced test error on the order of 8%.整组结论：等待复现0/3 项指标获得支持 · 0 项已有评估尚未安排实验，未证实不可复现3项测量结果展开结果表

Initial preparation has not resolved this question; retain it for subsequent investigation and coverage assessment.

测量结果

已评估 0/3 项

获得支持 0有争议或冲突 0尚未评估 3

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	50 examples	—	尚未评估
	0.001%	—	尚未评估
	8%	—	尚未评估

打开 Claim 详情

On the CPU regression dataset, Fourier features with least squares had the lowest normalized RMS test error and trained faster than the binning, CVM, and ASVM entries; the exact ASVM time was second fastest but its error was highest.整组结论：等待复现0/8 项指标获得支持 · 0 项已有评估8项测量结果展开结果表

实验方案已生成，还没有运行记录

测量结果

已评估 0/8 项

获得支持 0有争议或冲突 0尚未评估 8

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	3.6%	—	尚未评估
	20 seconds	—	尚未评估
	5.3%	—	尚未评估
	3 minutes	—	尚未评估
	5.5%	—	尚未评估
	51 seconds	—	尚未评估
	11%	—	尚未评估
	31 seconds	—	尚未评估

打开 Claim 详情

On KDDCUP99, Fourier+LS and Binning+LS each reported 7.3% test error. CVM reported 6.2% error and 1.4 seconds in the original ordering, but 18% and 20 seconds after shuffling. The SVM-with-sampling entry reported 8.3% error and less than one second.整组结论：等待复现0/10 项指标获得支持 · 0 项已有评估10项测量结果展开结果表

实验方案已生成，还没有运行记录

测量结果

已评估 0/10 项

获得支持 0有争议或冲突 0尚未评估 10

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	7.3%	—	尚未评估
	1.5 minutes	—	尚未评估
	7.3%	—	尚未评估
	35 minutes	—	尚未评估
	6.2%	—	尚未评估
	1.4 seconds	—	尚未评估
	18%	—	尚未评估
	20 seconds	—	尚未评估
	8.3%	—	尚未评估
	1 seconds	—	尚未评估

打开 Claim 详情

In the Forest Cover random-binning experiment, test accuracy continued to improve as more training data were used, and doubling the training-set size reduced test error by as much as 40%.等待复现0/1 项指标获得支持 · 0 项已有评估尚未安排实验，未证实不可复现报告 40%

报告

40%

观测

—

Initial preparation has not resolved this question; retain it for subsequent investigation and coverage assessment.

测量结果

已评估 0/1 项

获得支持 0有争议或冲突 0尚未评估 1

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	40%	—	尚未评估

打开 Claim 详情

Even with the original KDDCUP99 training order, the paper reports that changing the CVM regularization parameter by 15% produced a 49% test error, indicating strong sensitivity of this comparison to the parameter setting.整组结论：等待复现0/2 项指标获得支持 · 0 项已有评估尚未安排实验，未证实不可复现2项测量结果展开结果表

Initial preparation has not resolved this question; retain it for subsequent investigation and coverage assessment.

测量结果

已评估 0/2 项

获得支持 0有争议或冲突 0尚未评估 2

保留同一结论下的完整结果组。已有评估排在前面；单项判断不替代整组结论。展开行查看条件、来源与历次证据。

每行是一项测量，分别显示论文报告、最近可用实测和累计证据状态。
指标与条件	论文报告	最近可用实测	证据判断
	15%	—	尚未评估
	49%	—	尚未评估

打开 Claim 详情

定性结论

Figure 3 reports that test error decreases quickly as the number P of random binning partitions grows, while training-plus-testing time grows slowly; the authors conclude that good performance can be obtained with a modest number of features.实验受阻，详见具体原因

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打开 Claim 详情

Across the five benchmark datasets, the authors characterize ridge regression on random features as faster than and competitively accurate with alternative large-scale kernel methods, while Table 1 shows that the advantage depends on dataset and feature family rather than holding for every individual entry.实验受阻，详见具体原因

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打开 Claim 详情

The paper proves exponential concentration for random Fourier kernel estimates. For a fixed pair, the stated tail bound is Pr(|z(x)'z(y)-k(x,y)| >= epsilon) <= 2 exp(-D epsilon^2/2). Uniformly over a compact M, Claim 1 bounds the failure probability by 2^8 (sigma_p diam(M)/epsilon)^2 exp(-D epsilon^2/[4(d+2)]), and states that constant-probability uniform error at most epsilon follows for D = Omega((d/epsilon^2) log(sigma_p diam(M)/epsilon)).实验受阻，详见具体原因

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打开 Claim 详情

The paper states that the binary random-binning estimator converges exponentially in P for a fixed pair and gives a uniform convergence guarantee in Claim 2. For compact M, the probability of uniform error at most epsilon is at least 1 - 36 d P alpha diam(M) exp(-(P epsilon^2/8 + ln(epsilon/L_k))/(d+1)).实验受阻，详见具体原因

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打开 Claim 详情

The authors report that random Fourier features perform better on tasks relying largely on interpolation, whereas random binning features perform better on memorization tasks where a standard SVM requires many support vectors; they identify Forest Cover as the most dramatic example.实验受阻，详见具体原因

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其余结论4

The paper contrasts evaluating a conventional kernel expansion, which requires O(Nd) operations and retaining much of the dataset unless sparse, with evaluating a learned linear hyperplane on the proposed random features, which it states requires O(D+d) operations and storage.随其他结论间接验证

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For a properly scaled continuous positive-definite shift-invariant kernel, drawing frequencies from the kernel's Fourier transform produces random sinusoidal features whose inner product is an unbiased estimator of the kernel; averaging D independent frequency draws lowers estimator variance.随其他结论间接验证

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Randomly shifted grids give binary features whose collision probability, and hence expected inner product, equals an eligible kernel. For separable multivariate kernels, independent one-dimensional grids multiply the collision probabilities across dimensions; averaging P independent partitions lowers variance. The appendix derives the pitch density p(delta)=delta k''(delta) for kernels expressible as convex mixtures of hat kernels.随其他结论间接验证

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The random-binning construction based on p(delta)=delta k''(delta) does not yield a random map for the Gaussian kernel because its second derivative is not everywhere positive.论文自述边界

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