At the same significance level, our approach's test power is empirically

Although the popular MNIST dataset [LeCun et al., 1994] is derived from the NIST database [Grother and Hanaoka, 1995], the precise processing steps for this derivation have been lost to time. We propose a reconstruction that is accurate enough to serve as a replacement for the MNIST dataset, with insignificant changes in accuracy. We trace each MNIST digit to its NIST source and its rich metadata such as writer identifier, partition identifier, etc. We also reconstruct the complete MNIST test set with 60,000 samples instead of the usual 10,000. Since the balance 50,000 were never distributed, they can be used to investigate the impact of twenty-five years of MNIST experiments on the reported testing performances. Our limited results unambiguously confirm the trends observed by Recht et al. [2018, 2019]: although the misclassification rates are slightly off, classifier ordering and model selection remain broadly reliable. We attribute this phenomenon to the pairing benefits of comparing classifiers on the same digits.

Thanks for the valuable comments and questions. 1) We understand the reviewer's concern that the ratio of Besides, there are various methods specially for data imbalance to alleviate the issues. Flawfinder and a commercial tool CXXX which we hide the name for legal concern. Static analyzers tend to miss most vulnerable functions and have high false positives, e.g., Cppcheck found 0 One important note is that [19] didn't To verify it, we tested trained models with different sizes of the combined dataset, i.e., 1/3, 2/3 As shown in Table 2, both accuracy and F1 increases as the data volume increases.

One approach to improving the running time of kernel-based methods is to build a small sketch of the kernel matrix and use it in lieu of the full matrix in the machine learning task of interest. Here, we describe a version of this approach that comes with running time guarantees as well as improved guarantees on its statistical performance. By extending the notion of statistical leverage scores to the setting of kernel ridge regression, we are able to identify a sampling distribution that reduces the size of the sketch (i.e., the required number of columns to be sampled) to the effective dimensionality of the problem. This latter quantity is often much smaller than previous bounds that depend on the maximal degrees of freedom. We give an empirical evidence supporting this fact. Our second contribution is to present a fast algorithm to quickly compute coarse approximations to these scores in time linear in the number of samples.

A.2 Proof of Theorem 1 We restate the theorem for completeness: Theorem 1. Assume Any ODE's solution, if it exists and converges, converges to an's estimate of the conditional effect is We now bound the remaining term. 's computation of the surrogate intervention involved Thus, such error does not accumulate even with large step sizes. Theorem 4. Effect Connectivity is necessary for nonparametric effect estimation in Let Effect Connectivity be violated, i.e. there exists a Thus, nonparametric effect estimation is impossible. The effect threshold here is 0.1.Figure 7: True positive vs. False negative rate as we vary the threshold on average

Causal inference relies on two fundamental assumptions: ignorability and positivity .