In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for highly accurate classification algorithms, in particular when dealing with class-imbalanced data. To correct this bias, the algorithm's classification error rates have to be estimated. In this estimation, two issues arise when applying existing bias correction methods. First, inaccuracies in estimating classification error rates have to be taken into account. Second, impermissible estimates, such as a negative estimate for a positive value, have to be dismissed. We show that both issues are relevant in applications where the true labels are known only for a small set of data points. We propose a novel bias correction method using Bayesian inference. The novelty of our method is that it imposes constraints on the model parameters. We show that our method solves the problem of biased classification-based aggregates as well as the two issues above, in the general setting of multi-class classification. In the empirical evaluation, using a binary classifier on a real-world dataset of company tax returns, we show that our method outperforms existing methods in terms of mean squared error.
@cite_14: Publications in official statistics are increasingly based on a combination of sources. Although combining data sources may result in nearly complete coverage of the target population, the outcomes are not error free. Estimating the effect of nonsampling errors on the accuracy of mixed-source statistics is crucial for decision making, but it is not straightforward. Here we simulate the effect of classification errors on the accuracy of turnover-level estimates in car-trade industries. We combine an audit sample, the dynamics in the business register, and expert knowledge to estimate a transition matrix of classification-error probabilities. Bias and variance of the turnover estimates caused by classification errors are estimated by a bootstrap resampling approach. In addition, we study the extent to which manual selective editing at micro level can improve the accuracy. Our analyses reveal which industries do not meet preset quality criteria. Surprisingly, more selective editing can result in less accurate estimates for specific industries, and a fixed allocation of editing effort over industries is more effective than an allocation in proportion with the accuracy and population size of each industry. We discuss how to develop a practical method that can be implemented in production to estimate the accuracy of register-based estimates.
We partly adopt the notation from @cite_14 to formulate our problem statement. Consider a set @math of objects @math . Each object @math belongs to a class @math . The finite, ordered set of classes is denoted by @math and is of size @math . In addition, each object is attributed with a continuous variable @math of interest. We introduce the @math of dimension @math given by @math , where @math denotes the indicator function. The @math , where @math is an @math -vector of ones, counts the number of occurrences of the classes @math in the population. That is, @math equals the number of @math for which @math . The @math of length @math is given by @math for @math .