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- W4288043108 abstract "We study the performance -- and specifically the rate at which the error probability converges to zero -- of Machine Learning (ML) classification techniques. Leveraging the theory of large deviations, we provide the mathematical conditions for a ML classifier to exhibit error probabilities that vanish exponentially, say $sim expleft(-n,I + o(n) right)$, where $n$ is the number of informative observations available for testing (or another relevant parameter, such as the size of the target in an image) and $I$ is the error rate. Such conditions depend on the Fenchel-Legendre transform of the cumulant-generating function of the Data-Driven Decision Function (D3F, i.e., what is thresholded before the final binary decision is made) learned in the training phase. As such, the D3F and, consequently, the related error rate $I$, depend on the given training set, which is assumed of finite size. Interestingly, these conditions can be verified and tested numerically exploiting the available dataset, or a synthetic dataset, generated according to the available information on the underlying statistical model. In other words, the classification error probability convergence to zero and its rate can be computed on a portion of the dataset available for training. Coherently with the large deviations theory, we can also establish the convergence, for $n$ large enough, of the normalized D3F statistic to a Gaussian distribution. This property is exploited to set a desired asymptotic false alarm probability, which empirically turns out to be accurate even for quite realistic values of $n$. Furthermore, approximate error probability curves $sim zeta_n expleft(-n,I right)$ are provided, thanks to the refined asymptotic derivation (often referred to as exact asymptotics), where $zeta_n$ represents the most representative sub-exponential terms of the error probabilities." @default.
- W4288043108 created "2022-07-27" @default.
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- W4288043108 date "2022-07-22" @default.
- W4288043108 modified "2023-10-17" @default.
- W4288043108 title "Statistical Hypothesis Testing Based on Machine Learning: Large Deviations Analysis" @default.
- W4288043108 doi "https://doi.org/10.48550/arxiv.2207.10939" @default.
- W4288043108 hasPublicationYear "2022" @default.
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