Antonio De Maio

Paolo Braca, Leonardo M. Millefiori, Augusto Aubry et al.

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 $\sim \exp\left(-n\,I + o(n) \right)$, 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 $\sim ζ_n \exp\left(-n\,I \right)$ are provided, thanks to the refined asymptotic derivation (often referred to as exact asymptotics), where $ζ_n$ represents the most representative sub-exponential terms of the error probabilities.

Paolo Braca, Leonardo M. Millefiori, Augusto Aubry et al.

We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is thresholded before the final binary decision is made. Based on large deviations theory, we show that under appropriate conditions the classification error probabilities vanish exponentially, as $\sim \exp\left(-n\,I + o(n) \right)$, where $I$ is the error rate and $n$ is the number of observations available for testing. We also propose two different approximations for the error probability curves, one based on a refined asymptotic formula (often referred to as exact asymptotics), and another one based on the central limit theorem. The theoretical findings are finally tested using the popular MNIST dataset.

Carmine Clemente, Luca Pallotta, Ian Proudler et al.

The capability to exploit multiple sources of information is of fundamental importance in a battlefield scenario. Information obtained from different sources, and separated in space and time, provide the opportunity to exploit diversities in order to mitigate uncertainty. For the specific challenge of Automatic Target Recognition (ATR) from radar platforms, both channel (e.g. polarization) and spatial diversity can provide useful information for such a specific and critical task. In this paper the use of pseudo-Zernike moments applied to multi-channel multi-pass data is presented exploiting diversities and invariant properties leading to high confidence ATR, small computational complexity and data transfer requirements. The effectiveness of the proposed approach, in different configurations and data source availability is demonstrated using real data.