Novel tight classification error bounds under mismatch conditions based on f-Divergence

Abstract

By default, statistical classification/multiple hypothesis testing is faced with the model mismatch introduced by replacing the true distributions in Bayes decision rule by model distributions estimated on training samples. Although a large number of statistical measures exist w.r.t. to the mismatch introduced, these works rarely relate to the mismatch in accuracy, i.e. the difference between model error and Bayes error. In this work, the accuracy mismatch between the ideal Bayes decision rule/Bayes test and a mismatched decision rule in statistical classification/multiple hypothesis testing is investigated explicitly. A proof of a novel generalized tight statistical bound on the accuracy mismatch is presented. This result is compared to existing statistical bounds related to the total variational distance that can be extended to bounds of the accuracy mismatch. The analytic results are supported by distribution simulations.

Mismatch in the classification of linear subspaces: Upper bound to the probability of error

“…This characterization leads to sufficient conditions for perfect classification in the low-noise regime, that can be expressed via the principal angles associated with the subspaces of the true or mismatched model as well as the dimension of the overlap between such subspaces. In contrast, the bound proposed in [10] does not exhibit a phase transition in the lownoise regime. Furthermore, the bound in [10] is a function of the differences between the true and the mismatched models of each class and neglects the interplay between the mismatched models of different classes.…”

“…In contrast, the bound proposed in [10] does not exhibit a phase transition in the lownoise regime. Furthermore, the bound in [10] is a function of the differences between the true and the mismatched models of each class and neglects the interplay between the mismatched models of different classes. On the other hand, the proposed bound also captures the interplay between the geometry of the mismatched models of different classes.…”

“…Signal classification and estimation using mismatched models is also considered in [9]- [11]. For example, [10] expresses performance bounds via the f -Divergence between the true and mismatched source distributions, and [11] expresses the mean-squared error penalty in terms of the derivative of the KL distance between the true and the mismatched distributions with respect to the decoder signal to noise ration (SNR).…”

Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification

“…In particular, the work in [23] is closely related to our work in the sense that it also establishes bounds to the error probability in the presence of mismatch. The bounds presented in [23] are more general since they do not assume a particular form of probability density functions. Our work, on the other hand, leverages the assumption that signals are contained in linear subspaces in order to derive an upper bound that sharply predicts the presence or absence of an error floor.…”

“…Our work, on the other hand, leverages the assumption that signals are contained in linear subspaces in order to derive an upper bound that sharply predicts the presence or absence of an error floor. The bounds in [23] fail to capture the presence or absence of an error floor when specialized to the proposed signal model.…”