Classification with Noisy Labels by Importance Reweighting

Abstract

Abstract-In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability ρ ∈ [0, 0.5), and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate ρ. We show that the rate is upper bounded by the conditional probability P (Ŷ |X) of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods.

Addressing Complexities of Machine Learning in Big Data: Principles, Trends and Challenges from Systematical Perspectives

“…Using a probabilistic model for embedded label noise, algorithms such as robust logistic regression [116] [117] have been shown to be more robust to such noise than the originals. Among these algorithms, surrogate loss functions are widely studied [118] [119]. The core idea of these algorithms is to revise the bias in the risk function using importance reweighting…”

“…, ^ * (ℎ( ), ^) (18) The optimality and convergence of reweighting have been demonstrated in [118] [119]. The critical difficulty in this approach lies in estimating the hidden parameters in the probabilistic noise model or the revision coefficients in the objective function.…”

Pseudo-marginal Markov Chain Monte Carlo for Nonnegative Matrix Factorization

“…A sample is then drawn from the distribution p(dθ M |X, M), which is approximately distributed according to the posterior p(θ M |X, M). Note that the importance sampling has also been applied to classification problems [11].…”

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“…However, face recognition still faces a lot of challenges such as the various lightings, facial expressions, poses and environments [10,13,14,33,35,42,54,57,65,68]. In order to overcome these challenges, a lot of representation-based classification methods (RBCMs) [15,29,31,37,52,53,63,64,68] are proposed such as SRC [52], collaborative representation classification (CRC) [63], two-phase test sample representation (TPTSR) [53], linear regression classification (LRC) [37], feature space representation method [61], an improvement to the nearest neighbor (INNC) classification [55], etc. SRC tries to represent the test sample by an optimal linear combination of the training samples.…”