No Bias Left behind: Covariate Shift Adaptation for Discriminative 3D Pose Estimation

Abstract

Abstract. Discriminative, or (structured) prediction, methods have proved effective for variety of problems in computer vision; a notable example is 3D monocular pose estimation. All methods to date, however, relied on an assumption that training (source) and test (target) data come from the same underlying joint distribution. In many real cases, including standard datasets, this assumption is flawed. In presence of training set bias, the learning results in a biased model whose performance degrades on the (target) test set. Under the assumption of covariate shift we propose an unsupervised domain adaptation approach to address this problem. The approach takes the form of training instance re-weighting, where the weights are assigned based on the ratio of training and test marginals evaluated at the samples. Learning with the resulting weighted training samples, alleviates the bias in the learned models. We show the efficacy of our approach by proposing weighted variants of Kernel Regression (KR) and Twin Gaussian Processes (TGP). We show that our weighted variants outperform their un-weighted counterparts and improve on the state-of-the-art performance in the public (HumanEva) dataset.

Domain Adaptation for Structured Regression

“…However, as we show here, the entirely unsupervised approach may be ineffective in dealing with more severe biases (e.g., those that induce structured changes between the training and test data) that make the training and test domains largely disjoint (e.g., see Figure 3 (a)). Here we expand on the findings in Yamada et al (2012), and propose a much more aggressive semi-supervised approach that is able to work even in the cases where the earlier formulation becomes less effective. It's important to note that the proposed approach is a strict generalization.…”

“…To address these issues we propose a new Semi-supervised Domain Adaptation (SSDA) approach, which is a generalization of the Unsupervised Domain Adaptation (USDA) we proposed earlier in Yamada et al (2012). Our domain adaptation method allows us to easily adapt a model learned on a (source) training set of featurepose pairs -{(x tr i , y tr i )} ntr i=1 , to a partially labeled (target) test set consisting of very few labeled examples -{(x te j , y te j )} n te j=1 (for which outputs are known) and many unlabeled samples for which outputs should be inferred -{(x te j )} nte j=n te .…”

“…Second, we apply importance weight estimation to correct for sampling bias in the augmented feature space. Finally, we use the resulting weighted augmented samples to learn a non-linear multivariate regression model in the form of Importance Weighted Twin Gaussian Processes (Yamada et al, 2012). Moreover, we propose a computationally efficient alternative to TGP (Bo and Sminchisescu, 2010), that we call direct TGP (dTGP).…”

“…The issue of dataset bias was partially addressed in our preliminary work in Yamada et al (2012). As we observe in Yamada et al (2012), the key assumption that training and test samples come from the same underlying density (i.e., (x tr i , y tr i ) ∼ p tr (x, y), (x te j , y te j ) ∼ p tr (x, y)), is often flawed, even for large datasets; this fact leads to biased models that perform sub-optimally on the test set.…”

“…As we observe in Yamada et al (2012), the key assumption that training and test samples come from the same underlying density (i.e., (x tr i , y tr i ) ∼ p tr (x, y), (x te j , y te j ) ∼ p tr (x, y)), is often flawed, even for large datasets; this fact leads to biased models that perform sub-optimally on the test set. In Yamada et al (2012), we have proposed a simple unsupervised approach for removing certain biases, most notably those that adhere to the assumption of covariate shift, where both the training and test sets are defined on the same domain (overlap) but the density of samples may be different. This setting is well suited for reducing effects of sampling bias.…”