Multi-Task Multi-Sample Learning
Yusuf Aytar,Andrew Zisserman +1 more
- 06 Sep 2014
- pp 78-91
TL;DR: A multi-sample learning (MSL) model is developed which enables joint regularization of the E-SVMs without any additional cost over the original ensemble learning.
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Abstract: In the exemplar SVM (E-SVM) approach of Malisiewicz et al., ICCV 2011, an ensemble of SVMs is learnt, with each SVM trained independently using only a single positive sample and all negative samples for the class. In this paper we develop a multi-sample learning (MSL) model which enables joint regularization of the E-SVMs without any additional cost over the original ensemble learning. The advantage of the MSL model is that the degree of sharing between positive samples can be controlled, such that the classification performance of either an ensemble of E-SVMs (sample independence) or a standard SVM (all positive samples used) is reproduced. However, between these two limits the model can exceed the performance of either. This MSL framework is inspired by multi-task learning approaches.
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Figures
Fig. 3. Different models of joint regularization can be explored via regularization graphs. Each node represents a sample specific classifier and the links represent the weights of the joint regularization terms ||wi − wj ||2 ∀i, j This paper particularly explores a type of fully connected regularization displayed in (a) with different levels of uniform weights on the edges which can be thought as springs. As the weight of edges increase classifiers are all forced to be as close as possible which in the limit reaches to a single class SVM, or if the weights become looser the classifiers become independent and in the limit reaches to the ensemble of exemplar svms displayed in (d). However, in between these two ends there are many other structural choices of the regularization graph to be explored as displayed in (b) and (c). 
Table 2. The multi-class classification accuracy comparison of methods on Animal dataset. 
Fig. 2. The effect of the hyperparameter β in MSL on the Animal dataset. Note the increase in performance before reaching to the single class SVM limit (i.e. β = 1e+ 2). See caption of figure 1. 
Table 3. Average Precision results on side-facing category detection experiments. Evaluations are perfomed on all positive (side-facing) instances of the particular class and 20K negative instances extracted from PASCAL VOC 2007 test set. ![Table 1. The multi-class classification accuracy comparison of methods on MNIST dataset. Note that MSL with 100 positive samples per class (MNIST-100) performs as well as SVM with 1000 positive samples per class (MNIST-1K). Note, the first row shows the individual task learning results from [16], and the MTL result in the first row is the learned grouping MTL of [16].](/figures/table-1-the-multi-class-classification-accuracy-comparison-31llrgh1.png)
Table 1. The multi-class classification accuracy comparison of methods on MNIST dataset. Note that MSL with 100 positive samples per class (MNIST-100) performs as well as SVM with 1000 positive samples per class (MNIST-1K). Note, the first row shows the individual task learning results from [16], and the MTL result in the first row is the learned grouping MTL of [16]. 
Fig. 1. The effect of the hyperparameter β in MSL on the MNIST dataset. The hyperparameter λ is fixed and the performance on both validation and test sets are shown. The multi-class classification accuracy as a function of the hyperparameter β is displayed. With a large enough β, the MSL gives the same result as the single class SVM. Moving towards the single class SVM (from left to right) the performance increases and then decreases back. Thus for an optimum β MSL outperforms both ensemble of E-SVMs and single class SVM.
![Table 1. The multi-class classification accuracy comparison of methods on MNIST dataset. Note that MSL with 100 positive samples per class (MNIST-100) performs as well as SVM with 1000 positive samples per class (MNIST-1K). Note, the first row shows the individual task learning results from [16], and the MTL result in the first row is the learned grouping MTL of [16].](/figures/table-1-the-multi-class-classification-accuracy-comparison-31llrgh1.webp)
Citations
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