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Presented by

Milad Sikaroudi

Introduction

Transfer learning is a line of research in machine learning which focuses on storing knowledge from one domain (source domain) to solve a similar problem in another domain (target domain). In addition to regular transfer learning, one can use "transfer metric learning" in which through utilizing similarity relationship between samples [1], [2] a more robust and discriminative data representation is formed. However, both of these kinds of techniques work insofar as the domain shift, between source and target domains, is negligible. Domain shift is defined as the deviation in the distribution of the source domain and the target domain and it would cause the DNN model to completely fail. The multi-domain learning is the solution when the assumption of "source domain and target domain comes from an almost same distribution" may not hold. There are two variants of MDL in the literature that can be confused, i.e. domain generalization, and domain adaptation; however in domain adaptation, we have access to the target domain data somehow, while that is not the case in domain generalization. This paper introduces a technique for domain generalization based on two complementary losses that regularize the semantic structure of the feature space through an episodic training scheme originally inspired by the model-agnostic meta-learning.

Previous Work

Originated from model-agnostic meta-learning (MAML), episodic training has been vastly leveraged for addressing domain generalization [1, 26, 27, 31, 12, 28, 30, 34, 35]. The method of MLDG [26] closely follows MAML in terms of back-propagating the gradients from an ordinary task loss on meta-test data, but it has its own limitation as the use of the task objective might be sub-optimal since it only uses class probabilities. Most of the works [1,31] in the literature lack notable guidance from the semantics of feature space, which contains crucial domain-independent ‘general knowledge’ that can be useful for domain generalization. The authors claim that their method is orthogonal to previous works.


Model Agnostic Meta Learning

a.k.a learning to learn is a learning paradigm in which optimal initial weights are found incrementally (episodic training) by minimizing a loss function over some similar tasks (meta-train, meta-test sets). Imagine a 4-shot 2-class image classification task as below:

p5.png

Each of the training tasks provides an optimal initial weight for the next round of the training. By considering all of these sets of updates and meta-test set, the updated weights are calculated using the below algorithm.

algo1.PNG

Method

In domain generalization, we assume that there are some domain-invariant patterns in the inputs (e.g. semantic features). These features can be extracted to learn a predictor that performs well across seen and unseen domains. This paper assumes that there are inter-class relationships across domains. In total, the MASF is composed of a task loss, global class alignment term and a local sample clustering term.

Task loss

[math] F_{\psi}: X \rightarrow Z[/math] where [math] Z [/math] is a feature space [math] T_{\theta}: X \rightarrow \mathbf {R}^{C}[/math] where [math] C [/math] is the number of classes in [math] Y [/math] Assume that [math]\hat{y}= softmax(T_{\theta}(F_{\psi}(x))) [/math]. The parameters [math] (\psi, \theta) [/math] are optimized with minimizing a cross-entropy loss namely [math] \mathbf{L}_{task} [/math] formulated as:

[math] l_{task}(y, \hat{y} = - \sum_{c}1[y=C]log(\hat{y}_{c})) [/math]

Although the task loss is a decent predictor nothing prevents the model from overfitting to the source domains and suffering from degradation on unseen test domains. So the other loss terms are responsible for this aim.

Global class alignment

Since [math] L_{task} [/math] focuses only on the dominant hard label prediction the inter-class alignment across domains is disregarded. Hence, minimising symmetrized Kullback–Leibler (KL) divergence across domains, averaged over all [math] C [/math] classes has been used:

[math] l_{global}(D_{i}, D{j}; \psi^{'}, \theta^{'}) = 1/C \sum_{c=1}^{C} 1/2[D_{KL}(s_{c}^{(i)}||s_{c}^{(j)}) + D_{KL}(s_{c}^{(j)}||s_{c}^{(i)})], [/math]

The authors stated that symmetric divergences such as Jensen–Shannon (JS) showed no significant difference with KL over symm.

Local cluster sampling

Explicit metric learning, i.e. contrastive or triplet losses, have been used to ensure that the semantic features, locally cluster according to only class labels, regardless of the domain.

[math] l_{triplet}^{a,p,n} = \sum_{i=1}^{b} \sum_{k=1}^{c-1} \sum_{\ell=1}^{c-1}\! [m\!+\!\|x_{i}\!- \!x_{k}\|_2^2 \!-\! \|x_{i}\!-\!x_{\ell}\|_2^2 ]_+, [/math]

Model agnostic learning of semantic features

These losses are used in an episodic training scheme showed in the below figure:

Experiments

The Proposed method is exploited in 4 different experiment results (2 supervised and 2 reinforcement learning experiments).

Illustrative Synthetic Experiment

In this experiment, nine domains by sampling curved deviations are synthesized from a diagonal line classifier. We treat eight of these as sources for meta-learning and hold out the last for final-test. Fig. 1 shows the nine synthetic domains which are related in form but differ in the details of their decision boundary. The results show that MLDG performs near perfect and the baseline model without considering domains overfits in the bottom left corner.

ashraf3.jpg
Figure 1: Synthetic experiment illustrating MLDG.

Object Detection

For object detection, the PACS multi-domain recognition benchmark is exploited; a dataset designed for the cross-domain recognition problems .This dataset has 7 categories (‘dog’, ‘elephant’, ‘giraffe’, ‘guitar’, ‘house’, ‘horse’ and ‘person’) and 4 domains of different stylistic depictions (‘Photo’, ‘Art painting’, ‘Cartoon’ and ‘Sketch’). The diverse depiction styles provide a significant domain gap. The Result of Current approach compared to other approaches are presented in Table 1. The baseline models are D-MTAE[5],Deep-All (Vanilla AlexNet)[2], DSN[6]and AlexNet+TF[2]. On average, the Proposed method outperforms other methods.

ashraf4.jpg
Table 1: Cross-domain recognition accuracy (Multi-class accuracy) on the PACS dataset. Best performance in bold.

Cartpole

The objective is to balance a pole upright by moving a cart. The action space is discrete – left or right. The state it has four elements: the position and velocity of cart and angular position and velocity of the pole. There are two sub-experiments designed. In the first one, domain factor is varied by changing the pole length. They simulate 9 domains with pole lengths. In the second they vary multiple domain factors – pole length and cart mass. In both experiments, we randomly choose 6 source domains for training and hold out 3 domains for (true) testing. Since the game can last forever, if the pole does not fall, we cap the maximum steps to 200. The result of both experiments are presented in Tables 2 and 3. The baseline methods are RL-All (Trains a single policy by aggregating the reward from all six source domains) RL-Random-Source (trains on a single randomly selected source domain) and RL-undo-bias: Adaptation of the (linear) undo-bias model of [7]. The proposed MLDG outperform the baselines.

ashraf5.jpg
Table 2: Cart-Pole RL. Domain generalisation performance across pole length. Average reward testing on 3 held out domains with random lengths. Upper bound: 200.
ashraf5.jpg
Table 3: Cart-Pole RL. Generalisation performance across both pole length and cart mass. Return testing on 3 held out domains with random length and mass. Upper bound: 200.

Mountain Car

In this classic RL problem, a car is positioned between two mountains, and the agent needs to drive the car so that it can hit the peak of the right mountain. The difficulty of this problem is that the car engine is not strong enough to drive up the right mountain directly. The agent has to figure out a solution of driving up the left mountain to first generate momentum before driving up the right mountain. The state observation in this game consists two elements: the position and velocity of the car. There are three available actions: drive left, do nothing, and drive right. Here the baselines are the same as Cartpole. The model doesn't outperform the RL-undo-bias but has a close return value. The results are shown in Table 4.

ashraf7.jpg
Table 4: Domain generalisation performance for mountain car. Failure rate (↓) and reward (↑) on held out testing domains with random mountain heights.

Conclusion

This paper proposed a model-agnostic approach to domain generalization unlike prior model-based domain generalisation approaches, and it scales well with number of domains and it can also be applied to different Neural Network models. Experimental evaluation shows state-of-the-art results on a recent challenging visual recognition benchmark and promising results on multiple classic RL problems.

References

[1]: Koch, Gregory, Richard Zemel, and Ruslan Salakhutdinov. "Siamese neural networks for one-shot image recognition." ICML deep learning workshop. Vol. 2. 2015.

[2]: Hoffer, Elad, and Nir Ailon. "Deep metric learning using triplet network." International Workshop on Similarity-Based Pattern Recognition. Springer, Cham, 2015.

[3]: [Muandet, Balduzzi, and Scholkopf 2013] ¨ Muandet, K.; Balduzzi, D.; and Scholkopf, B. 2013. Domain generalization via invariant feature representation. In ICML.

[4]: [Ganin and Lempitsky 2015] Ganin, Y., and Lempitsky, V. 2015. Unsupervised domain adaptation by backpropagation. In ICML.

[5]: [Ghifary et al. 2015] Ghifary, M.; Bastiaan Kleijn, W.; Zhang, M.; and Balduzzi, D. 2015. Domain generalization for object recognition with multi-task autoencoders. In ICCV.

[6]: [Bousmalis et al. 2016] Bousmalis, K.; Trigeorgis, G.; Silberman, N.; Krishnan, D.; and Erhan, D. 2016. Domain separation networks. In NIPS.

[7]: [Khosla et al. 2012] Khosla, A.; Zhou, T.; Malisiewicz, T.; Efros, A. A.; and Torralba, A. 2012. Undoing the damage of dataset bias. In ECCV.