Universal Physiological Representation Learning with Soft-Disentangled Rateless Autoencoders

In [13] and [12], disentangled feature extraction method was proposed to improve subject-transfer performance. As shown in Fig. 2(a), the features $z$ are divided into two parts of $z_a$ and $z_n$, which are intended to conceal subject-invariant and subject-specific information, respectively. Despite the gain of the disentangled method, determining the split sizes of $z_a$ and $z_n$ is still challenging. In this paper, we extend the method with soft disentanglement motivated by RAE as shown in Fig. 2(b), to mitigate the sensitivity of the splitting parameter.

For implementing the soft-disentangled adversarial transfer learning, encoder output $z$ is forwarded into two additional units, the adversary network and nuisance network, with different dropout rate distributions. As illustrated in Fig. 2(b), the dropout rate distributions of representation $z$ to the adversary network and nuisance network are designed as $p_a\left(d\right)$ and $p_n\left(d\right)=1-p_a\left(d\right)$, respectively. Complete latent representation $z$ is further fed into the decoder $h(z,s;\eta )$ without any dropout. Through the stochastic disentangling, the representations $z$ are re-organized into two sub-parts related to task and subject respectively: upper feature units with lower $p_a\left(d\right)$ (higher $p_n\left(d\right)$) to adversary network aim to conceal more subject information regarding $s$, while lower units with lower $p_n\left(d\right)$ (higher $p_a\left(d\right)$) to nuisance network are designed to include more subject-related features. By dissociating the nuisance variable from task-related feature in a more clear way, the model is extrapolated into a broader domain of subjects and tasks. For the input data from an unknown user, task-related features with lower $p_a\left(d\right)$ would be incorporated into the final prediction; simultaneously, the biological characteristics which are similar to known subjects could also be projected to representations with lower $p_n\left(d\right)$ as a reference.

In addition to the training of encoder-decoder pair, at every optimization iteration, the parameters of adversary and nuisance networks are learned towards maximizing the likelihoods $q_{\varphi }\left(s|z,p_a\right)$ and $q_{\psi }\left(s|z,p_n\right)$ respectively to estimate the ID $s$ among $S$ subjects. The parameter updates and optimizations among the encoder-decoder pair, adversary network and nuisance network are performed alternatingly by stochastic gradient descent, where the two adversarial discriminators are separately trained to minimize their corresponding cross-entropy losses.

For the particular case when the dropout rate $p_a\left(d\right)=1-p_n\left(d\right)$ is either $0$ or $1$ for each feature node $d$, i.e., when the feature output of node $d$ is either input to the adversary network only or the nuisance network only along with decoder, the representation $z$ is hard split into two sub-parts $z_a$ and $z_n$, corresponding respectively to the adversary and nuisance blocks, as shown in Fig. 2(a). The sub-part feature $z_a$ with $p_a\left(d\right)=0$ and $p_n\left(d\right)=1$ for $d\in z_a$ aims at preserving task-related feature information, while subject-related feature would be embedded in representation $z_n$ with $p_a\left(d\right)=1$ and $p_n\left(d\right)=0$ for $d\in z_n$. In this case, it reduces to a regular disentangled adversarial cAE structure (DA-cAE) with adversary and nuisance networks attached but no rateless property, as introduced in [13, 12].

For the more generic case of soft-split representation $z$, dropout rates to adversary and nuisance blocks are arbitrary, provided that they satisfy $p_a\left(d\right)=1-p_n\left(d\right)\in [0,1]$ for each feature node $d\in \{1,2,\dots ,D\}$. Therefore, the bottleneck architecture $z$ is soft split into adversary and nuisance counterparts stochastically according to the distribution $p_a\left(d\right)$ and $p_n\left(d\right)=1-p_a\left(d\right)$, respectively, as depicted in Fig. 2(b). This conditional RAE with soft-disentangled adversarial structure (DA-cRAE) can partly resolve the issue of hard split which requires pre-determined dimensionality for two disentangled latent vectors, whereas the proposed method can automatically consider different ratio of hard splits in a non-deterministic ensemble manner.

The utilized model structure for experiment evaluations is presented in Table 1, where representation $z$ has a dimensionality of $D$. The adversary and nuisance networks have a same input dimension $D$ from the latent representation and output dimension $S$ for the classification of subject IDs. We note that we did not observe significant improvements by deepening the network or altering the number of units for our physiological biosignal dataset under test. To assess the robustness of the proposed soft-disentangled adversarial feature encoder, we implemented various classifiers for evluating the final task classification, including MLP, nearest neighbors, decision tree, linear discriminant analysis (LDA), and logistic regression classifiers with $L$ output dimensions for task classification.

Representation $z$ with dimension $D=15$ is fed into adversary network and nuisance network respectively with dropout rates $p_a\left(d\right)$ and $p_n\left(d\right)$. For the soft-split case in Section 2.4.2, we take $p_a\left(d\right)=\left(\right(d-1\left)/\right(D-1){)}^{\alpha }$ and $p_n\left(d\right)=1-p_a\left(d\right)$ for $d\in \{1,2,\dots ,D\}$, where parameter $\alpha$ can adjust the ascent speed of dropout rate $p_a\left(d\right)$ along $d$, and we take $\alpha =3$ in the experimental assessments. In the implementation for hard split of Section 2.4.1, we fix the ratio of dimensions between $z_a$ and $z_n$ to $2:1$.

We denote AE as a baseline architecture of a regular encoder-decoder pair for feature extraction as presented in [25] and [26], whose decoder is $h(z;\eta )$ without adversarial disentangling units, and cAE as a conditional AE feature extractor with decoder $h(z,s;\eta )$ conditioned on $s$ as described in [28]. A-cAE and A-cRAE denote the cAE models with the aforementioned hard-split and soft-split bottleneck features respectively attached to the adversary network only. D-cAE and D-cRAE represent cAE with hard-split and soft-split bottleneck variables respectively linked to the nuisance network only. DA-cAE and DA-cRAE specify hard-split and soft-split representations connected to both adversary and nuisance networks respectively with decoder conditioned on $s$. Note that the A-cAE resembles to the traditional adversarial learning methods presented in [6, 27, 24, 17] where only one adversarial unit is adopted.

Accuracies of transfer analysis across $20$ held-out subjects based on different feature encoders and classifiers are presented in Fig. 3, where AE, cAE, A-cAE, D-cAE, DA-cAE, A-cRAE, D-cRAE, and DA-cRAE as defined in Section 2.5.3 were trained and compared. Corresponding parameter settings for each case in Fig. 3 are displayed in Table 2, which were selected and optimized through the aforementioned parameter optimization procedure. The model architecture is as shown in Table 1, where feature dimension is $D=15$.

As shown in Fig. 3 and Table 2, first we observe that simply feeding the decoder an extra conditional input $s$ could yield slightly better classification performance when comparing cAE with AE. Furthermore, we notice accuracy improvements from A-cAE and D-cAE to cAE, demonstrating that more cross-subject features observed in the hard-split representation $z_a$ lead to better identification of $y$. In addition, DA-cAE realizes further accuracy improvements with both adversary and nuisance networks compared to individual regularization approaches A-cAE and D-cAE. Under the disentangled adversarial transfer learning framework, our feature extractor results in lower variation of performances across all task classifiers and all subjects universally. More importantly, the soft-split RAE structures of A-cRAE, D-cRAE and DA-cRAE bring even more accuracy gain compared to the hard-split cases of A-cAE, D-cAE and DA-cAE. For the hard-split case, determining the split ratio of dimensions between subject-related and task-specified features is difficult since the representation nature is still unkown. However, the rateless property enables the encoder-decoder pair to seamlessly adjust dimensionalities of subject-related and task-specified features, and employs a smooth transition between the two stochastic counterparts by a probabilistic bottleneck representation, even though the underlying nature of the bottleneck is still vague. In general, the disentangled adversarial models of DA-cRAE with both adversary and nuisance networks attached to conditional decoder lead to significant improvements in average accuracy up to $11.6\%$ (e.g., the MLP classifier in Table 2) with respect to the non-adversarial baseline AE. Furthermore, as observed in Fig. 3, the cross-validation accuracies of the worst cases are also significantly improved, indicating that the proposed transfer learning architecture presents higher stability to a wider range of unknown individuals through reorganizing the subject- and task-relevant representations from the end of feature extractor.

We take the MLP classifier as an example to particularly illustrate the impact of disentangled adversarial RAE. As presented in Table 3, the baseline models of AE and cAE were first assessed with ${\lambda }_A={\lambda }_N=0$ while training the MLP discriminative classifier. Then the D-cRAE was evaluated with ${\lambda }_N\in \{0,0.005,0.01,0.05,0.2,0.5\}$ and ${\lambda }_A=0$. Finally, we froze ${\lambda }_N=0.05$ to observe the representation learning capability of the complete soft-disentangled adversarial transfer learning model DA-cRAE with different choices of ${\lambda }_A\in \{0,0.01,0.05,0.1,0.2,0.5\}$. For each parameter selection, the average accuracy of the MLP task classifier for identifying $4$ stress levels is shown in Table 3, along with the discriminator accuracies of the adversary and nuisance blocks for decoding $20$-class ID. With an increasing accuracy of MLP task classifier, stress levels are better discriminated; with a growing accuracy of nuisance network, more person-discriminative features are preserved in the nuisance counterpart; and with a decreasing accuracy of adversary network, more task-specific information are inherent in the adversary counterpart. We observe that the nuisance network produces higher accuracy with increasing ${\lambda }_N$, where ${\lambda }_N=0.05$ particularly results in the better performance on task classification. Furthermore, with fixed ${\lambda }_N=0.05$, growing ${\lambda }_A$ leads to lower accuracy of adversary network, and thus imposes less extraction of subject features but more task-related information on the adversary counterpart.

Other than the adversarial parameters ${\lambda }_A$ and ${\lambda }_N$, we further inspect the impact of different feature dimensions $D$ on the performance of the proposed DA-cRAE model. We trained MLP classifiers with the DA-cRAE feature extractor and its optimized parameters as given in Table 2 (${\lambda }_A=0.5$ and ${\lambda }_N=0.05$), using various feature dimensions $D\in \{3,5,\cdots ,25\}$. Corresponding cross-validation accuracies for $20$ held-out subjects are shown as a function of $D$ in Fig. 4, where the average accuracy for each $D$ is also marked. The same assessments on $D$ were also applied to baseline AE feature extractor, and we present its curve of average accuracies in Fig. 4 as a reference to compare with DA-cRAE. It is verified that the proposed DA-cRAE consistently outperforms the baseline AE and $D=15$ latent dimensionality was sufficient for the problem. We observe that after a specific value of dimension $D$, the performance of DA-cRAE remains relatively stable with varying $D$ value compared to AE. On one hand, when the feature dimension is large enough to carry necessary information for the classification task, higher $D$ value might not be able to bring more benefits when extracting features; on the other hand, the rateless property of DA-cRAE resolves the entanglement between task-related and subject-discriminative information and exploits the latent features in a more efficient manner, thus leading to a stronger robustness on the variance of latent representation dimensionality.

In order to evaluate the robustness of our transfer learning method on data with smaller sizes, we investigated the performance of the proposed model when we reduced the available training data size from $100$% to $50$%, $25$%, or $10$%. Corresponding classification accuracies as a function of training data size are shown in Fig. 5. Here we consider the MLP classifier as the same example of Table 2, to make comparisons among DA-cRAE (${\lambda }_A=0.5$ and ${\lambda }_N=0.05$), DA-cAE (${\lambda }_A=0.01$ and ${\lambda }_N=0.005$), cAE and AE (${\lambda }_A={\lambda }_N=0$). From Fig. 5 we observe that DA-cRAE still performs best regardless of the amount of available training data. Even with $10$% data only, there is no significant drawback of DA-cRAE and DA-cAE compared to non-adversarial methods, showing the transfer learning ability of our method to the size deficiency of physiological data. Note that with more available training data, even better performance is expected to be implemented by the model.

In addition, training convergence curves for a specific DA-cRAE (${\lambda }_A=0.5$ and ${\lambda }_N=0.05$) case with different training data sizes are presented in Fig. 6. When using the full $100$% set of available training data, i.e., in Fig. 6(a), the total training loss value of DA-cRAE converges within $15$ epochs, while the nuisance loss decreases steadily with more training iterations and the loss value of the adversary unit keeps steady due to its antagonistic relationship with DA-cRAE, where the adversary unit continues to conceal subject-specific representations without undermining the discriminative performance of the entire network. With less data, as illustrated in Fig. 6(b), convergences are achieved after more training epochs, while the convergences of the DA-cRAE loss, adversary loss and nuisance loss are observed in a similar pattern with the full $100$% data case, indicating the capability of the proposed model to learn universal features from data with even smaller sizes. Overall, we observe that with both adversary and nuisance networks attached to the encoder, the classifier improves the accuracy substantially and shows more stable performance across different left-out subjects.