Fully Embedded Time-Series Generative Adversarial Networks

TL;DR

FETSGAN addresses the challenge of realistic real-valued time-series generation by jointly modeling static and temporal distributions through a seq2seq-style adversarial autoencoder that embeds entire sequences into a latent space. A First Above Threshold (FAT) operator stabilizes training by enforcing reconstruction loss progressively at a single time instance, enabling robust handling of long sequences without autoregressive exposure bias. The method introduces a three-pronged objective with discriminators in both feature and latent spaces plus a reconstruction term, yielding improved distribution matching, selective sampling ability, and state-of-the-art predictive and discriminative performance among direct feature-space adversaries. This approach provides an interpretable latent space for style-controlled synthesis and has practical implications for generating realistic synthetic time-series while mitigating mode collapse and training instability, with considerations for privacy and ethical use in real-world applications.

Abstract

Generative Adversarial Networks (GANs) should produce synthetic data that fits the underlying distribution of the data being modeled. For real valued time-series data, this implies the need to simultaneously capture the static distribution of the data, but also the full temporal distribution of the data for any potential time horizon. This temporal element produces a more complex problem that can potentially leave current solutions under-constrained, unstable during training, or prone to varying degrees of mode collapse. In FETSGAN, entire sequences are translated directly to the generator's sampling space using a seq2seq style adversarial auto encoder (AAE), where adversarial training is used to match the training distribution in both the feature space and the lower dimensional sampling space. This additional constraint provides a loose assurance that the temporal distribution of the synthetic samples will not collapse. In addition, the First Above Threshold (FAT) operator is introduced to supplement the reconstruction of encoded sequences, which improves training stability and the overall quality of the synthetic data being generated. These novel contributions demonstrate a significant improvement to the current state of the art for adversarial learners in qualitative measures of temporal similarity and quantitative predictive ability of data generated through FETSGAN.

Figures (4)

• Figure 1: The overall training scheme is shown. Above the dashed line, the RNN style architectures are detailed, showing the model outputs (red) of each network as a function of the inputs. $h^{(d)}_t$ indicates a hidden state of the network, where $d$ represents the weights associated with a specific depth and $t$ represents that state any specific time. FC indicates a fully connected output layer, and these weights are shared for every output across time, i.e. in the case of the generator $\hat{{x}}_{1:T}$. Below the dashed line, the training flow is visualized. The mechanisms for producing FETSGAN's five objective functions are shown in red.
• Figure 2: For the encoding and reconstruction of $\bar{x}_{1:T} = g(e(x_{1:T}))$, the reconstruction objectives of \ref{['sum_recon']} and \ref{['recon']} are compared for the sines dataset. The average value for each epoch in $200$ epochs of training is plotted. Here, training occurs under the complete model objective of \ref{['objective']}. In the first row, we can see that the model is unable to apply adversarial learning and simultaneously learn the proper encodings to reconstruct $x_{1:T}$ under \ref{['sum_recon']}. This causes the optimization to immediately fall into a local minimum. With $\tau$ gradually increasing to progressively learn longer sequences in the second row, the $\mathop{\mathrm{FAT}}\nolimits_{t}$ operation facilitates minimizing reconstruction loss better than applying \ref{['sum_recon']} directly.
• Figure 3: The qualitative visualization results are shown. Sines data is shown on the top row, with the dominant component of the DFT for each sequence's frequency, amplitude, and phase (left to right) is shown as both a histogram and kernel density estimate (KDE). On the bottom row, we show a TSNE visualization for the stock dataset (left) and energy data (right), following the same procedure from yoonTimeseriesGenerativeAdversarial2019. In all graphs, real data $x_{1:T}$ is shown in blue, synthetic data $\hat{x}_{1:T}$ (FETSGAN) is in orange, and the synthetic data generated by TimeGAN is shown in red. FETSGAN produces data that more closely matches the original data by a substantial margin.
• Figure 4: Selective sampling of the prior distribution $p_z$ is shown. Sines data is shown, where $100$ random samples $z_s$ were taken near the encodings of three sine waves with frequencies $f=2,5,8$ and then fed to the generator. Similar to \ref{['datasimfig']}, the corresponding histogram and KDE plot for $DFT(g(z_s))$ is shown on the left. Projections of the intermediate encodings are shown on the right, demonstrating spatial interpretability.