VAE for Time Series

🌈 Abstract

The article discusses how variational autoencoders (VAEs) can be used to generate realistic time series data, using the example of simulating temperature data from Phoenix, Arizona. The key points covered include:

• Adapting the standard VAE model to capture periodic and sequential patterns in time series data
• Using 1-D convolutional layers, strategic strides, flexible time dimensions, and a seasonally dependent prior to improve the model's ability to generate plausible time series
• Applying a linear transformation to the training data to account for the upward temperature trend due to climate change
• Leveraging the shift-invariant and periodic properties of convolutional layers to model the cyclical patterns in the temperature data
• Allowing the latent variable to have an unconstrained time dimension to generate time series of arbitrary length
• Incorporating a seasonal prior distribution to capture the variations in temperature characteristics throughout the year

🙋 Q&A

[01] Variational Autoencoders for Time Series Modeling

1. What are the key characteristics of the temperature data that the VAE model needs to capture?

• The model needs to capture the periodic and sequential patterns in the temperature data, as well as account for the upward trend due to climate change.
• The training data should be stationary, without a long-term trend. To achieve this, the author applied a linear transformation to the raw observations to erase the upward trend.

2. How does the VAE model architecture leverage convolutional layers to capture the periodic patterns in the temperature data?

• The encoder uses 1-D convolutional layers, where the stride determines the size of the next layer. The strategic selection of strides allows the model to replicate the periodic patterns in the data.
• The convolutional layers apply the kernel cyclically, repeating the same weights with a period equal to the stride. This gives the training process the freedom to customize the weights based on the input's position in the cycle.
• Stacking multiple convolutional layers results in a larger effective period made of nested sub-convolutions, allowing the model to capture long-range effects in the data.

3. How does the VAE model handle the flexible time dimension of the temperature data?

• The model uses an unconstrained time dimension in the neural network, allowing it to generate time series of arbitrary length.
• The latent variable includes a time dimension, where each time step corresponds to a 96-hour period in the input data.
• The convolutional and deconvolutional layers enable the model to generate smooth, continuous time series, rather than discrete 96-hour chunks.

4. How does the seasonal prior distribution improve the generated temperature data?

• The prior distribution is a normal distribution with mean and log-variance that are periodic functions of the time of year (represented as an angle θ).
• This seasonal prior allows the generated data to have characteristics that vary by the time of year, with January data looking different from July data, and data from the same month sharing similar features.
• The periodic function of the prior distribution parameters is approximated using a third-degree trigonometric polynomial, which can represent the seasonal patterns in the temperature data.

[02] Implementation Details

1. How is the VAE model implemented in Tensorflow?

• The encoder is a neural network with 1-D convolutional layers, where the input has a flexible time dimension.
• The decoder uses 1-D transposed convolutional (deconvolution) layers to project the latent features into overlapping sequences and generate the output time series.
• The prior distribution is implemented as a separate neural network that takes in the time-of-year features (sin(θ), cos(θ), etc.) and outputs the mean and log-variance of the latent variable distribution.
• The loss function includes a reconstruction term and a latent regularization term (Kullback-Leibler divergence between the latent and prior distributions).

2. What are the key components of the custom VAE class?

• The VAE class inherits from the tf.keras.models.Model class and contains the encoder, decoder, and prior networks as attributes.
• The vae_loss method calculates the reconstruction loss and KL divergence loss, which are then combined to form the total loss.
• The train_step method applies the gradients to the trainable variables during the training process.

3. Where can the full implementation of the VAE model be found?

• The author mentions that the full implementation of the VAE model can be found in their GitHub repository.