For autonomous agents to successfully operate in the real world, anticipation of future events and states of their environment is a key competence. This problem has been formalized as a sequence extrapolation problem, where a number of observations are used to predict the sequence into the future. Real-world scenarios demand a model of uncertainty of such predictions, as predictions become increasingly uncertain -- in particular on long time horizons. While impressive results have been shown on point estimates, scenarios that induce multi-modal distributions over future sequences remain challenging. Our work addresses these challenges in a Gaussian Latent Variable model for sequence prediction. Our core contribution is a "Best of Many" sample objective that leads to more accurate and more diverse predictions that better capture the true variations in real-world sequence data. Beyond our analysis of improved model fit, our models also empirically outperform prior work on three diverse tasks ranging from traffic scenes to weather data.
In @cite_8 a multi-sample objective for Conditional Generative Models is also proposed in order to better capture multi-modal distributions. However, the key difference to our proposed objective is that during training samples are drawn from the prior. Sampling directly from the prior leads to high variance model updates. In contrast, we perform importance sampling through a jointly learned proposal distribution in order to deal with this problem.
@cite_8
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Generative models such as Variational Auto Encoders (VAEs) and Generative Adversarial Networks (GANs) are typically trained for a fixed prior distribution in the latent space, such as uniform or Gaussian. After a trained model is obtained, one can sample the Generator in various forms for exploration and understanding, such as interpolating between two samples, sampling in the vicinity of a sample or exploring differences between a pair of samples applied to a third sample. In this paper, we show that the latent space operations used in the literature so far induce a distribution mismatch between the resulting outputs and the prior distribution the model was trained on. To address this, we propose to use distribution matching transport maps to ensure that such latent space operations preserve the prior distribution, while minimally modifying the original operation. Our experimental results validate that the proposed operations give higher quality samples compared to the original operations.