Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung IOSB

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  • Publication
    Bézier Curve Gaussian Processes
    ( 2022-11-18)
    Hug, Ronny
    ;
    Becker, Stefan
    ;
    Hübner, Wolfgang
    ;
    Arens, Michael
    ;
    Beyerer, Jürgen
    Probabilistic models for sequential data are the basis for a variety of applications concerned with processing timely ordered information. The predominant approach in this domain is given by recurrent neural networks, implementing either an approximate Bayesian approach (e.g. Variational Autoencoders or Generative Adversarial Networks) or a regression-based approach, i.e. variations of Mixture Density networks (MDN). In this paper, we focus on the N-MDN variant, which parameterizes (mixtures of) probabilistic Bézier curves (N-Curves) for modeling stochastic processes. While in favor in terms of computational cost and stability, MDNs generally fall behind approximate Bayesian approaches in terms of expressiveness. Towards this end, we present an approach for closing this gap by enabling full Bayesian inference on top of N-MDNs. For this, we show that N-Curves are a special case of Gaussian processes (denoted as N-GP) and then derive corresponding mean and kernel functions for different modalities. Following this, we propose the use of the N-MDN as a data-dependent generator for N-GP prior distributions. We show the advantages granted by this combined model in an application context, using human trajectory prediction as an example.
  • Publication
    Modeling continuous-time stochastic processes using N-Curve mixtures
    ( 2019)
    Hug, Ronny
    ;
    Hübner, Wolfgang
    ;
    Arens, Michael
    Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this context the model must be able to capture the multi-modal nature of the data, without blurring between modes. This property is essential for applications like trajectory prediction or human motion modeling. Towards this end, a neural network model for continuous-time stochastic processes usable for sequence prediction is proposed. The model is based on Mixture Density Networks using Bézier curves with Gaussian random variables as control points (abbrev.: N-Curves). Key advantages of the model include the ability of generating smooth multi-mode predictions in a single inference step which reduces the need for Monte Carlo simulation, as required in many multi-step prediction models, based on state-of-the-art neural networks. Essential properties of the proposed approach are illustrated by several toy examples and the task of multi-step sequence prediction. Further, the model performance is evaluated on two real world use-cases, i.e. human trajectory prediction and human motion modeling, outperforming different state-of-the-art models.