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Revisiting semi-supervised training objectives for differentiable particle filters

Jiaxi Li, John-Joseph Brady, Xiongjie Chen, Yunpeng Li

TL;DR

This work evaluates two semi-supervised objectives for differentiable particle filters (DPFs) when ground-truth latent states are scarce. It contrasts an ELBO-based unsupervised loss with a pseudo-likelihood loss, each combined with a supervised mean-squared error term to form semi-supervised objectives. In two simulated environments, the ELBO-based approach improves performance at extreme label scarcity in a multivariate linear Gaussian model, while the pseudo-likelihood term offers little or no benefit. The maze-domain results suggest that semi-supervised gains are sensitive to task and architecture, highlighting the need for careful objective selection and further ablations for practical semi-supervised DPF training.

Abstract

Differentiable particle filters combine the flexibility of neural networks with the probabilistic nature of sequential Monte Carlo methods. However, traditional approaches rely on the availability of labelled data, i.e., the ground truth latent state information, which is often difficult to obtain in real-world applications. This paper compares the effectiveness of two semi-supervised training objectives for differentiable particle filters. We present results in two simulated environments where labelled data are scarce.

Revisiting semi-supervised training objectives for differentiable particle filters

TL;DR

This work evaluates two semi-supervised objectives for differentiable particle filters (DPFs) when ground-truth latent states are scarce. It contrasts an ELBO-based unsupervised loss with a pseudo-likelihood loss, each combined with a supervised mean-squared error term to form semi-supervised objectives. In two simulated environments, the ELBO-based approach improves performance at extreme label scarcity in a multivariate linear Gaussian model, while the pseudo-likelihood term offers little or no benefit. The maze-domain results suggest that semi-supervised gains are sensitive to task and architecture, highlighting the need for careful objective selection and further ablations for practical semi-supervised DPF training.

Abstract

Differentiable particle filters combine the flexibility of neural networks with the probabilistic nature of sequential Monte Carlo methods. However, traditional approaches rely on the availability of labelled data, i.e., the ground truth latent state information, which is often difficult to obtain in real-world applications. This paper compares the effectiveness of two semi-supervised training objectives for differentiable particle filters. We present results in two simulated environments where labelled data are scarce.
Paper Structure (22 sections, 13 equations, 2 figures, 1 algorithm)

This paper contains 22 sections, 13 equations, 2 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Preliminaries
  4. Particle filtering
  5. Normalising flow-based particle filters
  6. Dynamic model with normalising flows
  7. Proposal distribution with conditional normalising flows
  8. Measurement model with conditional normalising flows
  9. Revisiting the unsupervised and semi-supervised training objectives
  10. Supervised loss
  11. Unsupervised loss
  12. Evidence lower bound
  13. Pseudo likelihood
  14. Semi-supervised loss
  15. Experiment results
  16. ...and 7 more sections

Figures (2)

  • Figure 1: The comparison of RMSEs using the DPF, the SDPF-PL, and the SDPF-ELBO for $d_{\mathcal{X}} =10$. (a) Mean RMSEs on validation data during training, with a labelling ratio of $0.1\%$. (b): Mean RMSEs on testing data with varying labelling ratios.
  • Figure 2: The comparison of RMSEs between the SDBPF-ELBO, the SDBPF-PL, the SDBPF-PL-vanilla, the DBPF and the DBPF-vanilla. (a): Mean RMSEs on validation data during training, with a labelling ratio of $0.1\%$. (b): Mean RMSEs on testing data with varying labelling ratios.