Log-Likelihood Ratio Minimizing Flows
We introduce a new adversarial log-likelihood ratio domain alignment objective, show how to upper-bound it with a simple stable minimization objective, if the domain transformation is a normalizing flow, and show its relation to Jensen–Shannon divergence and GANs.
Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment
Ben Usman, Nick Dufour, Avneesh Sud, Kate Seanko
Advances in Neural Information Processing Systems (NeurIPS) 2020
video [3min] / poster / proceedings / bib
Distribution alignment has many applications in deep learning, including domain adaptation and unsupervised image-to-image translation. Most prior work on unsupervised distribution alignment relies either on minimizing simple non-parametric statistical distances such as maximum mean discrepancy or on adversarial alignment. However, the former fails to capture the structure of complex real-world distributions, while the latter is difficult to train and does not provide any universal convergence guarantees or automatic quantitative validation procedures. In this paper, we propose a new distribution alignment method based on a log-likelihood ratio statistic and normalizing flows. We show that, under certain assumptions, this combination yields a deep neural likelihood-based minimization objective that attains a known lower bound upon convergence. We experimentally verify that minimizing the resulting objective results in domain alignment that preserves the local structure of input domains.
Experiments
This repo constains four (mostly) self-contained experiments implemented in JAX and Tensorflow Probability. Some of them are heavy enough to make the github viewer fail, so we suggest using colab links to view experiments in the following order:
jax_gaussian_and_real_nvp.ipynb[colab]: we define 1D and 2D Gaussian likelihood-ratio minimizing flows (LRMF) and see that they sucessfully align normally-distributed distributions, and first two moments of moons distributions. After that we define a RealNVP LRMF and apply it to normally distributed datasets confirming that LRMF works correctly in the overparameterized regime.tfp_moons_real_nvp_ffjord.ipynb[colab]: we define RealNVP and FFJORD LRMFs and show that they sucesfully align moon datasets. We also show that our approach produces more semantically meaningful alignment on this dataset than alternatives.tfp_digit_embeddings_real_nvp.ipynb[colab]: we embed MNIST and USPS into a lower-dimentional space using a shared VAEGAN and train RealNVP LRMF to align resulting embedding clouds.jax_gmm_vanishing_gradient.ipynb[colab]: we show that even 1D Equal Gaussian Mixture LRMF suffers from poly-exponentially vanishing generator gradients as distributions are drawn further apart (see Example 2.2 in the paper).tfp_digits_glow_fails.ipynb[colab] (usesglow_lrmf.pyfrom this repo): an example of a failure due to vanishing gradients in higher dimentions - GLOW fails to converge to a global minimum. We implemented stochastic Polyak step size, but it did not help.
Visualizations
An animated version of Figure 4 from the paper.
Columns (left to right): MMD, EMD, back-to-back flow, LRMF.
Rows: distributions (align red to blue), points colored according to their local coordinate system, class labels of the "red" dataset according = "moon arm", classification accuracy, corresponding loss.
Here is final flow that LRMF learned to align moon distributions:
Citation
@inproceedings{usman2020lrmf,
author = {Usman, Ben and Sud, Avneesh and Dufour, Nick and Saenko, Kate},
booktitle = {Advances in Neural Information Processing Systems},
editor = {H. Larochelle and M. Ranzato and R. Hadsell and M. F. Balcan and H. Lin},
pages = {21118--21129},
publisher = {Curran Associates, Inc.},
title = {Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment},
url = {https://proceedings.neurips.cc/paper/2020/file/f169b1a771215329737c91f70b5bf05c-Paper.pdf},
volume = {33},
year = {2020}
}