Invertible Flow Non Equilibrium sampling

Simultaneously sampling from a complex distribution with intractable normalizing constant and approximating expectations under this distribution is a notoriously challenging problem. We introduce a novel scheme, Invertible Flow Non Equilibrium Sampling (InFine), which departs from classical Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) approaches. InFine constructs unbiased estimators of expectations and in particular of normalizing constants by combining the orbits of a deterministic transform started from random initializations.When this transform is chosen as an appropriate integrator of a conformal Hamiltonian system, these orbits are optimization paths. InFine is also naturally suited to design new MCMC sampling schemes by selecting samples on the optimization paths.Additionally, InFine can be used to construct an Evidence Lower Bound (ELBO) leading to a new class of Variational AutoEncoders (VAE).

COIN: COmpression with Implicit Neural representations

We propose a new simple approach for image compression: instead of storing the RGB values for each pixel of an image, we store the weights of a neural network overfitted to the image. Specifically, to encode an image, we fit it with an MLP which maps pixel locations to RGB values. We then quantize and store the weights of this MLP as a code for the image. To decode the image, we simply evaluate the MLP at every pixel location. We found that this simple approach outperforms JPEG at low bit-rates, even without entropy coding or learning a distribution over weights. While our framework is not yet competitive with state of the art compression methods, we show that it has various attractive properties which could make it a viable alternative to other neural data compression approaches.

Improving Lossless Compression Rates via Monte Carlo Bits-Back Coding

Latent variable models have been successfully applied in lossless compression with the bits-back coding algorithm. However, bits-back suffers from an increase in the bitrate equal to the KL divergence between the approximate posterior and the true posterior. In this paper, we show how to remove this gap asymptotically by deriving bits-back coding algorithms from tighter variational bounds. The key idea is to exploit extended space representations of Monte Carlo estimators of the marginal likelihood. Naively applied, our schemes would require more initial bits than the standard bits-back coder, but we show how to drastically reduce this additional cost with couplings in the latent space. When parallel architectures can be exploited, our coders can achieve better rates than bits-back with little additional cost. We demonstrate improved lossless compression rates in a variety of settings, including entropy coding for lossy compression.

Differentiable Particle Filtering via Entropy-Regularized Optimal Transport

Particle Filtering (PF) methods are an established class of procedures for performing inference in non-linear state-space models. Resampling is a key ingredient of PF, necessary to obtain low variance likelihood and states estimates. However, traditional resampling methods result in PF-based loss functions being non-differentiable with respect to model and PF parameters. In a variational inference context, resampling also yields high variance gradient estimates of the PF-based evidence lower bound. By leveraging optimal transport ideas, we introduce a principled differentiable particle filter and provide convergence results. We demonstrate this novel method on a variety of applications.

Annealed Flow Transport Monte Carlo

Annealed Importance Sampling (AIS) and its Sequential Monte Carlo (SMC) extensions are state-of-the-art methods for estimating normalizing constants of probability distributions. We propose here a novel Monte Carlo algorithm, Annealed Flow Transport (AFT), that builds upon AIS and SMC and combines them with normalizing flows (NF) for improved performance. This method transports a set of particles using not only importance sampling (IS), Markov chain Monte Carlo (MCMC) and resampling steps - as in SMC, but also relies on NF which are learned sequentially to push particles towards the successive annealed targets. We provide limit theorems for the resulting Monte Carlo estimates of the normalizing constant and expectations with respect to the target distribution. Additionally, we show that a continuous-time scaling limit of the population version of AFT is given by a Feynman--Kac measure which simplifies to the law of a controlled diffusion for expressive NF. We demonstrate experimentally the benefits and limitations of our methodology on a variety of applications.

Generative Models as Distributions of Functions

Generative models are typically trained on grid-like data such as images. As a result, the size of these models usually scales directly with the underlying grid resolution. In this paper, we abandon discretized grids and instead parameterize individual data points by continuous functions. We then build generative models by learning distributions over such functions. By treating data points as functions, we can abstract away from the specific type of data we train on and construct models that scale independently of signal resolution and dimension. To train our model, we use an adversarial approach with a discriminator that acts directly on continuous signals. Through experiments on both images and 3D shapes, we demonstrate that our model can learn rich distributions of functions independently of data type and resolution.

Learning Deep Features in Instrumental Variable Regression

Instrumental variable (IV) regression is a standard strategy for learning causal relationships between confounded treatment and outcome variables from observational data by utilizing an instrumental variable, which affects the outcome only through the treatment. In classical IV regression, learning proceeds in two stages: stage 1 performs linear regression from the instrument to the treatment; and stage 2 performs linear regression from the treatment to the outcome, conditioned on the instrument. We propose a novel method, deep feature instrumental variable regression (DFIV), to address the case where relations between instruments, treatments, and outcomes may be nonlinear. In this case, deep neural nets are trained to define informative nonlinear features on the instruments and treatments. We propose an alternating training regime for these features to ensure good end-to-end performance when composing stages 1 and 2, thus obtaining highly flexible feature maps in a computationally efficient manner. DFIV outperforms recent state-of-the-art methods on challenging IV benchmarks, including settings involving high dimensional image data. DFIV also exhibits competitive performance in off-policy policy evaluation for reinforcement learning, which can be understood as an IV regression task.

Stable ResNet

Deep ResNet architectures have achieved state of the art performance on many tasks. While they solve the problem of gradient vanishing, they might suffer from gradient exploding as the depth becomes large (Yang et al. 2017). Moreover, recent results have shown that ResNet might lose expressivity as the depth goes to infinity (Yang et al. 2017, Hayou et al. 2019). To resolve these issues, we introduce a new class of ResNet architectures, called Stable ResNet, that have the property of stabilizing the gradient while ensuring expressivity in the infinite depth limit.