Structural Autoencoders Improve Representations for Generation and Transfer

We study the problem of structuring a learned representation to significantly improve performance without supervision. Unlike most methods which focus on using side information like weak supervision or defining new regularization objectives, we focus on improving the learned representation by structuring the architecture of the model. We propose a self-attention based architecture to make the encoder explicitly associate parts of the representation with parts of the input observation. Meanwhile, our structural decoder architecture encourages a hierarchical structure in the latent space, akin to structural causal models, and learns a natural ordering of the latent mechanisms. We demonstrate how these models learn a representation which improves results in a variety of downstream tasks including generation, disentanglement, and transfer using several challenging and natural image datasets.

predCOVID-19: A Systematic Study of Clinical Predictive Models for Coronavirus Disease 2019

Coronavirus Disease 2019 (COVID-19) is a rapidly emerging respiratory disease caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Due to the rapid human-to-human transmission of SARS-CoV-2, many healthcare systems are at risk of exceeding their healthcare capacities, in particular in terms of SARS-CoV-2 tests, hospital and intensive care unit (ICU) beds and mechanical ventilators. Predictive algorithms could potentially ease the strain on healthcare systems by identifying those who are most likely to receive a positive SARS-CoV-2 test, be hospitalised or admitted to the ICU. Here, we study clinical predictive models that estimate, using machine learning and based on routinely collected clinical data, which patients are likely to receive a positive SARS-CoV-2 test, require hospitalisation or intensive care. To evaluate the predictive performance of our models, we perform a retrospective evaluation on clinical and blood analysis data from a cohort of 5644 patients. Our experimental results indicate that our predictive models identify (i) patients that test positive for SARS-CoV-2 a priori at a sensitivity of 75% (95% CI: 67%, 81%) and a specificity of 49% (95% CI: 46%, 51%), (ii) SARS-CoV-2 positive patients that require hospitalisation with 0.92 AUC (95% CI: 0.81, 0.98), and (iii) SARS-CoV-2 positive patients that require critical care with 0.98 AUC (95% CI: 0.95, 1.00). In addition, we determine which clinical features are predictive to what degree for each of the aforementioned clinical tasks. Our results indicate that predictive models trained on routinely collected clinical data could be used to predict clinical pathways for COVID-19, and therefore help inform care and prioritise resources.

SLEIPNIR: Deterministic and Provably Accurate Feature Expansion for Gaussian Process Regression with Derivatives

Gaussian processes are an important regression tool with excellent analytic properties which allow for direct integration of derivative observations. However, vanilla GP methods scale cubically in the amount of observations. In this work, we propose a novel approach for scaling GP regression with derivatives based on quadrature Fourier features. We then prove deterministic, non-asymptotic and exponentially fast decaying error bounds which apply for both the approximated kernel as well as the approximated posterior. To furthermore illustrate the practical applicability of our method, we then apply it to ODIN, a recently developed algorithm for ODE parameter inference. In an extensive experiments section, all results are empirically validated, demonstrating the speed, accuracy, and practical applicability of this approach.

Learning Neural Causal Models from Unknown Interventions

Meta-learning over a set of distributions can be interpreted as learning different types of parameters corresponding to short-term vs long-term aspects of the mechanisms underlying the generation of data. These are respectively captured by quickly-changing parameters and slowly-changing meta-parameters. We present a new framework for meta-learning causal models where the relationship between each variable and its parents is modeled by a neural network, modulated by structural meta-parameters which capture the overall topology of a directed graphical model. Our approach avoids a discrete search over models in favour of a continuous optimization procedure. We study a setting where interventional distributions are induced as a result of a random intervention on a single unknown variable of an unknown ground truth causal model, and the observations arising after such an intervention constitute one meta-example. To disentangle the slow-changing aspects of each conditional from the fast-changing adaptations to each intervention, we parametrize the neural network into fast parameters and slow meta-parameters. We introduce a meta-learning objective that favours solutions robust to frequent but sparse interventional distribution change, and which generalize well to previously unseen interventions. Optimizing this objective is shown experimentally to recover the structure of the causal graph.

On the Transfer of Inductive Bias from Simulation to the Real World: a New Disentanglement Dataset

Learning meaningful and compact representations with structurally disentangled semantic aspects is considered to be of key importance in representation learning. Since real-world data is notoriously costly to collect, many recent state-of-the-art disentanglement models have heavily relied on synthetic toy data-sets. In this paper, we propose a novel data-set which consists of over 450'000 images of physical 3D objects with seven factors of variation, such as object color, shape, size and position. In order to be able to control all the factors of variation precisely, we built an experimental platform where the objects are being moved by a robotic arm. In addition, we provide two more datasets which consist of simulations of the experimental setup. These datasets provide for the first time the possibility to systematically investigate how well different disentanglement methods perform on real data in comparison to simulation, and how simulated data can be leveraged to build better representations of the real world.

Disentangled State Space Representations

Sequential data often originates from diverse domains across which statistical regularities and domain specifics exist. To specifically learn cross-domain sequence representations, we introduce disentangled state space models (DSSM) -- a class of SSM in which domain-invariant state dynamics is explicitly disentangled from domain-specific information governing that dynamics. We analyze how such separation can improve knowledge transfer to new domains, and enable robust prediction, sequence manipulation and domain characterization. We furthermore propose an unsupervised VAE-based training procedure to implement DSSM in form of Bayesian filters. In our experiments, we applied VAE-DSSM framework to achieve competitive performance in online ODE system identification and regression across experimental settings, and controlled generation and prediction of bouncing ball video sequences across varying gravitational influences.

On the Fairness of Disentangled Representations

Recently there has been a significant interest in learning disentangled representations, as they promise increased interpretability, generalization to unseen scenarios and faster learning on downstream tasks. In this paper, we investigate the usefulness of different notions of disentanglement for improving the fairness of downstream prediction tasks based on representations. We consider the setting where the goal is to predict a target variable based on the learned representation of high-dimensional observations (such as images) that depend on both the target variable and an unobserved sensitive variable. We show that in this setting both the optimal and empirical predictions can be unfair, even if the target variable and the sensitive variable are independent. Analyzing more than 12600 trained representations of state-of-the-art disentangled models, we observe that various disentanglement scores are consistently correlated with increased fairness, suggesting that disentanglement may be a useful property to encourage fairness when sensitive variables are not observed.

Disentangling Factors of Variation Using Few Labels

Learning disentangled representations is considered a cornerstone problem in representation learning. Recently, Locatello et al. (2019) demonstrated that unsupervised disentanglement learning without inductive biases is theoretically impossible and that existing inductive biases and unsupervised methods do not allow to consistently learn disentangled representations. However, in many practical settings, one might have access to a very limited amount of supervision, for example through manual labeling of training examples. In this paper, we investigate the impact of such supervision on state-of-the-art disentanglement methods and perform a large scale study, training over 29000 models under well-defined and reproducible experimental conditions. We first observe that a very limited number of labeled examples (0.01--0.5% of the data set) is sufficient to perform model selection on state-of-the-art unsupervised models. Yet, if one has access to labels for supervised model selection, this raises the natural question of whether they should also be incorporated into the training process. As a case-study, we test the benefit of introducing (very limited) supervision into existing state-of-the-art unsupervised disentanglement methods exploiting both the values of the labels and the ordinal information that can be deduced from them. Overall, we empirically validate that with very little and potentially imprecise supervision it is possible to reliably learn disentangled representations.

Orthogonal Structure Search for Efficient Causal Discovery from Observational Data

The problem of inferring the direct causal parents of a response variable among a large set of explanatory variables is of high practical importance in many disciplines. Recent work exploits stability of regression coefficients or invariance properties of models across different experimental conditions for reconstructing the full causal graph. These approaches generally do not scale well with the number of the explanatory variables and are difficult to extend to nonlinear relationships. Contrary to existing work, we propose an approach which even works for observational data alone, while still offering theoretical guarantees including the case of partially nonlinear relationships. Our algorithm requires only one estimation for each variable and in our experiments we apply our causal discovery algorithm even to large graphs, demonstrating significant improvements compared to well established approaches.

AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs

Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we circumvent the use of the discretization schemes as seen in classical approaches. This yields significant improvements in parameter estimation accuracy and robustness given random initial guesses. On four commonly used benchmark systems, we demonstrate the performance of our algorithms compared to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.