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.

Hijacking Malaria Simulators with Probabilistic Programming

Epidemiology simulations have become a fundamental tool in the fight against the epidemics of various infectious diseases like AIDS and malaria. However, the complicated and stochastic nature of these simulators can mean their output is difficult to interpret, which reduces their usefulness to policymakers. In this paper, we introduce an approach that allows one to treat a large class of population-based epidemiology simulators as probabilistic generative models. This is achieved by hijacking the internal random number generator calls, through the use of a universal probabilistic programming system (PPS). In contrast to other methods, our approach can be easily retrofitted to simulators written in popular industrial programming frameworks. We demonstrate that our method can be used for interpretable introspection and inference, thus shedding light on black-box simulators. This reinstates much-needed trust between policymakers and evidence-based methods.

Variational Estimators for Bayesian Optimal Experimental Design

Bayesian optimal experimental design (BOED) is a principled framework for making efficient use of limited experimental resources. Unfortunately, its applicability is hampered by the difficulty of obtaining accurate estimates of the expected information gain (EIG) of an experiment. To address this, we introduce several classes of fast EIG estimators suited to the experiment design context by building on ideas from variational inference and mutual information estimation. We show theoretically and empirically that these estimators can provide significant gains in speed and accuracy over previous approaches. We demonstrate the practicality of our approach via a number of experiments, including an adaptive experiment with human participants.

LF-PPL: A Low-Level First Order Probabilistic Programming Language for Non-Differentiable Models

We develop a new Low-level, First-order Probabilistic Programming Language (LF-PPL) suited for models containing a mix of continuous, discrete, and/or piecewise-continuous variables. The key success of this language and its compilation scheme is in its ability to automatically distinguish parameters the density function is discontinuous with respect to, while further providing runtime checks for boundary crossings. This enables the introduction of new inference engines that are able to exploit gradient information, while remaining efficient for models which are not everywhere differentiable. We demonstrate this ability by incorporating a discontinuous Hamiltonian Monte Carlo (DHMC) inference engine that is able to deliver automated and efficient inference for non-differentiable models. Our system is backed up by a mathematical formalism that ensures that any model expressed in this language has a density with measure zero discontinuities to maintain the validity of the inference engine.

Disentangling Disentanglement

We develop a generalised notion of disentanglement in Variational Auto-Encoders (VAEs) by casting it as a \emph{decomposition} of the latent representation, characterised by i) enforcing an appropriate level of overlap in the latent encodings of the data, and ii) regularisation of the average encoding to a desired structure, represented through the prior. We motivate this by showing that a) the $\beta$-VAE disentangles purely through regularisation of the overlap in latent encodings, and through its average (Gaussian) encoder variance, and b) disentanglement, as independence between latents, can be cast as a regularisation of the aggregate posterior to a prior with specific characteristics. We validate this characterisation by showing that simple manipulations of these factors, such as using rotationally variant priors, can help improve disentanglement, and discuss how this characterisation provides a more general framework to incorporate notions of decomposition beyond just independence between the latents.

A Statistical Approach to Assessing Neural Network Robustness

We present a new approach to assessing the robustness of neural networks based on estimating the proportion of inputs for which a property is violated. Specifically, we estimate the probability of the event that the property is violated under an input model. Our approach critically varies from the formal verification framework in that when the property can be violated, it provides an informative notion of how robust the network is, rather than just the conventional assertion that the network is not verifiable. Furthermore, it provides an ability to scale to larger networks than formal verification approaches. Though the framework still provides a formal guarantee of satisfiability whenever it successfully finds one or more violations, these advantages do come at the cost of only providing a statistical estimate of unsatisfiability whenever no violation is found. Key to the practical success of our approach is an adaptation of multi-level splitting, a Monte Carlo approach for estimating the probability of rare events, to our statistical robustness framework. We demonstrate that our approach is able to emulate formal verification procedures on benchmark problems, while scaling to larger networks and providing reliable additional information in the form of accurate estimates of the violation probability.

On Exploration, Exploitation and Learning in Adaptive Importance Sampling

We study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade-off between exploration and exploitation in this adaptation. Borrowing ideas from the bandits literature, we propose Daisee, a partition-based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has $\mathcal{O}(\sqrt{T}(\log T)^{\frac{3}{4}})$ cumulative pseudo-regret, where $T$ is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.

Faithful Inversion of Generative Models for Effective Amortized Inference

Inference amortization methods share information across multiple posterior-inference problems, allowing each to be carried out more efficiently. Generally, they require the inversion of the dependency structure in the generative model, as the modeller must learn a mapping from observations to distributions approximating the posterior. Previous approaches have involved inverting the dependency structure in a heuristic way that fails to capture these dependencies correctly, thereby limiting the achievable accuracy of the resulting approximations. We introduce an algorithm for faithfully, and minimally, inverting the graphical model structure of any generative model. Such inverses have two crucial properties: (a) they do not encode any independence assertions that are absent from the model and; (b) they are local maxima for the number of true independencies encoded. We prove the correctness of our approach and empirically show that the resulting minimally faithful inverses lead to better inference amortization than existing heuristic approaches.

Nesting Probabilistic Programs

We formalize the notion of nesting probabilistic programming queries and investigate the resulting statistical implications. We demonstrate that while query nesting allows the definition of models which could not otherwise be expressed, such as those involving agents reasoning about other agents, existing systems take approaches which lead to inconsistent estimates. We show how to correct this by delineating possible ways one might want to nest queries and asserting the respective conditions required for convergence. We further introduce a new online nested Monte Carlo estimator that makes it substantially easier to ensure these conditions are met, thereby providing a simple framework for designing statistically correct inference engines. We prove the correctness of this online estimator and show that, when using the recommended setup, its asymptotic variance is always better than that of the equivalent fixed estimator, while its bias is always within a factor of two.

Tighter Variational Bounds are Not Necessarily Better

We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better variational objectives for simultaneous model learning and inference amortization schemes. Based on our insights, we introduce three new algorithms: the partially importance weighted auto-encoder (PIWAE), the multiply importance weighted auto-encoder (MIWAE), and the combination importance weighted auto-encoder (CIWAE), each of which includes the standard importance weighted auto-encoder (IWAE) as a special case. We show that each can deliver improvements over IWAE, even when performance is measured by the IWAE target itself. Furthermore, our results suggest that PIWAE may be able to deliver simultaneous improvements in the training of both the inference and generative networks.