Frank Wood

Matthew Niedoba, Jonathan Wilder Lavington, Yunpeng Liu et al.

Simulation of autonomous vehicle systems requires that simulated traffic participants exhibit diverse and realistic behaviors. The use of prerecorded real-world traffic scenarios in simulation ensures realism but the rarity of safety critical events makes large scale collection of driving scenarios expensive. In this paper, we present DJINN - a diffusion based method of generating traffic scenarios. Our approach jointly diffuses the trajectories of all agents, conditioned on a flexible set of state observations from the past, present, or future. On popular trajectory forecasting datasets, we report state of the art performance on joint trajectory metrics. In addition, we demonstrate how DJINN flexibly enables direct test-time sampling from a variety of valuable conditional distributions including goal-based sampling, behavior-class sampling, and scenario editing.

Saeid Naderiparizi, Xiaoxuan Liang, Setareh Cohan et al.

Score-based diffusion models are a powerful class of generative models, widely utilized across diverse domains. Despite significant advancements in large-scale tasks such as text-to-image generation, their application to constrained domains has received considerably less attention. This work addresses model learning in a setting where, in addition to the training dataset, there further exists side-information in the form of an oracle that can label samples as being outside the support of the true data generating distribution. Specifically we develop a new denoising diffusion probabilistic modeling methodology, Gen-neG, that leverages this additional side-information. Gen-neG builds on classifier guidance in diffusion models to guide the generation process towards the positive support region indicated by the oracle. We empirically establish the utility of Gen-neG in applications including collision avoidance in self-driving simulators and safety-guarded human motion generation.

Jason Yoo, Tony Joseph, Dylan Yung et al.

There are currently many barriers that prevent non-experts from exploiting machine learning solutions ranging from the lack of intuition on statistical learning techniques to the trickiness of hyperparameter tuning. Such barriers have led to an explosion of interest in automated machine learning (AutoML), whereby an off-the-shelf system can take care of many of the steps for end-users without the need for expertise in machine learning. This paper presents Ensemble Squared (Ensemble$^2$), an AutoML system that ensembles the results of state-of-the-art open-source AutoML systems. Ensemble$^2$ exploits the diversity of existing AutoML systems by leveraging the differences in their model search space and heuristics. Empirically, we show that diversity of each AutoML system is sufficient to justify ensembling at the AutoML system level. In demonstrating this, we also establish new state-of-the-art AutoML results on the OpenML tabular classification benchmark.

Manuel Gloeckler, Michael Deistler, Christian Weilbach et al.

Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current simulation-based amortized inference methods are simulation-hungry and inflexible: They require the specification of a fixed parametric prior, simulator, and inference tasks ahead of time. Here, we present a new amortized inference method -- the Simformer -- which overcomes these limitations. By training a probabilistic diffusion model with transformer architectures, the Simformer outperforms current state-of-the-art amortized inference approaches on benchmark tasks and is substantially more flexible: It can be applied to models with function-valued parameters, it can handle inference scenarios with missing or unstructured data, and it can sample arbitrary conditionals of the joint distribution of parameters and data, including both posterior and likelihood. We showcase the performance and flexibility of the Simformer on simulators from ecology, epidemiology, and neuroscience, and demonstrate that it opens up new possibilities and application domains for amortized Bayesian inference on simulation-based models.

Laura Manduchi, Clara Meister, Kushagra Pandey et al.

The field of deep generative modeling has grown rapidly in the last few years. With the availability of massive amounts of training data coupled with advances in scalable unsupervised learning paradigms, recent large-scale generative models show tremendous promise in synthesizing high-resolution images and text, as well as structured data such as videos and molecules. However, we argue that current large-scale generative AI models exhibit several fundamental shortcomings that hinder their widespread adoption across domains. In this work, our objective is to identify these issues and highlight key unresolved challenges in modern generative AI paradigms that should be addressed to further enhance their capabilities, versatility, and reliability. By identifying these challenges, we aim to provide researchers with insights for exploring fruitful research directions, thus fostering the development of more robust and accessible generative AI solutions.

Jason Yoo, Yunpeng Liu, Frank Wood et al.

In online continual learning, a neural network incrementally learns from a non-i.i.d. data stream. Nearly all online continual learning methods employ experience replay to simultaneously prevent catastrophic forgetting and underfitting on past data. Our work demonstrates a limitation of this approach: neural networks trained with experience replay tend to have unstable optimization trajectories, impeding their overall accuracy. Surprisingly, these instabilities persist even when the replay buffer stores all previous training examples, suggesting that this issue is orthogonal to catastrophic forgetting. We minimize these instabilities through a simple modification of the optimization geometry. Our solution, Layerwise Proximal Replay (LPR), balances learning from new and replay data while only allowing for gradual changes in the hidden activation of past data. We demonstrate that LPR consistently improves replay-based online continual learning methods across multiple problem settings, regardless of the amount of available replay memory.

Saeid Naderiparizi, Xiaoxuan Liang, Berend Zwartsenberg et al.

In this paper we describe a novel framework for diffusion-based generative modeling on constrained spaces. In particular, we introduce manual bridges, a framework that expands the kinds of constraints that can be practically used to form so-called diffusion bridges. We develop a mechanism for combining multiple such constraints so that the resulting multiply-constrained model remains a manual bridge that respects all constraints. We also develop a mechanism for training a diffusion model that respects such multiple constraints while also adapting it to match a data distribution. We develop and extend theory demonstrating the mathematical validity of our mechanisms. Additionally, we demonstrate our mechanism in constrained generative modeling tasks, highlighting a particular high-value application in modeling trajectory initializations for path planning and control in autonomous vehicles.

Yingchen He, Christian D. Weilbach, Martyna E. Wojciechowska et al.

Advances in deep generative modelling have made it increasingly plausible to train human-level embodied agents. Yet progress has been limited by the absence of large-scale, real-time, multi-modal, and socially interactive datasets that reflect the sensory-motor complexity of natural environments. To address this, we present PLAICraft, a novel data collection platform and dataset capturing multiplayer Minecraft interactions across five time-aligned modalities: video, game output audio, microphone input audio, mouse, and keyboard actions. Each modality is logged with millisecond time precision, enabling the study of synchronous, embodied behaviour in a rich, open-ended world. The dataset comprises over 10,000 hours of gameplay from more than 10,000 global participants.\footnote{We have done a privacy review for the public release of an initial 200-hour subset of the dataset, with plans to release most of the dataset over time.} Alongside the dataset, we provide an evaluation suite for benchmarking model capabilities in object recognition, spatial awareness, language grounding, and long-term memory. PLAICraft opens a path toward training and evaluating agents that act fluently and purposefully in real time, paving the way for truly embodied artificial intelligence.

Vasileios Lioutas, Adam Scibior, Matthew Niedoba et al.

Simulating realistic driving behavior is crucial for developing and testing autonomous systems in complex traffic environments. Equally important is the ability to control the behavior of simulated agents to tailor scenarios to specific research needs and safety considerations. This paper extends the general-purpose multi-agent driving behavior model ITRA (Scibior et al., 2021), by introducing a method called Control-ITRA to influence agent behavior through waypoint assignment and target speed modulation. By conditioning agents on these two aspects, we provide a mechanism for them to adhere to specific trajectories and indirectly adjust their aggressiveness. We compare different approaches for integrating these conditions during training and demonstrate that our method can generate controllable, infraction-free trajectories while preserving realism in both seen and unseen locations.

Vaden Masrani, Rob Brekelmans, Thang Bui et al.

Many common machine learning methods involve the geometric annealing path, a sequence of intermediate densities between two distributions of interest constructed using the geometric average. While alternatives such as the moment-averaging path have demonstrated performance gains in some settings, their practical applicability remains limited by exponential family endpoint assumptions and a lack of closed form energy function. In this work, we introduce $q$-paths, a family of paths which is derived from a generalized notion of the mean, includes the geometric and arithmetic mixtures as special cases, and admits a simple closed form involving the deformed logarithm function from nonextensive thermodynamics. Following previous analysis of the geometric path, we interpret our $q$-paths as corresponding to a $q$-exponential family of distributions, and provide a variational representation of intermediate densities as minimizing a mixture of $α$-divergences to the endpoints. We show that small deviations away from the geometric path yield empirical gains for Bayesian inference using Sequential Monte Carlo and generative model evaluation using Annealed Importance Sampling.

Adam Ścibior, Frank Wood

Particle filters are not compatible with automatic differentiation due to the presence of discrete resampling steps. While known estimators for the score function, based on Fisher's identity, can be computed using particle filters, up to this point they required manual implementation. In this paper we show that such estimators can be computed using automatic differentiation, after introducing a simple correction to the particle weights. This correction utilizes the stop-gradient operator and does not modify the particle filter operation on the forward pass, while also being cheap and easy to compute. Surprisingly, with the same correction automatic differentiation also produces good estimators for gradients of expectations under the posterior. We can therefore regard our method as a general recipe for making particle filters differentiable. We additionally show that it produces desired estimators for second-order derivatives and how to extend it to further reduce variance at the expense of additional computation.

Andrew Warrington, J. Wilder Lavington, Adam Ścibior et al.

Policies for partially observed Markov decision processes can be efficiently learned by imitating policies for the corresponding fully observed Markov decision processes. Unfortunately, existing approaches for this kind of imitation learning have a serious flaw: the expert does not know what the trainee cannot see, and so may encourage actions that are sub-optimal, even unsafe, under partial information. We derive an objective to instead train the expert to maximize the expected reward of the imitating agent policy, and use it to construct an efficient algorithm, adaptive asymmetric DAgger (A2D), that jointly trains the expert and the agent. We show that A2D produces an expert policy that the agent can safely imitate, in turn outperforming policies learned by imitating a fixed expert.

Rob Brekelmans, Vaden Masrani, Thang Bui et al.

Annealed importance sampling (AIS) is the gold standard for estimating partition functions or marginal likelihoods, corresponding to importance sampling over a path of distributions between a tractable base and an unnormalized target. While AIS yields an unbiased estimator for any path, existing literature has been primarily limited to the geometric mixture or moment-averaged paths associated with the exponential family and KL divergence. We explore AIS using $q$-paths, which include the geometric path as a special case and are related to the homogeneous power mean, deformed exponential family, and $α$-divergence.

Vu Nguyen, Vaden Masrani, Rob Brekelmans et al.

Achieving the full promise of the Thermodynamic Variational Objective (TVO), a recently proposed variational lower bound on the log evidence involving a one-dimensional Riemann integral approximation, requires choosing a "schedule" of sorted discretization points. This paper introduces a bespoke Gaussian process bandit optimization method for automatically choosing these points. Our approach not only automates their one-time selection, but also dynamically adapts their positions over the course of optimization, leading to improved model learning and inference. We provide theoretical guarantees that our bandit optimization converges to the regret-minimizing choice of integration points. Empirical validation of our algorithm is provided in terms of improved learning and inference in Variational Autoencoders and Sigmoid Belief Networks.

Saeid Naderiparizi, Kenny Chiu, Benjamin Bloem-Reddy et al.

We explore the effects of architecture and training objective choice on amortized posterior predictive inference in probabilistic conditional generative models. We aim this work to be a counterpoint to a recent trend in the literature that stresses achieving good samples when the amount of conditioning data is large. We instead focus our attention on the case where the amount of conditioning data is small. We highlight specific architecture and objective choices that we find lead to qualitative and quantitative improvement to posterior inference in this low data regime. Specifically we explore the effects of choices of pooling operator and variational family on posterior quality in neural processes. Superior posterior predictive samples drawn from our novel neural process architectures are demonstrated via image completion/in-painting experiments.

Andreas Munk, William Harvey, Frank Wood

Some of the most popular methods for improving the stability and performance of GANs involve constraining or regularizing the discriminator. In this paper we consider a largely overlooked regularization technique which we refer to as the Adversary's Assistant (AdvAs). We motivate this using a different perspective to that of prior work. Specifically, we consider a common mismatch between theoretical analysis and practice: analysis often assumes that the discriminator reaches its optimum on each iteration. In practice, this is essentially never true, often leading to poor gradient estimates for the generator. To address this, AdvAs is a theoretically motivated penalty imposed on the generator based on the norm of the gradients used to train the discriminator. This encourages the generator to move towards points where the discriminator is optimal. We demonstrate the effect of applying AdvAs to several GAN objectives, datasets and network architectures. The results indicate a reduction in the mismatch between theory and practice and that AdvAs can lead to improvement of GAN training, as measured by FID scores.

Rob Brekelmans, Vaden Masrani, Frank Wood et al.

The recently proposed Thermodynamic Variational Objective (TVO) leverages thermodynamic integration to provide a family of variational inference objectives, which both tighten and generalize the ubiquitous Evidence Lower Bound (ELBO). However, the tightness of TVO bounds was not previously known, an expensive grid search was used to choose a "schedule" of intermediate distributions, and model learning suffered with ostensibly tighter bounds. In this work, we propose an exponential family interpretation of the geometric mixture curve underlying the TVO and various path sampling methods, which allows us to characterize the gap in TVO likelihood bounds as a sum of KL divergences. We propose to choose intermediate distributions using equal spacing in the moment parameters of our exponential family, which matches grid search performance and allows the schedule to adaptively update over the course of training. Finally, we derive a doubly reparameterized gradient estimator which improves model learning and allows the TVO to benefit from more refined bounds. To further contextualize our contributions, we provide a unified framework for understanding thermodynamic integration and the TVO using Taylor series remainders.

Michael Teng, Tuan Anh Le, Adam Scibior et al.

We introduce a novel objective for training deep generative time-series models with discrete latent variables for which supervision is only sparsely available. This instance of semi-supervised learning is challenging for existing methods, because the exponential number of possible discrete latent configurations results in high variance gradient estimators. We first overcome this problem by extending the standard semi-supervised generative modeling objective with reweighted wake-sleep. However, we find that this approach still suffers when the frequency of available labels varies between training sequences. Finally, we introduce a unified objective inspired by teacher-forcing and show that this approach is robust to variable length supervision. We call the resulting method caffeinated wake-sleep (CWS) to emphasize its additional dependence on real data. We demonstrate its effectiveness with experiments on MNIST, handwriting, and fruit fly trajectory data.

Frank Wood, Andrew Warrington, Saeid Naderiparizi et al.

In this work we demonstrate how to automate parts of the infectious disease-control policy-making process via performing inference in existing epidemiological models. The kind of inference tasks undertaken include computing the posterior distribution over controllable, via direct policy-making choices, simulation model parameters that give rise to acceptable disease progression outcomes. Among other things, we illustrate the use of a probabilistic programming language that automates inference in existing simulators. Neither the full capabilities of this tool for automating inference nor its utility for planning is widely disseminated at the current time. Timely gains in understanding about how such simulation-based models and inference automation tools applied in support of policymaking could lead to less economically damaging policy prescriptions, particularly during the current COVID-19 pandemic.

Andrew Warrington, Saeid Naderiparizi, Frank Wood

Deterministic models are approximations of reality that are easy to interpret and often easier to build than stochastic alternatives. Unfortunately, as nature is capricious, observational data can never be fully explained by deterministic models in practice. Observation and process noise need to be added to adapt deterministic models to behave stochastically, such that they are capable of explaining and extrapolating from noisy data. We investigate and address computational inefficiencies that arise from adding process noise to deterministic simulators that fail to return for certain inputs; a property we describe as "brittle." We show how to train a conditional normalizing flow to propose perturbations such that the simulator succeeds with high probability, increasing computational efficiency.

Peyman Bateni, Raghav Goyal, Vaden Masrani et al.

Few-shot learning is a fundamental task in computer vision that carries the promise of alleviating the need for exhaustively labeled data. Most few-shot learning approaches to date have focused on progressively more complex neural feature extractors and classifier adaptation strategies, as well as the refinement of the task definition itself. In this paper, we explore the hypothesis that a simple class-covariance-based distance metric, namely the Mahalanobis distance, adopted into a state of the art few-shot learning approach (CNAPS) can, in and of itself, lead to a significant performance improvement. We also discover that it is possible to learn adaptive feature extractors that allow useful estimation of the high dimensional feature covariances required by this metric from surprisingly few samples. The result of our work is a new "Simple CNAPS" architecture which has up to 9.2% fewer trainable parameters than CNAPS and performs up to 6.1% better than state of the art on the standard few-shot image classification benchmark dataset.

Saeid Naderiparizi, Adam Ścibior, Andreas Munk et al.

Naive approaches to amortized inference in probabilistic programs with unbounded loops can produce estimators with infinite variance. This is particularly true of importance sampling inference in programs that explicitly include rejection sampling as part of the user-programmed generative procedure. In this paper we develop a new and efficient amortized importance sampling estimator. We prove finite variance of our estimator and empirically demonstrate our method's correctness and efficiency compared to existing alternatives on generative programs containing rejection sampling loops and discuss how to implement our method in a generic probabilistic programming framework.

Renhao Wang, Adam Scibior, Frank Wood

Imitation learning is a promising approach to end-to-end training of autonomous vehicle controllers. Typically the driving process with such approaches is entirely automatic and black-box, although in practice it is desirable to control the vehicle through high-level commands, such as telling it which way to go at an intersection. In existing work this has been accomplished by the application of a branched neural architecture, since directly providing the command as an additional input to the controller often results in the command being ignored. In this work we overcome this limitation by learning a disentangled probabilistic latent variable model that generates the steering commands. We achieve faithful command-conditional generation without using a branched architecture and demonstrate improved stability of the controller, applying only a variational objective without any domain-specific adjustments. On top of that, we extend our model with an additional latent variable and augment the dataset to train a controller that is robust to unsafe commands, such as asking it to turn into a wall. The main contribution of this work is a recipe for building controllable imitation driving agents that improves upon multiple aspects of the current state of the art relating to robustness and interpretability.

Andrew Warrington, Arthur Spencer, Frank Wood

We develop a stochastic whole-brain and body simulator of the nematode roundworm Caenorhabditis elegans (C. elegans) and show that it is sufficiently regularizing to allow imputation of latent membrane potentials from partial calcium fluorescence imaging observations. This is the first attempt we know of to "complete the circle," where an anatomically grounded whole-connectome simulator is used to impute a time-varying "brain" state at single-cell fidelity from covariates that are measurable in practice. The sequential Monte Carlo (SMC) method we employ not only enables imputation of said latent states but also presents a strategy for learning simulator parameters via variational optimization of the noisy model evidence approximation provided by SMC. Our imputation and parameter estimation experiments were conducted on distributed systems using novel implementations of the aforementioned techniques applied to synthetic data of dimension and type representative of that which are measured in laboratories currently.

Adam Goliński, Frank Wood, Tom Rainforth

Current approaches to amortizing Bayesian inference focus solely on approximating the posterior distribution. Typically, this approximation is, in turn, used to calculate expectations for one or more target functions - a computational pipeline which is inefficient when the target function(s) are known upfront. In this paper, we address this inefficiency by introducing AMCI, a method for amortizing Monte Carlo integration directly. AMCI operates similarly to amortized inference but produces three distinct amortized proposals, each tailored to a different component of the overall expectation calculation. At runtime, samples are produced separately from each amortized proposal, before being combined to an overall estimate of the expectation. We show that while existing approaches are fundamentally limited in the level of accuracy they can achieve, AMCI can theoretically produce arbitrarily small errors for any integrable target function using only a single sample from each proposal at runtime. We further show that it is able to empirically outperform the theoretically optimal self-normalized importance sampler on a number of example problems. Furthermore, AMCI allows not only for amortizing over datasets but also amortizing over target functions.

Vaden Masrani, Tuan Anh Le, Frank Wood

We introduce the thermodynamic variational objective (TVO) for learning in both continuous and discrete deep generative models. The TVO arises from a key connection between variational inference and thermodynamic integration that results in a tighter lower bound to the log marginal likelihood than the standard variational variational evidence lower bound (ELBO) while remaining as broadly applicable. We provide a computationally efficient gradient estimator for the TVO that applies to continuous, discrete, and non-reparameterizable distributions and show that the objective functions used in variational inference, variational autoencoders, wake sleep, and inference compilation are all special cases of the TVO. We use the TVO to learn both discrete and continuous deep generative models and empirically demonstrate state of the art model and inference network learning.

Michael Teng, Tuan Anh Le, Adam Scibior et al.

We apply recent advances in deep generative modeling to the task of imitation learning from biological agents. Specifically, we apply variations of the variational recurrent neural network model to a multi-agent setting where we learn policies of individual uncoordinated agents acting based on their perceptual inputs and their hidden belief state. We learn stochastic policies for these agents directly from observational data, without constructing a reward function. An inference network learned jointly with the policy allows for efficient inference over the agent's belief state given a sequence of its current perceptual inputs and the prior actions it performed, which lets us extrapolate observed sequences of behavior into the future while maintaining uncertainty estimates over future trajectories. We test our approach on a dataset of flies interacting in a 2D environment, where we demonstrate better predictive performance than existing approaches which learn deterministic policies with recurrent neural networks. We further show that the uncertainty estimates over future trajectories we obtain are well calibrated, which makes them useful for a variety of downstream processing tasks.

Yuan Zhou, Bradley J. Gram-Hansen, Tobias Kohn et al.

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.

Tom Rainforth, Yuan Zhou, Xiaoyu Lu et al.

We introduce inference trees (ITs), a new class of inference methods that build on ideas from Monte Carlo tree search to perform adaptive sampling in a manner that balances exploration with exploitation, ensures consistency, and alleviates pathologies in existing adaptive methods. ITs adaptively sample from hierarchical partitions of the parameter space, while simultaneously learning these partitions in an online manner. This enables ITs to not only identify regions of high posterior mass, but also maintain uncertainty estimates to track regions where significant posterior mass may have been missed. ITs can be based on any inference method that provides a consistent estimate of the marginal likelihood. They are particularly effective when combined with sequential Monte Carlo, where they capture long-range dependencies and yield improvements beyond proposal adaptation alone.

Maximilian Igl, Luisa Zintgraf, Tuan Anh Le et al.

Many real-world sequential decision making problems are partially observable by nature, and the environment model is typically unknown. Consequently, there is great need for reinforcement learning methods that can tackle such problems given only a stream of incomplete and noisy observations. In this paper, we propose deep variational reinforcement learning (DVRL), which introduces an inductive bias that allows an agent to learn a generative model of the environment and perform inference in that model to effectively aggregate the available information. We develop an n-step approximation to the evidence lower bound (ELBO), allowing the model to be trained jointly with the policy. This ensures that the latent state representation is suitable for the control task. In experiments on Mountain Hike and flickering Atari we show that our method outperforms previous approaches relying on recurrent neural networks to encode the past.

Tuan Anh Le, Adam R. Kosiorek, N. Siddharth et al.

Stochastic control-flow models (SCFMs) are a class of generative models that involve branching on choices from discrete random variables. Amortized gradient-based learning of SCFMs is challenging as most approaches targeting discrete variables rely on their continuous relaxations---which can be intractable in SCFMs, as branching on relaxations requires evaluating all (exponentially many) branching paths. Tractable alternatives mainly combine REINFORCE with complex control-variate schemes to improve the variance of naive estimators. Here, we revisit the reweighted wake-sleep (RWS) (Bornschein and Bengio, 2015) algorithm, and through extensive evaluations, show that it outperforms current state-of-the-art methods in learning SCFMs. Further, in contrast to the importance weighted autoencoder, we observe that RWS learns better models and inference networks with increasing numbers of particles. Our results suggest that RWS is a competitive, often preferable, alternative for learning SCFMs.

Bradley Gram-Hansen, Yuan Zhou, Tobias Kohn et al.

Hamiltonian Monte Carlo (HMC) is arguably the dominant statistical inference algorithm used in most popular "first-order differentiable" Probabilistic Programming Languages (PPLs). However, the fact that HMC uses derivative information causes complications when the target distribution is non-differentiable with respect to one or more of the latent variables. In this paper, we show how to use extensions to HMC to perform inference in probabilistic programs that contain discontinuities. To do this, we design a Simple first-order Probabilistic Programming Language (SPPL) that contains a sufficient set of language restrictions together with a compilation scheme. This enables us to preserve both the statistical and syntactic interpretation of if-else statements in the probabilistic program, within the scope of first-order PPLs. We also provide a corresponding mathematical formalism that ensures any joint density denoted in such a language has a suitably low measure of discontinuities.

Michael Teng, Frank Wood

We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation times of all worker-nodes in a parallel computing cluster. We show that a synchronous parameter server can, by utilizing such a model, choose an optimal cutoff time beyond which mini-batch gradient messages from slow workers are ignored that maximizes overall mini-batch gradient computations per second. In keeping with earlier findings we observe that, under realistic conditions, eagerly discarding the mini-batch gradient computations of stragglers not only increases throughput but actually increases the overall rate of convergence as a function of wall-clock time by virtue of eliminating idleness. The principal novel contribution and finding of this work goes beyond this by demonstrating that using the predicted run-times from a generative model of cluster worker performance to dynamically adjust the cutoff improves substantially over the static-cutoff prior art, leading to, among other things, significantly reduced deep neural net training times on large computer clusters.

Tom Rainforth, Adam R. Kosiorek, Tuan Anh Le et al.

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.

Mario Lezcano Casado, Atilim Gunes Baydin, David Martinez Rubio et al.

We consider the problem of Bayesian inference in the family of probabilistic models implicitly defined by stochastic generative models of data. In scientific fields ranging from population biology to cosmology, low-level mechanistic components are composed to create complex generative models. These models lead to intractable likelihoods and are typically non-differentiable, which poses challenges for traditional approaches to inference. We extend previous work in "inference compilation", which combines universal probabilistic programming and deep learning methods, to large-scale scientific simulators, and introduce a C++ based probabilistic programming library called CPProb. We successfully use CPProb to interface with SHERPA, a large code-base used in particle physics. Here we describe the technical innovations realized and planned for this library.

Stefan Webb, Adam Golinski, Robert Zinkov et al.

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.

Andrew Warrington, Frank Wood

We present an updated version of the VESICLE-CNN algorithm presented by Roncal et al. (2014). The original implementation makes use of a patch-based approach. This methodology is known to be slow due to repeated computations. We update this implementation to be fully convolutional through the use of dilated convolutions, recovering the expanded field of view achieved through the use of strided maxpools, but without a degradation of spatial resolution. This updated implementation performs as well as the original implementation, but with a $600\times$ speedup at test time. We release source code and data into the public domain.

Tom Rainforth, Robert Cornish, Hongseok Yang et al.

Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calculation of a separate, nested, estimation. We investigate the statistical implications of nesting MC estimators, including cases of multiple levels of nesting, and establish the conditions under which they converge. We derive corresponding rates of convergence and provide empirical evidence that these rates are observed in practice. We further establish a number of pitfalls that can arise from naive nesting of MC estimators, provide guidelines about how these can be avoided, and lay out novel methods for reformulating certain classes of nested expectation problems into single expectations, leading to improved convergence rates. We demonstrate the applicability of our work by using our results to develop a new estimator for discrete Bayesian experimental design problems and derive error bounds for a class of variational objectives.

Tom Rainforth, Tuan Anh Le, Jan-Willem van de Meent et al.

We present the first general purpose framework for marginal maximum a posteriori estimation of probabilistic program variables. By using a series of code transformations, the evidence of any probabilistic program, and therefore of any graphical model, can be optimized with respect to an arbitrary subset of its sampled variables. To carry out this optimization, we develop the first Bayesian optimization package to directly exploit the source code of its target, leading to innovations in problem-independent hyperpriors, unbounded optimization, and implicit constraint satisfaction; delivering significant performance improvements over prominent existing packages. We present applications of our method to a number of tasks including engineering design and parameter optimization.

N. Siddharth, Brooks Paige, Jan-Willem van de Meent et al.

Variational autoencoders (VAEs) learn representations of data by jointly training a probabilistic encoder and decoder network. Typically these models encode all features of the data into a single variable. Here we are interested in learning disentangled representations that encode distinct aspects of the data into separate variables. We propose to learn such representations using model architectures that generalise from standard VAEs, employing a general graphical model structure in the encoder and decoder. This allows us to train partially-specified models that make relatively strong assumptions about a subset of interpretable variables and rely on the flexibility of neural networks to learn representations for the remaining variables. We further define a general objective for semi-supervised learning in this model class, which can be approximated using an importance sampling procedure. We evaluate our framework's ability to learn disentangled representations, both by qualitative exploration of its generative capacity, and quantitative evaluation of its discriminative ability on a variety of models and datasets.

Tuan Anh Le, Maximilian Igl, Tom Rainforth et al.

We build on auto-encoding sequential Monte Carlo (AESMC): a method for model and proposal learning based on maximizing the lower bound to the log marginal likelihood in a broad family of structured probabilistic models. Our approach relies on the efficiency of sequential Monte Carlo (SMC) for performing inference in structured probabilistic models and the flexibility of deep neural networks to model complex conditional probability distributions. We develop additional theoretical insights and introduce a new training procedure which improves both model and proposal learning. We demonstrate that our approach provides a fast, easy-to-implement and scalable means for simultaneous model learning and proposal adaptation in deep generative models.

Atilim Gunes Baydin, Robert Cornish, David Martinez Rubio et al.

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov momentum, and Adam, showing that it significantly reduces the need for the manual tuning of the initial learning rate for these commonly used algorithms. Our method works by dynamically updating the learning rate during optimization using the gradient with respect to the learning rate of the update rule itself. Computing this "hypergradient" needs little additional computation, requires only one extra copy of the original gradient to be stored in memory, and relies upon nothing more than what is provided by reverse-mode automatic differentiation.

Tuan Anh Le, Atilim Gunes Baydin, Robert Zinkov et al.

We draw a formal connection between using synthetic training data to optimize neural network parameters and approximate, Bayesian, model-based reasoning. In particular, training a neural network using synthetic data can be viewed as learning a proposal distribution generator for approximate inference in the synthetic-data generative model. We demonstrate this connection in a recognition task where we develop a novel Captcha-breaking architecture and train it using synthetic data, demonstrating both state-of-the-art performance and a way of computing task-specific posterior uncertainty. Using a neural network trained this way, we also demonstrate successful breaking of real-world Captchas currently used by Facebook and Wikipedia. Reasoning from these empirical results and drawing connections with Bayesian modeling, we discuss the robustness of synthetic data results and suggest important considerations for ensuring good neural network generalization when training with synthetic data.

Tom Rainforth, Robert Cornish, Hongseok Yang et al.

There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this paper, we analyse the behaviour of nested Monte Carlo (NMC) schemes, for which classical convergence proofs are insufficient. We give conditions under which NMC will converge, establish a rate of convergence, and provide empirical data that suggests that this rate is observable in practice. Finally, we prove that general-purpose nested inference schemes are inherently biased. Our results serve to warn of the dangers associated with naive composition of inference and models.

N. Siddharth, Brooks Paige, Alban Desmaison et al.

We develop a framework for incorporating structured graphical models in the \emph{encoders} of variational autoencoders (VAEs) that allows us to induce interpretable representations through approximate variational inference. This allows us to both perform reasoning (e.g. classification) under the structural constraints of a given graphical model, and use deep generative models to deal with messy, high-dimensional domains where it is often difficult to model all the variation. Learning in this framework is carried out end-to-end with a variational objective, applying to both unsupervised and semi-supervised schemes.

David Janz, Brooks Paige, Tom Rainforth et al.

Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.

Tuan Anh Le, Atilim Gunes Baydin, Frank Wood

We introduce a method for using deep neural networks to amortize the cost of inference in models from the family induced by universal probabilistic programming languages, establishing a framework that combines the strengths of probabilistic programming and deep learning methods. We call what we do "compilation of inference" because our method transforms a denotational specification of an inference problem in the form of a probabilistic program written in a universal programming language into a trained neural network denoted in a neural network specification language. When at test time this neural network is fed observational data and executed, it performs approximate inference in the original model specified by the probabilistic program. Our training objective and learning procedure are designed to allow the trained neural network to be used as a proposal distribution in a sequential importance sampling inference engine. We illustrate our method on mixture models and Captcha solving and show significant speedups in the efficiency of inference.

Mike Wu, Yura Perov, Frank Wood et al.

Spreadsheet workbook contents are simple programs. Because of this, probabilistic programming techniques can be used to perform Bayesian inversion of spreadsheet computations. What is more, existing execution engines in spreadsheet applications such as Microsoft Excel can be made to do this using only built-in functionality. We demonstrate this by developing a native Excel implementation of both a particle Markov Chain Monte Carlo variant and black-box variational inference for spreadsheet probabilistic programming. The resulting engine performs probabilistically coherent inference over spreadsheet computations, notably including spreadsheets that include user-defined black-box functions. Spreadsheet engines that choose to integrate the functionality we describe in this paper will give their users the ability to both easily develop probabilistic models and maintain them over time by including actuals via a simple user-interface mechanism. For spreadsheet end-users this would mean having access to efficient and probabilistically coherent probabilistic modeling and inference for use in all kinds of decision making under uncertainty.

Brooks Paige, Frank Wood

We introduce a new approach for amortizing inference in directed graphical models by learning heuristic approximations to stochastic inverses, designed specifically for use as proposal distributions in sequential Monte Carlo methods. We describe a procedure for constructing and learning a structured neural network which represents an inverse factorization of the graphical model, resulting in a conditional density estimator that takes as input particular values of the observed random variables, and returns an approximation to the distribution of the latent variables. This recognition model can be learned offline, independent from any particular dataset, prior to performing inference. The output of these networks can be used as automatically-learned high-quality proposal distributions to accelerate sequential Monte Carlo across a diverse range of problem settings.

Tom Rainforth, Christian A. Naesseth, Fredrik Lindsten et al.

We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an extended space. We present empirical results that show significant improvements in mixing rates relative to both non-interacting PMCMC samplers, and a single PMCMC sampler with an equivalent memory and computational budget. An additional advantage of the iPMCMC method is that it is suitable for distributed and multi-core architectures.