An Introduction to Probabilistic Programming

This document is designed to be a first-year graduate-level introduction to probabilistic programming. It not only provides a thorough background for anyone wishing to use a probabilistic programming system, but also introduces the techniques needed to design and build these systems. It is aimed at people who have an undergraduate-level understanding of either or, ideally, both probabilistic machine learning and programming languages. We start with a discussion of model-based reasoning and explain why conditioning as a foundational computation is central to the fields of probabilistic machine learning and artificial intelligence. We then introduce a simple first-order probabilistic programming language (PPL) whose programs define static-computation-graph, finite-variable-cardinality models. In the context of this restricted PPL we introduce fundamental inference algorithms and describe how they can be implemented in the context of models denoted by probabilistic programs. In the second part of this document, we introduce a higher-order probabilistic programming language, with a functionality analogous to that of established programming languages. This affords the opportunity to define models with dynamic computation graphs, at the cost of requiring inference methods that generate samples by repeatedly executing the program. Foundational inference algorithms for this kind of probabilistic programming language are explained in the context of an interface between program executions and an inference controller. This document closes with a chapter on advanced topics which we believe to be, at the time of writing, interesting directions for probabilistic programming research; directions that point towards a tight integration with deep neural network research and the development of systems for next-generation artificial intelligence applications.

Take a Look Around: Using Street View and Satellite Images to Estimate House Prices

When an individual purchases a home, they simultaneously purchase its structural features, its accessibility to work, and the neighborhood amenities. Some amenities, such as air quality, are measurable whilst others, such as the prestige or the visual impression of a neighborhood, are difficult to quantify. Despite the well-known impacts intangible housing features have on house prices, limited attention has been given to systematically quantifying these difficult to measure amenities. Two issues have lead to this neglect. Not only do few quantitative methods exist that can measure the urban environment, but that the collection of such data is both costly and subjective. We show that street image and satellite image data can capture these urban qualities and improve the estimation of house prices. We propose a pipeline that uses a deep neural network model to automatically extract visual features from images to estimate house prices in London, UK. We make use of traditional housing features such as age, size and accessibility as well as visual features from Google Street View images and Bing aerial images in estimating the house price model. We find encouraging results where learning to characterize the urban quality of a neighborhood improves house price prediction, even when generalizing to previously unseen London boroughs. We explore the use of non-linear vs. linear methods to fuse these cues with conventional models of house pricing, and show how the interpretability of linear models allows us to directly extract the visual desirability of neighborhoods as proxy variables that are both of interest in their own right, and could be used as inputs to other econometric methods. This is particularly valuable as once the network has been trained with the training data, it can be applied elsewhere, allowing us to generate vivid dense maps of the desirability of London streets.

Structured Disentangled Representations

Deep latent-variable models learn representations of high-dimensional data in an unsupervised manner. A number of recent efforts have focused on learning representations that disentangle statistically independent axes of variation by introducing modifications to the standard objective function. These approaches generally assume a simple diagonal Gaussian prior and as a result are not able to reliably disentangle discrete factors of variation. We propose a two-level hierarchical objective to control relative degree of statistical independence between blocks of variables and individual variables within blocks. We derive this objective as a generalization of the evidence lower bound, which allows us to explicitly represent the trade-offs between mutual information between data and representation, KL divergence between representation and prior, and coverage of the support of the empirical data distribution. Experiments on a variety of datasets demonstrate that our objective can not only disentangle discrete variables, but that doing so also improves disentanglement of other variables and, importantly, generalization even to unseen combinations of factors.

Predicting Electron Paths

Chemical reactions can be described as the stepwise redistribution of electrons in molecules. As such, reactions are often depicted using "arrow-pushing" diagrams which show this movement as a sequence of arrows. We propose an electron path prediction model (ELECTRO) to learn these sequences directly from raw reaction data. Instead of predicting product molecules directly from reactant molecules in one shot, learning a model of electron movement has the benefits of (a) being easy for chemists to interpret, (b) incorporating constraints of chemistry, such as balanced atom counts before and after the reaction, and (c) naturally encoding the sparsity of chemical reactions, which usually involve changes in only a small number of atoms in the reactants. We design a method to extract approximate reaction paths from any dataset of atom-mapped reaction SMILES strings. Our model achieves state-of-the-art results on a subset of the UPSTO reaction dataset. Furthermore, we show that our model recovers a basic knowledge of chemistry without being explicitly trained to do so.

Inference Networks for Sequential Monte Carlo in Graphical Models

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.

Learning Disentangled Representations with Semi-Supervised Deep Generative Models

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.

Kernel Sequential Monte Carlo

We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator's geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator's ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples.

Interacting Particle Markov Chain Monte Carlo

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.

Grammar Variational Autoencoder

Deep generative models have been wildly successful at learning coherent latent representations for continuous data such as video and audio. However, generative modeling of discrete data such as arithmetic expressions and molecular structures still poses significant challenges. Crucially, state-of-the-art methods often produce outputs that are not valid. We make the key observation that frequently, discrete data can be represented as a parse tree from a context-free grammar. We propose a variational autoencoder which encodes and decodes directly to and from these parse trees, ensuring the generated outputs are always valid. Surprisingly, we show that not only does our model more often generate valid outputs, it also learns a more coherent latent space in which nearby points decode to similar discrete outputs. We demonstrate the effectiveness of our learned models by showing their improved performance in Bayesian optimization for symbolic regression and molecular synthesis.

Inducing Interpretable Representations with Variational Autoencoders

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.