arXiv subjects

José Miguel Hernández-Lobato

Publications and source records attributed to José Miguel Hernández-Lobato.

At least 91 records · Page 5Linked to original sources

arXiv2022

Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo

Variational Autoencoders (VAEs) have recently been highly successful at imputing and acquiring heterogeneous missing data. However, within this specific application domain, existing VAE methods are restricted by using only one layer of latent variables and strictly Gaussian posterior approximations. To address these limitations, we present HH-VAEM, a Hierarchical VAE model for mixed-type incomplete data that uses Hamiltonian Monte Carlo with automatic hyper-parameter tuning for improved approximate inference. Our experiments show that HH-VAEM outperforms existing baselines in the tasks of missing data imputation and supervised learning with missing features. Finally, we also present a sampling-based approach for efficiently computing the information gain when missing features are to be acquired with HH-VAEM. Our experiments show that this sampling-based approach is superior to alternatives based on Gaussian approximations.

cs.LG↗

arXiv2022

Adapting the Linearised Laplace Model Evidence for Modern Deep Learning

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection. We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting. We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.

stat.ML↗

arXiv2022

Uncertainty Estimation for Computed Tomography with a Linearised Deep Image Prior

Existing deep-learning based tomographic image reconstruction methods do not provide accurate estimates of reconstruction uncertainty, hindering their real-world deployment. This paper develops a method, termed as the linearised deep image prior (DIP), to estimate the uncertainty associated with reconstructions produced by the DIP with total variation regularisation (TV). Specifically, we endow the DIP with conjugate Gaussian-linear model type error-bars computed from a local linearisation of the neural network around its optimised parameters. To preserve conjugacy, we approximate the TV regulariser with a Gaussian surrogate. This approach provides pixel-wise uncertainty estimates and a marginal likelihood objective for hyperparameter optimisation. We demonstrate the method on synthetic data and real-measured high-resolution 2D $μ$CT data, and show that it provides superior calibration of uncertainty estimates relative to previous probabilistic formulations of the DIP. Our code is available at https://github.com/educating-dip/bayes_dip.

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arXiv2022

Bayesian Experimental Design for Computed Tomography with the Linearised Deep Image Prior

We investigate adaptive design based on a single sparse pilot scan for generating effective scanning strategies for computed tomography reconstruction. We propose a novel approach using the linearised deep image prior. It allows incorporating information from the pilot measurements into the angle selection criteria, while maintaining the tractability of a conjugate Gaussian-linear model. On a synthetically generated dataset with preferential directions, linearised DIP design allows reducing the number of scans by up to 30% relative to an equidistant angle baseline.

cs.CV↗

arXiv2022

Action-Sufficient State Representation Learning for Control with Structural Constraints

Perceived signals in real-world scenarios are usually high-dimensional and noisy, and finding and using their representation that contains essential and sufficient information required by downstream decision-making tasks will help improve computational efficiency and generalization ability in the tasks. In this paper, we focus on partially observable environments and propose to learn a minimal set of state representations that capture sufficient information for decision-making, termed \textit{Action-Sufficient state Representations} (ASRs). We build a generative environment model for the structural relationships among variables in the system and present a principled way to characterize ASRs based on structural constraints and the goal of maximizing cumulative reward in policy learning. We then develop a structured sequential Variational Auto-Encoder to estimate the environment model and extract ASRs. Our empirical results on CarRacing and VizDoom demonstrate a clear advantage of learning and using ASRs for policy learning. Moreover, the estimated environment model and ASRs allow learning behaviors from imagined outcomes in the compact latent space to improve sample efficiency.

cs.LG↗

arXiv2022

Fast Relative Entropy Coding with A* coding

Relative entropy coding (REC) algorithms encode a sample from a target distribution $Q$ using a proposal distribution $P$, such that the expected codelength is $\mathcal{O}(D_{KL}[Q \,||\, P])$. REC can be seamlessly integrated with existing learned compression models since, unlike entropy coding, it does not assume discrete $Q$ or $P$, and does not require quantisation. However, general REC algorithms require an intractable $Ω(e^{D_{KL}[Q \,||\, P]})$ runtime. We introduce AS* and AD* coding, two REC algorithms based on A* sampling. We prove that, for continuous distributions over $\mathbb{R}$, if the density ratio is unimodal, AS* has $\mathcal{O}(D_{\infty}[Q \,||\, P])$ expected runtime, where $D_{\infty}[Q \,||\, P]$ is the Rényi $\infty$-divergence. We provide experimental evidence that AD* also has $\mathcal{O}(D_{\infty}[Q \,||\, P])$ expected runtime. We prove that AS* and AD* achieve an expected codelength of $\mathcal{O}(D_{KL}[Q \,||\, P])$. Further, we introduce DAD*, an approximate algorithm based on AD* which retains its favourable runtime and has bias similar to that of alternative methods. Focusing on VAEs, we propose the IsoKL VAE (IKVAE), which can be used with DAD* to further improve compression efficiency. We evaluate A* coding with (IK)VAEs on MNIST, showing that it can losslessly compress images near the theoretically optimal limit.

cs.IT↗

arXiv2022

Depth Uncertainty Networks for Active Learning

In active learning, the size and complexity of the training dataset changes over time. Simple models that are well specified by the amount of data available at the start of active learning might suffer from bias as more points are actively sampled. Flexible models that might be well suited to the full dataset can suffer from overfitting towards the start of active learning. We tackle this problem using Depth Uncertainty Networks (DUNs), a BNN variant in which the depth of the network, and thus its complexity, is inferred. We find that DUNs outperform other BNN variants on several active learning tasks. Importantly, we show that on the tasks in which DUNs perform best they present notably less overfitting than baselines.

cs.LG↗

arXiv2022

Scalable One-Pass Optimisation of High-Dimensional Weight-Update Hyperparameters by Implicit Differentiation

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable computational cost. Some hypergradient-based one-pass methods exist, but these either cannot be applied to arbitrary optimiser hyperparameters (such as learning rates and momenta) or take several times longer to train than their base models. We extend these existing methods to develop an approximate hypergradient-based hyperparameter optimiser which is applicable to any continuous hyperparameter appearing in a differentiable model weight update, yet requires only one training episode, with no restarts. We also provide a motivating argument for convergence to the true hypergradient, and perform tractable gradient-based optimisation of independent learning rates for each model parameter. Our method performs competitively from varied random hyperparameter initialisations on several UCI datasets and Fashion-MNIST (using a one-layer MLP), Penn Treebank (using an LSTM) and CIFAR-10 (using a ResNet-18), in time only 2-3x greater than vanilla training.

cs.LG↗

arXiv2022

Bayesian Deep Learning via Subnetwork Inference

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace as a simple, scalable Bayesian deep learning method: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork using the linearized Laplace approximation. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach compares favorably to ensembles and less expressive posterior approximations over full networks. Our proposed subnetwork (linearized) Laplace method is implemented within the laplace PyTorch library at https://github.com/AlexImmer/Laplace.

cs.LG↗

arXiv2022

Bootstrap Your Flow

Normalizing flows are flexible, parameterized distributions that can be used to approximate expectations from intractable distributions via importance sampling. However, current flow-based approaches are limited on challenging targets where they either suffer from mode seeking behaviour or high variance in the training loss, or rely on samples from the target distribution, which may not be available. To address these challenges, we combine flows with annealed importance sampling (AIS), while using the $α$-divergence as our objective, in a novel training procedure, FAB (Flow AIS Bootstrap). Thereby, the flow and AIS improve each other in a bootstrapping manner. We demonstrate that FAB can be used to produce accurate approximations to complex target distributions, including Boltzmann distributions, in problems where previous flow-based methods fail.

cs.LG↗

arXiv2022

Resampling Base Distributions of Normalizing Flows

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.

stat.ML↗

arXiv2022

BSODA: A Bipartite Scalable Framework for Online Disease Diagnosis

A growing number of people are seeking healthcare advice online. Usually, they diagnose their medical conditions based on the symptoms they are experiencing, which is also known as self-diagnosis. From the machine learning perspective, online disease diagnosis is a sequential feature (symptom) selection and classification problem. Reinforcement learning (RL) methods are the standard approaches to this type of tasks. Generally, they perform well when the feature space is small, but frequently become inefficient in tasks with a large number of features, such as the self-diagnosis. To address the challenge, we propose a non-RL Bipartite Scalable framework for Online Disease diAgnosis, called BSODA. BSODA is composed of two cooperative branches that handle symptom-inquiry and disease-diagnosis, respectively. The inquiry branch determines which symptom to collect next by an information-theoretic reward. We employ a Product-of-Experts encoder to significantly improve the handling of partial observations of a large number of features. Besides, we propose several approximation methods to substantially reduce the computational cost of the reward to a level that is acceptable for online services. Additionally, we leverage the diagnosis model to estimate the reward more precisely. For the diagnosis branch, we use a knowledge-guided self-attention model to perform predictions. In particular, BSODA determines when to stop inquiry and output predictions using both the inquiry and diagnosis models. We demonstrate that BSODA outperforms the state-of-the-art methods on several public datasets. Moreover, we propose a novel evaluation method to test the transferability of symptom checking methods from synthetic to real-world tasks. Compared to existing RL baselines, BSODA is more effectively scalable to large search spaces.

cs.LG↗

arXiv2021

Addressing Bias in Active Learning with Depth Uncertainty Networks... or Not

Farquhar et al. [2021] show that correcting for active learning bias with underparameterised models leads to improved downstream performance. For overparameterised models such as NNs, however, correction leads either to decreased or unchanged performance. They suggest that this is due to an "overfitting bias" which offsets the active learning bias. We show that depth uncertainty networks operate in a low overfitting regime, much like underparameterised models. They should therefore see an increase in performance with bias correction. Surprisingly, they do not. We propose that this negative result, as well as the results Farquhar et al. [2021], can be explained via the lens of the bias-variance decomposition of generalisation error.

cs.LG↗

arXiv2021

DOCKSTRING: easy molecular docking yields better benchmarks for ligand design

The field of machine learning for drug discovery is witnessing an explosion of novel methods. These methods are often benchmarked on simple physicochemical properties such as solubility or general druglikeness, which can be readily computed. However, these properties are poor representatives of objective functions in drug design, mainly because they do not depend on the candidate's interaction with the target. By contrast, molecular docking is a widely successful method in drug discovery to estimate binding affinities. However, docking simulations require a significant amount of domain knowledge to set up correctly which hampers adoption. To this end, we present DOCKSTRING, a bundle for meaningful and robust comparison of ML models consisting of three components: (1) an open-source Python package for straightforward computation of docking scores; (2) an extensive dataset of docking scores and poses of more than 260K ligands for 58 medically-relevant targets; and (3) a set of pharmaceutically-relevant benchmark tasks including regression, virtual screening, and de novo design. The Python package implements a robust ligand and target preparation protocol that allows non-experts to obtain meaningful docking scores. Our dataset is the first to include docking poses, as well as the first of its size that is a full matrix, thus facilitating experiments in multiobjective optimization and transfer learning. Overall, our results indicate that docking scores are a more appropriate evaluation objective than simple physicochemical properties, yielding more realistic benchmark tasks and molecular candidates.

stat.ML↗

arXiv2021

Active Slices for Sliced Stein Discrepancy

Sliced Stein discrepancy (SSD) and its kernelized variants have demonstrated promising successes in goodness-of-fit tests and model learning in high dimensions. Despite their theoretical elegance, their empirical performance depends crucially on the search of optimal slicing directions to discriminate between two distributions. Unfortunately, previous gradient-based optimisation approaches for this task return sub-optimal results: they are computationally expensive, sensitive to initialization, and they lack theoretical guarantees for convergence. We address these issues in two steps. First, we provide theoretical results stating that the requirement of using optimal slicing directions in the kernelized version of SSD can be relaxed, validating the resulting discrepancy with finite random slicing directions. Second, given that good slicing directions are crucial for practical performance, we propose a fast algorithm for finding such slicing directions based on ideas of active sub-space construction and spectral decomposition. Experiments on goodness-of-fit tests and model learning show that our approach achieves both improved performance and faster convergence. Especially, we demonstrate a 14-80x speed-up in goodness-of-fit tests when comparing with gradient-based alternatives.

cs.LG↗

arXiv2021

Improving black-box optimization in VAE latent space using decoder uncertainty

Optimization in the latent space of variational autoencoders is a promising approach to generate high-dimensional discrete objects that maximize an expensive black-box property (e.g., drug-likeness in molecular generation, function approximation with arithmetic expressions). However, existing methods lack robustness as they may decide to explore areas of the latent space for which no data was available during training and where the decoder can be unreliable, leading to the generation of unrealistic or invalid objects. We propose to leverage the epistemic uncertainty of the decoder to guide the optimization process. This is not trivial though, as a naive estimation of uncertainty in the high-dimensional and structured settings we consider would result in high estimator variance. To solve this problem, we introduce an importance sampling-based estimator that provides more robust estimates of epistemic uncertainty. Our uncertainty-guided optimization approach does not require modifications of the model architecture nor the training process. It produces samples with a better trade-off between black-box objective and validity of the generated samples, sometimes improving both simultaneously. We illustrate these advantages across several experimental settings in digit generation, arithmetic expression approximation and molecule generation for drug design.

cs.LG↗

arXiv2021

Compressing Images by Encoding Their Latent Representations with Relative Entropy Coding

Variational Autoencoders (VAEs) have seen widespread use in learned image compression. They are used to learn expressive latent representations on which downstream compression methods can operate with high efficiency. Recently proposed 'bits-back' methods can indirectly encode the latent representation of images with codelength close to the relative entropy between the latent posterior and the prior. However, due to the underlying algorithm, these methods can only be used for lossless compression, and they only achieve their nominal efficiency when compressing multiple images simultaneously; they are inefficient for compressing single images. As an alternative, we propose a novel method, Relative Entropy Coding (REC), that can directly encode the latent representation with codelength close to the relative entropy for single images, supported by our empirical results obtained on the Cifar10, ImageNet32 and Kodak datasets. Moreover, unlike previous bits-back methods, REC is immediately applicable to lossy compression, where it is competitive with the state-of-the-art on the Kodak dataset.

cs.IT↗

arXiv2021

Instructions and Guide for Diagnostic Questions: The NeurIPS 2020 Education Challenge

Digital technologies are becoming increasingly prevalent in education, enabling personalized, high quality education resources to be accessible by students across the world. Importantly, among these resources are diagnostic questions: the answers that the students give to these questions reveal key information about the specific nature of misconceptions that the students may hold. Analyzing the massive quantities of data stemming from students' interactions with these diagnostic questions can help us more accurately understand the students' learning status and thus allow us to automate learning curriculum recommendations. In this competition, participants will focus on the students' answer records to these multiple-choice diagnostic questions, with the aim of 1) accurately predicting which answers the students provide; 2) accurately predicting which questions have high quality; and 3) determining a personalized sequence of questions for each student that best predicts the student's answers. These tasks closely mimic the goals of a real-world educational platform and are highly representative of the educational challenges faced today. We provide over 20 million examples of students' answers to mathematics questions from Eedi, a leading educational platform which thousands of students interact with daily around the globe. Participants to this competition have a chance to make a lasting, real-world impact on the quality of personalized education for millions of students across the world.

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