Yingzhen Li

Hee Suk Yoon, Joshua Tian Jin Tee, Eunseop Yoon et al.

Studies have shown that modern neural networks tend to be poorly calibrated due to over-confident predictions. Traditionally, post-processing methods have been used to calibrate the model after training. In recent years, various trainable calibration measures have been proposed to incorporate them directly into the training process. However, these methods all incorporate internal hyperparameters, and the performance of these calibration objectives relies on tuning these hyperparameters, incurring more computational costs as the size of neural networks and datasets become larger. As such, we present Expected Squared Difference (ESD), a tuning-free (i.e., hyperparameter-free) trainable calibration objective loss, where we view the calibration error from the perspective of the squared difference between the two expectations. With extensive experiments on several architectures (CNNs, Transformers) and datasets, we demonstrate that (1) incorporating ESD into the training improves model calibration in various batch size settings without the need for internal hyperparameter tuning, (2) ESD yields the best-calibrated results compared with previous approaches, and (3) ESD drastically improves the computational costs required for calibration during training due to the absence of internal hyperparameter. The code is publicly accessible at https://github.com/hee-suk-yoon/ESD.

Yanzhi Chen, Weihao Sun, Yingzhen Li et al. · cambridge

The task of infomin learning aims to learn a representation with high utility while being uninformative about a specified target, with the latter achieved by minimising the mutual information between the representation and the target. It has broad applications, ranging from training fair prediction models against protected attributes, to unsupervised learning with disentangled representations. Recent works on infomin learning mainly use adversarial training, which involves training a neural network to estimate mutual information or its proxy and thus is slow and difficult to optimise. Drawing on recent advances in slicing techniques, we propose a new infomin learning approach, which uses a novel proxy metric to mutual information. We further derive an accurate and analytically computable approximation to this proxy metric, thereby removing the need of constructing neural network-based mutual information estimators. Experiments on algorithmic fairness, disentangled representation learning and domain adaptation verify that our method can effectively remove unwanted information with limited time budget.

Zijing Ou, Tingyang Xu, Qinliang Su et al.

Learning neural set functions becomes increasingly more important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function learning under the function value oracle, which, however, requires expensive supervision signals. This renders it impractical for applications with only weak supervisions under the Optimal Subset (OS) oracle, the study of which is surprisingly overlooked. In this work, we present a principled yet practical maximum likelihood learning framework, termed as EquiVSet, that simultaneously meets the following desiderata of learning set functions under the OS oracle: i) permutation invariance of the set mass function being modeled; ii) permission of varying ground set; iii) minimum prior; and iv) scalability. The main components of our framework involve: an energy-based treatment of the set mass function, DeepSet-style architectures to handle permutation invariance, mean-field variational inference, and its amortized variants. Thanks to the elegant combination of these advanced architectures, empirical studies on three real-world applications (including Amazon product recommendation, set anomaly detection, and compound selection for virtual screening) demonstrate that EquiVSet outperforms the baselines by a large margin.

Ryutaro Tanno, Melanie F. Pradier, Aditya Nori et al.

Prediction failures of machine learning models often arise from deficiencies in training data, such as incorrect labels, outliers, and selection biases. However, such data points that are responsible for a given failure mode are generally not known a priori, let alone a mechanism for repairing the failure. This work draws on the Bayesian view of continual learning, and develops a generic framework for both, identifying training examples that have given rise to the target failure, and fixing the model through erasing information about them. This framework naturally allows leveraging recent advances in continual learning to this new problem of model repairment, while subsuming the existing works on influence functions and data deletion as specific instances. Experimentally, the proposed approach outperforms the baselines for both identification of detrimental training data and fixing model failures in a generalisable manner.

Harrison Zhu, Carles Balsells Rodas, Yingzhen Li

Sequential VAEs have been successfully considered for many high-dimensional time series modelling problems, with many variant models relying on discrete-time mechanisms such as recurrent neural networks (RNNs). On the other hand, continuous-time methods have recently gained attraction, especially in the context of irregularly-sampled time series, where they can better handle the data than discrete-time methods. One such class are Gaussian process variational autoencoders (GPVAEs), where the VAE prior is set as a Gaussian process (GP). However, a major limitation of GPVAEs is that it inherits the cubic computational cost as GPs, making it unattractive to practioners. In this work, we leverage the equivalent discrete state space representation of Markovian GPs to enable linear time GPVAE training via Kalman filtering and smoothing. For our model, Markovian GPVAE (MGPVAE), we show on a variety of high-dimensional temporal and spatiotemporal tasks that our method performs favourably compared to existing approaches whilst being computationally highly scalable.

Wenlong Chen, Yingzhen Li

Transformer models have achieved profound success in prediction tasks in a wide range of applications in natural language processing, speech recognition and computer vision. Extending Transformer's success to safety-critical domains requires calibrated uncertainty estimation which remains under-explored. To address this, we propose Sparse Gaussian Process attention (SGPA), which performs Bayesian inference directly in the output space of multi-head attention blocks (MHAs) in transformer to calibrate its uncertainty. It replaces the scaled dot-product operation with a valid symmetric kernel and uses sparse Gaussian processes (SGP) techniques to approximate the posterior processes of MHA outputs. Empirically, on a suite of prediction tasks on text, images and graphs, SGPA-based Transformers achieve competitive predictive accuracy, while noticeably improving both in-distribution calibration and out-of-distribution robustness and detection.

Tobias Schröder, Zijing Ou, Jen Ning Lim et al.

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

Hee Suk Yoon, Eunseop Yoon, Joshua Tian Jin Tee et al.

In deep learning, test-time adaptation has gained attention as a method for model fine-tuning without the need for labeled data. A prime exemplification is the recently proposed test-time prompt tuning for large-scale vision-language models such as CLIP. Unfortunately, these prompts have been mainly developed to improve accuracy, overlooking the importance of calibration, which is a crucial aspect for quantifying prediction uncertainty. However, traditional calibration methods rely on substantial amounts of labeled data, making them impractical for test-time scenarios. To this end, this paper explores calibration during test-time prompt tuning by leveraging the inherent properties of CLIP. Through a series of observations, we find that the prompt choice significantly affects the calibration in CLIP, where the prompts leading to higher text feature dispersion result in better-calibrated predictions. Introducing the Average Text Feature Dispersion (ATFD), we establish its relationship with calibration error and present a novel method, Calibrated Test-time Prompt Tuning (C-TPT), for optimizing prompts during test-time with enhanced calibration. Through extensive experiments on different CLIP architectures and datasets, we show that C-TPT can effectively improve the calibration of test-time prompt tuning without needing labeled data. The code is publicly accessible at https://github.com/hee-suk-yoon/C-TPT.

Tobias Schröder, Zijing Ou, Yingzhen Li et al.

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only requires the evaluation of the energy function at data points and their perturbed counter parts, thus not relying on sampling strategies like Markov chain Monte Carlo (MCMC). Energy discrepancy offers theoretical guarantees for a broad class of perturbation processes of which we investigate three types: perturbations based on Bernoulli noise, based on deterministic transforms, and based on neighbourhood structures. We demonstrate their relative performance on lattice Ising models, binary synthetic data, and discrete image data sets.

Yanzhi Chen, Zijing Ou, Adrian Weller et al.

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. This preliminary estimate serves as a bridge between the joint and the marginal distribution, and by comparing with this bridge distribution we can easily obtain the true difference between the joint distributions and the marginal distributions. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.

Yohan Jung, Hyungi Lee, Wenlong Chen et al.

Despite recent progress, continual learning still does not match the performance of batch training. To avoid catastrophic forgetting, we need to build compact memory of essential past knowledge, but no clear solution has yet emerged, even for shallow neural networks with just one or two layers. In this paper, we present a new method to build compact memory for logistic regression. Our method is based on a result by Khan and Swaroop [2021] who show the existence of optimal memory for such models. We formulate the search for the optimal memory as Hessian-matching and propose a probabilistic PCA method to estimate them. Our approach can drastically improve accuracy compared to Experience Replay. For instance, on Split-ImageNet, we get 60% accuracy compared to 30% obtained by replay with memory-size equivalent to 0.3% of the data size. Increasing the memory size to 2% further boosts the accuracy to 74%, closing the gap to the batch accuracy of 77.6% on this task. Our work opens a new direction for building compact memory that can also be useful in the future for continual deep learning.

Theodore Papamarkou, Maria Skoularidou, Konstantina Palla et al.

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential.

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.

Tobias Schröder, Zijing Ou, Yingzhen Li et al.

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. Finally, we train EBMs on tabular data sets with applications in synthetic data generation and calibrated classification.

Zijing Ou, Chinmay Pani, Yingzhen Li

Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints. To this end, we propose a Sequential Monte Carlo (SMC) framework that enables scalable inference-time control of discrete diffusion models through principled importance weighting and optimal proposal construction. Specifically, our approach derives tractable importance weights for a range of intermediate targets and characterises the optimal proposal, for which we develop two practical approximations: a first-order gradient-based approximation and an amortised proposal trained to minimise the log-variance of the importance weights. Empirical results across synthetic tasks, language modelling, biology design, and text-to-image generation demonstrate that our framework enhances controllability and sample quality, highlighting the effectiveness of SMC as a versatile recipe for scaling discrete diffusion models at inference time.

Wuhao Chen, Zijing Ou, Yingzhen Li

Sampling from unnormalized densities presents a fundamental challenge with wide-ranging applications, from posterior inference to molecular dynamics simulations. Continuous flow-based neural samplers offer a promising approach, learning a velocity field that satisfies key principles of marginal density evolution (e.g., the continuity equation) to generate samples. However, this learning procedure requires accurate estimation of intractable terms linked to the computationally challenging partition function, for which existing estimators often suffer from high variance or low accuracy. To overcome this, we introduce an improved estimator for these challenging quantities, employing a velocity-driven Sequential Monte Carlo method enhanced with control variates. Furthermore, we introduce a shortcut consistency model to boost the runtime efficiency of the flow-based neural sampler by minimizing its required sampling steps. Our proposed Neural Flow Shortcut Sampler empirically outperforms existing flow-based neural samplers on both synthetic datasets and complex n-body system targets.

Junyu Xuan, Wenlong Chen, Yingzhen Li

Bayesian Optimisation (BO) is a powerful tool for optimising expensive blackbox functions but its effectiveness diminishes in highdimensional spaces due to sparse data and poor surrogate model scalability While Variational Autoencoder (VAE) based approaches address this by learning low-dimensional latent representations the reconstructionbased objective function often brings the functional distribution mismatch between the latent space and original space leading to suboptimal optimisation performance In this paper we first analyse the reason why reconstructiononly loss may lead to distribution mismatch and then propose HiBBO a novel BO framework that introduces the space consistency into the latent space construction in VAE using HiPPO - a method for longterm sequence modelling - to reduce the functional distribution mismatch between the latent space and original space Experiments on highdimensional benchmark tasks demonstrate that HiBBO outperforms existing VAEBO methods in convergence speed and solution quality Our work bridges the gap between high-dimensional sequence representation learning and efficient Bayesian Optimisation enabling broader applications in neural architecture search materials science and beyond.

I. Shavindra Jayasekera, Jacob Si, Filippo Valdettaro et al.

As large language models (LLMs) gain popularity in conducting prediction tasks in-context, understanding the sources of uncertainty in in-context learning becomes essential to ensuring reliability. The recent hypothesis of in-context learning performing predictive Bayesian inference opens the avenue for Bayesian uncertainty estimation, particularly for decomposing uncertainty into epistemic uncertainty due to lack of in-context data and aleatoric uncertainty inherent in the in-context prediction task. However, the decomposition idea remains under-explored due to the intractability of the latent parameter posterior from the underlying Bayesian model. In this work, we introduce a variational uncertainty decomposition framework for in-context learning without explicitly sampling from the latent parameter posterior, by optimising auxiliary queries as probes to obtain an upper bound to the aleatoric uncertainty of an LLM's in-context learning procedure, which also induces a lower bound to the epistemic uncertainty. Through experiments on synthetic and real-world tasks, we show quantitatively and qualitatively that the decomposed uncertainties obtained from our method exhibit desirable properties of epistemic and aleatoric uncertainty.

Wenlong Chen, Bolian Li, Ruqi Zhang et al.

Bayesian methods have shown success in deep learning applications. For example, in predictive tasks, Bayesian neural networks leverage Bayesian reasoning of model uncertainty to improve the reliability and uncertainty awareness of deep neural networks. In generative modeling domain, many widely used deep generative models, such as deep latent variable models, require approximate Bayesian inference to infer their latent variables for the training. In this chapter, we provide an introduction to approximate inference techniques as Bayesian computation methods applied to deep learning models, with a focus on Bayesian neural networks and deep generative models. We review two arguably most popular approximate Bayesian computational methods, stochastic gradient Markov chain Monte Carlo (SG-MCMC) and variational inference (VI), and explain their unique challenges in posterior inference as well as the solutions when applied to deep learning models.

Wenlong Chen, Wenlin Chen, Lapo Rastrelli et al.

Diffusion models, which can be viewed as a special case of hierarchical variational autoencoders (HVAEs), have shown profound success in generating photo-realistic images. In contrast, standard HVAEs often produce images of inferior quality compared to diffusion models. In this paper, we hypothesize that the success of diffusion models can be partly attributed to the additional self-supervision information for their intermediate latent states provided by corrupted images, which along with the original image form a pseudo video. Based on this hypothesis, we explore the possibility of improving other types of generative models with such pseudo videos. Specifically, we first extend a given image generative model to their video generative model counterpart, and then train the video generative model on pseudo videos constructed by applying data augmentation to the original images. Furthermore, we analyze the potential issues of first-order Markov data augmentation methods, which are typically used in diffusion models, and propose to use more expressive data augmentation to construct more useful information in pseudo videos. Our empirical results on the CIFAR10 and CelebA datasets demonstrate that improved image generation quality can be achieved with additional self-supervised information from pseudo videos.

Carles Balsells-Rodas, Yixin Wang, Pedro A. M. Mediano et al.

Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to nonstationary time series with time-dependent effects or heterogeneous noise. In this work we address nonstationarity via regime-dependent causal structures. We first establish identifiability for high-order Markov Switching Models, which provide the foundations for identifiable regime-dependent causal discovery. Our empirical studies demonstrate the scalability of our proposed approach for high-order regime-dependent structure estimation, and we illustrate its applicability on brain activity data.

Zijing Ou, Mingtian Zhang, Andi Zhang et al.

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed covariance moment matching technique and introduce a novel method for learning the diagonal covariance. Unlike traditional data-driven diagonal covariance approximation approaches, our method involves directly regressing the optimal diagonal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency, recall rate and likelihood of commonly used diffusion models.

Carles Balsells-Rodas, Yixin Wang, Yingzhen Li

The identifiability of latent variable models has received increasing attention due to its relevance in interpretability and out-of-distribution generalisation. In this work, we study the identifiability of Switching Dynamical Systems, taking an initial step toward extending identifiability analysis to sequential latent variable models. We first prove the identifiability of Markov Switching Models, which commonly serve as the prior distribution for the continuous latent variables in Switching Dynamical Systems. We present identification conditions for first-order Markov dependency structures, whose transition distribution is parametrised via non-linear Gaussians. We then establish the identifiability of the latent variables and non-linear mappings in Switching Dynamical Systems up to affine transformations, by leveraging identifiability analysis techniques from identifiable deep latent variable models. We finally develop estimation algorithms for identifiable Switching Dynamical Systems. Throughout empirical studies, we demonstrate the practicality of identifiable Switching Dynamical Systems for segmenting high-dimensional time series such as videos, and showcase the use of identifiable Markov Switching Models for regime-dependent causal discovery in climate data.

Wenbo Gong, Yingzhen Li

Scoring matching (SM), and its related counterpart, Stein discrepancy (SD) have achieved great success in model training and evaluations. However, recent research shows their limitations when dealing with certain types of distributions. One possible fix is incorporating the original score matching (or Stein discrepancy) with a diffusion matrix, which is called diffusion score matching (DSM) (or diffusion Stein discrepancy (DSD)). However, the lack of interpretation of the diffusion limits its usage within simple distributions and manually chosen matrix. In this work, we plan to fill this gap by interpreting the diffusion matrix using normalizing flows. Specifically, we theoretically prove that DSM (or DSD) is equivalent to the original score matching (or Stein discrepancy) evaluated in the transformed space defined by the normalizing flow, where the diffusion matrix is the inverse of the flow's Jacobian matrix. In addition, we also build its connection to Riemannian manifolds and further extend it to continuous flows, where the change of DSM is characterized by an ODE.

Hippolyt Ritter, Martin Kukla, Cheng Zhang et al.

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage several times higher than their deterministic counterparts. To address this, we augment the weight matrix of each layer with a small number of inducing weights, thereby projecting the uncertainty quantification into such low dimensional spaces. We further extend Matheron's conditional Gaussian sampling rule to enable fast weight sampling, which enables our inference method to maintain reasonable run-time as compared with ensembles. Importantly, our approach achieves competitive performance to the state-of-the-art in prediction and uncertainty estimation tasks with fully connected neural networks and ResNets, while reducing the parameter size to $\leq 24.3\%$ of that of a $single$ neural network.

Angus Lamb, Evgeny Saveliev, Yingzhen Li et al.

While deep learning has obtained state-of-the-art results in many applications, the adaptation of neural network architectures to incorporate new output features remains a challenge, as neural networks are commonly trained to produce a fixed output dimension. This issue is particularly severe in online learning settings, where new output features, such as items in a recommender system, are added continually with few or no associated observations. As such, methods for adapting neural networks to novel features which are both time and data-efficient are desired. To address this, we propose the Contextual HyperNetwork (CHN), an auxiliary model which generates parameters for extending the base model to a new feature, by utilizing both existing data as well as any observations and/or metadata associated with the new feature. At prediction time, the CHN requires only a single forward pass through a neural network, yielding a significant speed-up when compared to re-training and fine-tuning approaches. To assess the performance of CHNs, we use a CHN to augment a partial variational autoencoder (P-VAE), a deep generative model which can impute the values of missing features in sparsely-observed data. We show that this system obtains improved few-shot learning performance for novel features over existing imputation and meta-learning baselines across recommender systems, e-learning, and healthcare tasks.

Wenbo Gong, Kaibo Zhang, Yingzhen Li et al.

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.

Yi Zhu, Ehsan Shareghi, Yingzhen Li et al.

Semi-supervised learning through deep generative models and multi-lingual pretraining techniques have orchestrated tremendous success across different areas of NLP. Nonetheless, their development has happened in isolation, while the combination of both could potentially be effective for tackling task-specific labelled data shortage. To bridge this gap, we combine semi-supervised deep generative models and multi-lingual pretraining to form a pipeline for document classification task. Compared to strong supervised learning baselines, our semi-supervised classification framework is highly competitive and outperforms the state-of-the-art counterparts in low-resource settings across several languages.

Haiyan Yin, Yingzhen Li, Sinno Jialin Pan et al.

Solving real-life sequential decision making problems under partial observability involves an exploration-exploitation problem. To be successful, an agent needs to efficiently gather valuable information about the state of the world for making rewarding decisions. However, in real-life, acquiring valuable information is often highly costly, e.g., in the medical domain, information acquisition might correspond to performing a medical test on a patient. This poses a significant challenge for the agent to perform optimally for the task while reducing the cost for information acquisition. In this paper, we propose a model-based reinforcement learning framework that learns an active feature acquisition policy to solve the exploration-exploitation problem during its execution. Key to the success is a novel sequential variational auto-encoder that learns high-quality representations from partially observed states, which are then used by the policy to maximize the task reward in a cost efficient manner. We demonstrate the efficacy of our proposed framework in a control domain as well as using a medical simulator. In both tasks, our proposed method outperforms conventional baselines and results in policies with greater cost efficiency.

Philip J. Ball, Yingzhen Li, Angus Lamb et al.

Humans are efficient continual learning systems; we continually learn new skills from birth with finite cells and resources. Our learning is highly optimized both in terms of capacity and time while not suffering from catastrophic forgetting. In this work we study the efficiency of continual learning systems, taking inspiration from human learning. In particular, inspired by the mechanisms of sleep, we evaluate popular pruning-based continual learning algorithms, using PackNet as a case study. First, we identify that weight freezing, which is used in continual learning without biological justification, can result in over $2\times$ as many weights being used for a given level of performance. Secondly, we note the similarity in human day and night time behaviors to the training and pruning phases respectively of PackNet. We study a setting where the pruning phase is given a time budget, and identify connections between iterative pruning and multiple sleep cycles in humans. We show there exists an optimal choice of iteration v.s. epochs given different tasks.

Victor Prokhorov, Yingzhen Li, Ehsan Shareghi et al.

It has been long known that sparsity is an effective inductive bias for learning efficient representation of data in vectors with fixed dimensionality, and it has been explored in many areas of representation learning. Of particular interest to this work is the investigation of the sparsity within the VAE framework which has been explored a lot in the image domain, but has been lacking even a basic level of exploration in NLP. Additionally, NLP is also lagging behind in terms of learning sparse representations of large units of text e.g., sentences. We use the VAEs that induce sparse latent representations of large units of text to address the aforementioned shortcomings. First, we move in this direction by measuring the success of unsupervised state-of-the-art (SOTA) and other strong VAE-based sparsification baselines for text and propose a hierarchical sparse VAE model to address the stability issue of SOTA. Then, we look at the implications of sparsity on text classification across 3 datasets, and highlight a link between performance of sparse latent representations on downstream tasks and its ability to encode task-related information.

Chaochao Lu, Richard E. Turner, Yingzhen Li et al.

Traditional deep generative models of images and other spatial modalities can only generate fixed sized outputs. The generated images have exactly the same resolution as the training images, which is dictated by the number of layers in the underlying neural network. Recent work has shown, however, that feeding spatial noise vectors into a fully convolutional neural network enables both generation of arbitrary resolution output images as well as training on arbitrary resolution training images. While this work has provided impressive empirical results, little theoretical interpretation was provided to explain the underlying generative process. In this paper we provide a firm theoretical interpretation for infinite spatial generation, by drawing connections to spatial stochastic processes. We use the resulting intuition to improve upon existing spatially infinite generative models to enable more efficient training through a model that we call an infinite generative adversarial network, or $\infty$-GAN. Experiments on world map generation, panoramic images and texture synthesis verify the ability of $\infty$-GAN to efficiently generate images of arbitrary size.

Ruqi Zhang, Yingzhen Li, Christopher De Sa et al.

Variational inference (VI) plays an essential role in approximate Bayesian inference due to its computational efficiency and broad applicability. Crucial to the performance of VI is the selection of the associated divergence measure, as VI approximates the intractable distribution by minimizing this divergence. In this paper we propose a meta-learning algorithm to learn the divergence metric suited for the task of interest, automating the design of VI methods. In addition, we learn the initialization of the variational parameters without additional cost when our method is deployed in the few-shot learning scenarios. We demonstrate our approach outperforms standard VI on Gaussian mixture distribution approximation, Bayesian neural network regression, image generation with variational autoencoders and recommender systems with a partial variational autoencoder.

Wenbo Gong, Yingzhen Li, José Miguel Hernández-Lobato

Kernelized Stein discrepancy (KSD), though being extensively used in goodness-of-fit tests and model learning, suffers from the curse-of-dimensionality. We address this issue by proposing the sliced Stein discrepancy and its scalable and kernelized variants, which employ kernel-based test functions defined on the optimal one-dimensional projections. When applied to goodness-of-fit tests, extensive experiments show the proposed discrepancy significantly outperforms KSD and various baselines in high dimensions. For model learning, we show its advantages over existing Stein discrepancy baselines by training independent component analysis models with different discrepancies. We further propose a novel particle inference method called sliced Stein variational gradient descent (S-SVGD) which alleviates the mode-collapse issue of SVGD in training variational autoencoders.

Cheng Zhang, Kun Zhang, Yingzhen Li

We present a causal view on the robustness of neural networks against input manipulations, which applies not only to traditional classification tasks but also to general measurement data. Based on this view, we design a deep causal manipulation augmented model (deep CAMA) which explicitly models possible manipulations on certain causes leading to changes in the observed effect. We further develop data augmentation and test-time fine-tuning methods to improve deep CAMA's robustness. When compared with discriminative deep neural networks, our proposed model shows superior robustness against unseen manipulations. As a by-product, our model achieves disentangled representation which separates the representation of manipulations from those of other latent causes.

Sebastian Lunz, Yingzhen Li, Andrew Fitzgibbon et al.

Recent work has shown the ability to learn generative models for 3D shapes from only unstructured 2D images. However, training such models requires differentiating through the rasterization step of the rendering process, therefore past work has focused on developing bespoke rendering models which smooth over this non-differentiable process in various ways. Such models are thus unable to take advantage of the photo-realistic, fully featured, industrial renderers built by the gaming and graphics industry. In this paper we introduce the first scalable training technique for 3D generative models from 2D data which utilizes an off-the-shelf non-differentiable renderer. To account for the non-differentiability, we introduce a proxy neural renderer to match the output of the non-differentiable renderer. We further propose discriminator output matching to ensure that the neural renderer learns to smooth over the rasterization appropriately. We evaluate our model on images rendered from our generated 3D shapes, and show that our model can consistently learn to generate better shapes than existing models when trained with exclusively unstructured 2D images.

Maximilian Igl, Kamil Ciosek, Yingzhen Li et al.

The ability for policies to generalize to new environments is key to the broad application of RL agents. A promising approach to prevent an agent's policy from overfitting to a limited set of training environments is to apply regularization techniques originally developed for supervised learning. However, there are stark differences between supervised learning and RL. We discuss those differences and propose modifications to existing regularization techniques in order to better adapt them to RL. In particular, we focus on regularization techniques relying on the injection of noise into the learned function, a family that includes some of the most widely used approaches such as Dropout and Batch Normalization. To adapt them to RL, we propose Selective Noise Injection (SNI), which maintains the regularizing effect the injected noise has, while mitigating the adverse effects it has on the gradient quality. Furthermore, we demonstrate that the Information Bottleneck (IB) is a particularly well suited regularization technique for RL as it is effective in the low-data regime encountered early on in training RL agents. Combining the IB with SNI, we significantly outperform current state of the art results, including on the recently proposed generalization benchmark Coinrun.

Victor Prokhorov, Ehsan Shareghi, Yingzhen Li et al.

Variational Autoencoders (VAEs) are known to suffer from learning uninformative latent representation of the input due to issues such as approximated posterior collapse, or entanglement of the latent space. We impose an explicit constraint on the Kullback-Leibler (KL) divergence term inside the VAE objective function. While the explicit constraint naturally avoids posterior collapse, we use it to further understand the significance of the KL term in controlling the information transmitted through the VAE channel. Within this framework, we explore different properties of the estimated posterior distribution, and highlight the trade-off between the amount of information encoded in a latent code during training, and the generative capacity of the model.

Andrew Y. K. Foong, David R. Burt, Yingzhen Li et al.

While Bayesian neural networks (BNNs) hold the promise of being flexible, well-calibrated statistical models, inference often requires approximations whose consequences are poorly understood. We study the quality of common variational methods in approximating the Bayesian predictive distribution. For single-hidden layer ReLU BNNs, we prove a fundamental limitation in function-space of two of the most commonly used distributions defined in weight-space: mean-field Gaussian and Monte Carlo dropout. We find there are simple cases where neither method can have substantially increased uncertainty in between well-separated regions of low uncertainty. We provide strong empirical evidence that exact inference does not have this pathology, hence it is due to the approximation and not the model. In contrast, for deep networks, we prove a universality result showing that there exist approximate posteriors in the above classes which provide flexible uncertainty estimates. However, we find empirically that pathologies of a similar form as in the single-hidden layer case can persist when performing variational inference in deeper networks. Our results motivate careful consideration of the implications of approximate inference methods in BNNs.

Andrew Y. K. Foong, Yingzhen Li, José Miguel Hernández-Lobato et al.

We describe a limitation in the expressiveness of the predictive uncertainty estimate given by mean-field variational inference (MFVI), a popular approximate inference method for Bayesian neural networks. In particular, MFVI fails to give calibrated uncertainty estimates in between separated regions of observations. This can lead to catastrophically overconfident predictions when testing on out-of-distribution data. Avoiding such overconfidence is critical for active learning, Bayesian optimisation and out-of-distribution robustness. We instead find that a classical technique, the linearised Laplace approximation, can handle 'in-between' uncertainty much better for small network architectures.

Hiske Overweg, Anna-Lena Popkes, Ari Ercole et al.

Clinical decision making is challenging because of pathological complexity, as well as large amounts of heterogeneous data generated as part of routine clinical care. In recent years, machine learning tools have been developed to aid this process. Intensive care unit (ICU) admissions represent the most data dense and time-critical patient care episodes. In this context, prediction models may help clinicians determine which patients are most at risk and prioritize care. However, flexible tools such as artificial neural networks (ANNs) suffer from a lack of interpretability limiting their acceptability to clinicians. In this work, we propose a novel interpretable Bayesian neural network architecture which offers both the flexibility of ANNs and interpretability in terms of feature selection. In particular, we employ a sparsity inducing prior distribution in a tied manner to learn which features are important for outcome prediction. We evaluate our approach on the task of mortality prediction using two real-world ICU cohorts. In collaboration with clinicians we found that, in addition to the predicted outcome results, our approach can provide novel insights into the importance of different clinical measurements. This suggests that our model can support medical experts in their decision making process.

Wenbo Gong, Yingzhen Li, José Miguel Hernández-Lobato

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) has become increasingly popular for simulating posterior samples in large-scale Bayesian modeling. However, existing SG-MCMC schemes are not tailored to any specific probabilistic model, even a simple modification of the underlying dynamical system requires significant physical intuition. This paper presents the first meta-learning algorithm that allows automated design for the underlying continuous dynamics of an SG-MCMC sampler. The learned sampler generalizes Hamiltonian dynamics with state-dependent drift and diffusion, enabling fast traversal and efficient exploration of neural network energy landscapes. Experiments validate the proposed approach on both Bayesian fully connected neural network and Bayesian recurrent neural network tasks, showing that the learned sampler out-performs generic, hand-designed SG-MCMC algorithms, and generalizes to different datasets and larger architectures.

Chao Ma, Yingzhen Li, José Miguel Hernández-Lobato

We introduce the implicit processes (IPs), a stochastic process that places implicitly defined multivariate distributions over any finite collections of random variables. IPs are therefore highly flexible implicit priors over functions, with examples including data simulators, Bayesian neural networks and non-linear transformations of stochastic processes. A novel and efficient approximate inference algorithm for IPs, namely the variational implicit processes (VIPs), is derived using generalised wake-sleep updates. This method returns simple update equations and allows scalable hyper-parameter learning with stochastic optimization. Experiments show that VIPs return better uncertainty estimates and lower errors over existing inference methods for challenging models such as Bayesian neural networks, and Gaussian processes.

Yingzhen Li, Stephan Mandt

We present a VAE architecture for encoding and generating high dimensional sequential data, such as video or audio. Our deep generative model learns a latent representation of the data which is split into a static and dynamic part, allowing us to approximately disentangle latent time-dependent features (dynamics) from features which are preserved over time (content). This architecture gives us partial control over generating content and dynamics by conditioning on either one of these sets of features. In our experiments on artificially generated cartoon video clips and voice recordings, we show that we can convert the content of a given sequence into another one by such content swapping. For audio, this allows us to convert a male speaker into a female speaker and vice versa, while for video we can separately manipulate shapes and dynamics. Furthermore, we give empirical evidence for the hypothesis that stochastic RNNs as latent state models are more efficient at compressing and generating long sequences than deterministic ones, which may be relevant for applications in video compression.

Yingzhen Li, John Bradshaw, Yash Sharma

There is a rising interest in studying the robustness of deep neural network classifiers against adversaries, with both advanced attack and defence techniques being actively developed. However, most recent work focuses on discriminative classifiers, which only model the conditional distribution of the labels given the inputs. In this paper, we propose and investigate the deep Bayes classifier, which improves classical naive Bayes with conditional deep generative models. We further develop detection methods for adversarial examples, which reject inputs with low likelihood under the generative model. Experimental results suggest that deep Bayes classifiers are more robust than deep discriminative classifiers, and that the proposed detection methods are effective against many recently proposed attacks.

Cuong V. Nguyen, Yingzhen Li, Thang D. Bui et al.

This paper develops variational continual learning (VCL), a simple but general framework for continual learning that fuses online variational inference (VI) and recent advances in Monte Carlo VI for neural networks. The framework can successfully train both deep discriminative models and deep generative models in complex continual learning settings where existing tasks evolve over time and entirely new tasks emerge. Experimental results show that VCL outperforms state-of-the-art continual learning methods on a variety of tasks, avoiding catastrophic forgetting in a fully automatic way.

Yingzhen Li, Richard E. Turner

Implicit models, which allow for the generation of samples but not for point-wise evaluation of probabilities, are omnipresent in real-world problems tackled by machine learning and a hot topic of current research. Some examples include data simulators that are widely used in engineering and scientific research, generative adversarial networks (GANs) for image synthesis, and hot-off-the-press approximate inference techniques relying on implicit distributions. The majority of existing approaches to learning implicit models rely on approximating the intractable distribution or optimisation objective for gradient-based optimisation, which is liable to produce inaccurate updates and thus poor models. This paper alleviates the need for such approximations by proposing the Stein gradient estimator, which directly estimates the score function of the implicitly defined distribution. The efficacy of the proposed estimator is empirically demonstrated by examples that include meta-learning for approximate inference, and entropy regularised GANs that provide improved sample diversity.

Yingzhen Li, Yarin Gal

To obtain uncertainty estimates with real-world Bayesian deep learning models, practical inference approximations are needed. Dropout variational inference (VI) for example has been used for machine vision and medical applications, but VI can severely underestimates model uncertainty. Alpha-divergences are alternative divergences to VI's KL objective, which are able to avoid VI's uncertainty underestimation. But these are hard to use in practice: existing techniques can only use Gaussian approximating distributions, and require existing models to be changed radically, thus are of limited use for practitioners. We propose a re-parametrisation of the alpha-divergence objectives, deriving a simple inference technique which, together with dropout, can be easily implemented with existing models by simply changing the loss of the model. We demonstrate improved uncertainty estimates and accuracy compared to VI in dropout networks. We study our model's epistemic uncertainty far away from the data using adversarial images, showing that these can be distinguished from non-adversarial images by examining our model's uncertainty.

Yingzhen Li, Richard E. Turner, Qiang Liu

We propose a novel approximate inference algorithm that approximates a target distribution by amortising the dynamics of a user-selected MCMC sampler. The idea is to initialise MCMC using samples from an approximation network, apply the MCMC operator to improve these samples, and finally use the samples to update the approximation network thereby improving its quality. This provides a new generic framework for approximate inference, allowing us to deploy highly complex, or implicitly defined approximation families with intractable densities, including approximations produced by warping a source of randomness through a deep neural network. Experiments consider image modelling with deep generative models as a challenging test for the method. Deep models trained using amortised MCMC are shown to generate realistic looking samples as well as producing diverse imputations for images with regions of missing pixels.

Thang D. Bui, Daniel Hernández-Lobato, Yingzhen Li et al.

Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. This paper develops a new approximate Bayesian learning scheme that enables DGPs to be applied to a range of medium to large scale regression problems for the first time. The new method uses an approximate Expectation Propagation procedure and a novel and efficient extension of the probabilistic backpropagation algorithm for learning. We evaluate the new method for non-linear regression on eleven real-world datasets, showing that it always outperforms GP regression and is almost always better than state-of-the-art deterministic and sampling-based approximate inference methods for Bayesian neural networks. As a by-product, this work provides a comprehensive analysis of six approximate Bayesian methods for training neural networks.