In the past years, deep learning has seen an increase in usage in the domain of histopathological applications. However, while these approaches have shown great potential, in high-risk environments deep learning models need to be able to judge their uncertainty and be able to reject inputs when there is a significant chance of misclassification. In this work, we conduct a rigorous evaluation of the most commonly used uncertainty and robustness methods for the classification of Whole Slide Images, with a focus on the task of selective classification, where the model should reject the classification in situations in which it is uncertain. We conduct our experiments on tile-level under the aspects of domain shift and label noise, as well as on slide-level. In our experiments, we compare Deep Ensembles, Monte-Carlo Dropout, Stochastic Variational Inference, Test-Time Data Augmentation as well as ensembles of the latter approaches. We observe that ensembles of methods generally lead to better uncertainty estimates as well as an increased robustness towards domain shifts and label noise, while contrary to results from classical computer vision benchmarks no systematic gain of the other methods can be shown. Across methods, a rejection of the most uncertain samples reliably leads to a significant increase in classification accuracy on both in-distribution as well as out-of-distribution data. Furthermore, we conduct experiments comparing these methods under varying conditions of label noise. Lastly, we publish our code framework to facilitate further research on uncertainty estimation on histopathological data.
Variational autoencoders model high-dimensional data by positing low-dimensional latent variables that are mapped through a flexible distribution parametrized by a neural network. Unfortunately, variational autoencoders often suffer from posterior collapse: the posterior of the latent variables is equal to its prior, rendering the variational autoencoder useless as a means to produce meaningful representations. Existing approaches to posterior collapse often attribute it to the use of neural networks or optimization issues due to variational approximation. In this paper, we consider posterior collapse as a problem of latent variable non-identifiability. We prove that the posterior collapses if and only if the latent variables are non-identifiable in the generative model. This fact implies that posterior collapse is not a phenomenon specific to the use of flexible distributions or approximate inference. Rather, it can occur in classical probabilistic models even with exact inference, which we also demonstrate. Based on these results, we propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. This model class resolves the problem of latent variable non-identifiability by leveraging bijective Brenier maps and parameterizing them with input convex neural networks, without special variational inference objectives or optimization tricks. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.
Uncertainty quantification is crucial to inverse problems, as it could provide decision-makers with valuable information about the inversion results. For example, seismic inversion is a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. It is therefore of paramount importance to quantify the uncertainties associated to the inversion process to ease the subsequent interpretation and decision making processes. Within this framework of reference, sampling from a target posterior provides a fundamental approach to quantifying the uncertainty in seismic inversion. However, selecting appropriate prior information in a probabilistic inversion is crucial, yet non-trivial, as it influences the ability of a sampling-based inference in providing geological realism in the posterior samples. To overcome such limitations, we present a regularized variational inference framework that performs posterior inference by implicitly regularizing the Kullback-Leibler divergence loss with a CNN-based denoiser by means of the Plug-and-Play methods. We call this new algorithm Plug-and-Play Stein Variational Gradient Descent (PnP-SVGD) and demonstrate its ability in producing high-resolution, trustworthy samples representative of the subsurface structures, which we argue could be used for post-inference tasks such as reservoir modelling and history matching. To validate the proposed method, numerical tests are performed on both synthetic and field post-stack seismic data.
The Information Bottleneck theory provides a theoretical and computational framework for finding approximate minimum sufficient statistics. Analysis of the Stochastic Gradient Descent (SGD) training of a neural network on a toy problem has shown the existence of two phases, fitting and compression. In this work, we analyze the SGD training process of a Deep Neural Network on MNIST classification and confirm the existence of two phases of SGD training. We also propose a setup for estimating the mutual information for a Deep Neural Network through Variational Inference.
Prior works on joint Information Extraction (IE) typically model instance (e.g., event triggers, entities, roles, relations) interactions by representation enhancement, type dependencies scoring, or global decoding. We find that the previous models generally consider binary type dependency scoring of a pair of instances, and leverage local search such as beam search to approximate global solutions. To better integrate cross-instance interactions, in this work, we introduce a joint IE framework (CRFIE) that formulates joint IE as a high-order Conditional Random Field. Specifically, we design binary factors and ternary factors to directly model interactions between not only a pair of instances but also triplets. Then, these factors are utilized to jointly predict labels of all instances. To address the intractability problem of exact high-order inference, we incorporate a high-order neural decoder that is unfolded from a mean-field variational inference method, which achieves consistent learning and inference. The experimental results show that our approach achieves consistent improvements on three IE tasks compared with our baseline and prior work.
We introduce ensembles of stochastic neural networks to approximate the Bayesian posterior, combining stochastic methods such as dropout with deep ensembles. The stochastic ensembles are formulated as families of distributions and trained to approximate the Bayesian posterior with variational inference. We implement stochastic ensembles based on Monte Carlo dropout, DropConnect and a novel non-parametric version of dropout and evaluate them on a toy problem and CIFAR image classification. For both tasks, we test the quality of the posteriors directly against Hamiltonian Monte Carlo simulations. Our results show that stochastic ensembles provide more accurate posterior estimates than other popular baselines for Bayesian inference.
We propose an alternative approach towards cost mitigation in volatility-managed portfolios based on smoothing the predictive density of an otherwise standard stochastic volatility model. Specifically, we develop a novel variational Bayes estimation method that flexibly encompasses different smoothness assumptions irrespective of the persistence of the underlying latent state. Using a large set of equity trading strategies, we show that smoothing volatility targeting helps to regularise the extreme leverage/turnover that results from commonly used realised variance estimates. This has important implications for both the risk-adjusted returns and the mean-variance efficiency of volatility-managed portfolios, once transaction costs are factored in. An extensive simulation study shows that our variational inference scheme compares favourably against existing state-of-the-art Bayesian estimation methods for stochastic volatility models.
Accurate traffic flow prediction, a hotspot for intelligent transportation research, is the prerequisite for mastering traffic and making travel plans. The speed of traffic flow can be affected by roads condition, weather, holidays, etc. Furthermore, the sensors to catch the information about traffic flow will be interfered with by environmental factors such as illumination, collection time, occlusion, etc. Therefore, the traffic flow in the practical transportation system is complicated, uncertain, and challenging to predict accurately. This paper proposes a deep encoder-decoder prediction framework based on variational Bayesian inference. A Bayesian neural network is constructed by combining variational inference with gated recurrent units (GRU) and used as the deep neural network unit of the encoder-decoder framework to mine the intrinsic dynamics of traffic flow. Then, the variational inference is introduced into the multi-head attention mechanism to avoid noise-induced deterioration of prediction accuracy. The proposed model achieves superior prediction performance on the Guangzhou urban traffic flow dataset over the benchmarks, particularly when the long-term prediction.
We present a unified probabilistic model that learns a representative set of discrete vehicle actions and predicts the probability of each action given a particular scenario. Our model also enables us to estimate the distribution over continuous trajectories conditioned on a scenario, representing what each discrete action would look like if executed in that scenario. While our primary objective is to learn representative action sets, these capabilities combine to produce accurate multimodal trajectory predictions as a byproduct. Although our learned action representations closely resemble semantically meaningful categories (e.g., "go straight", "turn left", etc.), our method is entirely self-supervised and does not utilize any manually generated labels or categories. Our method builds upon recent advances in variational inference and deep unsupervised clustering, resulting in full distribution estimates based on deterministic model evaluations.
Multilevel Stein variational gradient descent is a method for particle-based variational inference that leverages hierarchies of surrogate target distributions with varying costs and fidelity to computationally speed up inference. The contribution of this work is twofold. First, an extension of a previous cost complexity analysis is presented that applies even when the exponential convergence rate of single-level Stein variational gradient descent depends on iteration-varying parameters. Second, multilevel Stein variational gradient descent is applied to a large-scale Bayesian inverse problem of inferring discretized basal sliding coefficient fields of the Arolla glacier ice. The numerical experiments demonstrate that the multilevel version achieves orders of magnitude speedups compared to its single-level version.
Network pruning is a promising way to generate light but accurate models and enable their deployment on resource-limited edge devices. However, the current state-of-the-art assumes that the effective sub-network and the other superfluous parameters in the given network share the same distribution, where pruning inevitably involves a distribution truncation operation. They usually eliminate values near zero. While simple, it may not be the most appropriate method, as effective models may naturally have many small values associated with them. Removing near-zero values already embedded in model space may significantly reduce model accuracy. Another line of work has proposed to assign discrete prior over all possible sub-structures that still rely on human-crafted prior hypotheses. Worse still, existing methods use regularized point estimates, namely Hard Pruning, that can not provide error estimations and fail reliability justification for the pruned networks. In this paper, we propose a novel distribution-lossless pruning method, named DLLP, to theoretically find the pruned lottery within Bayesian treatment. Specifically, DLLP remodels the vanilla networks as discrete priors for the latent pruned model and the other redundancy. More importantly, DLLP uses Stein Variational Inference to approach the latent prior and effectively bypasses calculating KL divergence with unknown distribution. Extensive experiments based on small Cifar-10 and large-scaled ImageNet demonstrate that our method can obtain sparser networks with great generalization performance while providing quantified reliability for the pruned model.
We present a noisy channel generative model of two sequences, for example text and speech, which enables uncovering the association between the two modalities when limited paired data is available. To address the intractability of the exact model under a realistic data setup, we propose a variational inference approximation. To train this variational model with categorical data, we propose a KL encoder loss approach which has connections to the wake-sleep algorithm. Identifying the joint or conditional distributions by only observing unpaired samples from the marginals is only possible under certain conditions in the data distribution and we discuss under what type of conditional independence assumptions that might be achieved, which guides the architecture designs. Experimental results show that even tiny amount of paired data (5 minutes) is sufficient to learn to relate the two modalities (graphemes and phonemes here) when a massive amount of unpaired data is available, paving the path to adopting this principled approach for all seq2seq models in low data resource regimes.
Ultra-fine entity typing (UFET) aims to predict a wide range of type phrases that correctly describe the categories of a given entity mention in a sentence. Most recent works infer each entity type independently, ignoring the correlations between types, e.g., when an entity is inferred as a president, it should also be a politician and a leader. To this end, we use an undirected graphical model called pairwise conditional random field (PCRF) to formulate the UFET problem, in which the type variables are not only unarily influenced by the input but also pairwisely relate to all the other type variables. We use various modern backbones for entity typing to compute unary potentials, and derive pairwise potentials from type phrase representations that both capture prior semantic information and facilitate accelerated inference. We use mean-field variational inference for efficient type inference on very large type sets and unfold it as a neural network module to enable end-to-end training. Experiments on UFET show that the Neural-PCRF consistently outperforms its backbones with little cost and results in a competitive performance against cross-encoder based SOTA while being thousands of times faster. We also find Neural- PCRF effective on a widely used fine-grained entity typing dataset with a smaller type set. We pack Neural-PCRF as a network module that can be plugged onto multi-label type classifiers with ease and release it in https://github.com/modelscope/adaseq/tree/master/examples/NPCRF.
The standard closed-set domain adaptation approaches seek to mitigate distribution discrepancies between two domains under the constraint of both sharing identical label sets. However, in realistic scenarios, finding an optimal source domain with identical label space is a challenging task. Partial domain adaptation alleviates this problem of procuring a labeled dataset with identical label space assumptions and addresses a more practical scenario where the source label set subsumes the target label set. This, however, presents a few additional obstacles during adaptation. Samples with categories private to the source domain thwart relevant knowledge transfer and degrade model performance. In this work, we try to address these issues by coupling variational information and adversarial learning with a pseudo-labeling technique to enforce class distribution alignment and minimize the transfer of superfluous information from the source samples. The experimental findings in numerous cross-domain classification tasks demonstrate that the proposed technique delivers superior and comparable accuracy to existing methods.
Variational autoencoders employ an amortized inference model to approximate the posterior of latent variables. However, such amortized variational inference faces two challenges: (1) the limited posterior expressiveness of fully-factorized Gaussian assumption and (2) the amortization error of the inference model. We present a novel approach that addresses both challenges. First, we focus on ReLU networks with Gaussian output and illustrate their connection to probabilistic PCA. Building on this observation, we derive an iterative algorithm that finds the mode of the posterior and apply full-covariance Gaussian posterior approximation centered on the mode. Subsequently, we present a general framework named Variational Laplace Autoencoders (VLAEs) for training deep generative models. Based on the Laplace approximation of the latent variable posterior, VLAEs enhance the expressiveness of the posterior while reducing the amortization error. Empirical results on MNIST, Omniglot, Fashion-MNIST, SVHN and CIFAR10 show that the proposed approach significantly outperforms other recent amortized or iterative methods on the ReLU networks.
Bayesian neural networks (BNNs) have been an important framework in the study of uncertainty quantification. Deterministic variational inference, one of the inference methods, utilizes moment propagation to compute the predictive distributions and objective functions. Unfortunately, deriving the moments requires computationally expensive Taylor expansion in nonlinear functions, such as a rectified linear unit (ReLU) or a sigmoid function. Therefore, a new nonlinear function that realizes faster moment propagation than conventional functions is required. In this paper, we propose a novel nonlinear function named moment propagating-Gaussian error linear unit (MP-GELU) that enables the fast derivation of first and second moments in BNNs. MP-GELU enables the analytical computation of moments by applying nonlinearity to the input statistics, thereby reducing the computationally expensive calculations required for nonlinear functions. In empirical experiments on regression tasks, we observed that the proposed MP-GELU provides higher prediction accuracy and better quality of uncertainty with faster execution than those of ReLU-based BNNs.
Particle-based variational inference (VI) minimizes the KL divergence between model samples and the target posterior with gradient flow estimates. With the popularity of Stein variational gradient descent (SVGD), the focus of particle-based VI algorithms has been on the properties of functions in Reproducing Kernel Hilbert Space (RKHS) to approximate the gradient flow. However, the requirement of RKHS restricts the function class and algorithmic flexibility. This paper offers a general solution to this problem by introducing a functional regularization term that encompasses the RKHS norm as a special case. This allows us to propose a new particle-based VI algorithm called preconditioned functional gradient flow (PFG). Compared to SVGD, PFG has several advantages. It has a larger function class, improved scalability in large particle-size scenarios, better adaptation to ill-conditioned distributions, and provable continuous-time convergence in KL divergence. Additionally, non-linear function classes such as neural networks can be incorporated to estimate the gradient flow. Our theory and experiments demonstrate the effectiveness of the proposed framework.
The last decade witnessed a growing interest in Bayesian learning. Yet, the technicality of the topic and the multitude of ingredients involved therein, besides the complexity of turning theory into practical implementations, limit the use of the Bayesian learning paradigm, preventing its widespread adoption across different fields and applications. This self-contained survey engages and introduces readers to the principles and algorithms of Bayesian Learning for Neural Networks. It provides an introduction to the topic from an accessible, practical-algorithmic perspective. Upon providing a general introduction to Bayesian Neural Networks, we discuss and present both standard and recent approaches for Bayesian inference, with an emphasis on solutions relying on Variational Inference and the use of Natural gradients. We also discuss the use of manifold optimization as a state-of-the-art approach to Bayesian learning. We examine the characteristic properties of all the discussed methods, and provide pseudo-codes for their implementation, paying attention to practical aspects, such as the computation of the gradients.
The appearance of the same object may vary in different scene images due to perspectives and occlusions between objects. Humans can easily identify the same object, even if occlusions exist, by completing the occluded parts based on its canonical image in the memory. Achieving this ability is still a challenge for machine learning, especially under the unsupervised learning setting. Inspired by such an ability of humans, this paper proposes a compositional scene modeling method to infer global representations of canonical images of objects without any supervision. The representation of each object is divided into an intrinsic part, which characterizes globally invariant information (i.e. canonical representation of an object), and an extrinsic part, which characterizes scene-dependent information (e.g., position and size). To infer the intrinsic representation of each object, we employ a patch-matching strategy to align the representation of a potentially occluded object with the canonical representations of objects, and sample the most probable canonical representation based on the category of object determined by amortized variational inference. Extensive experiments are conducted on four object-centric learning benchmarks, and experimental results demonstrate that the proposed method not only outperforms state-of-the-arts in terms of segmentation and reconstruction, but also achieves good global object identification performance.
Air pollution kills around 7 million people annually, and approximately 2.4 billion people are exposed to hazardous air pollution. Accurate, fine-grained air quality (AQ) monitoring is essential to control and reduce pollution. However, AQ station deployment is sparse, and thus air quality inference for unmonitored locations is crucial. Conventional interpolation methods fail to learn the complex AQ phenomena. This work demonstrates that Deep Gaussian Process models (DGPs) are a promising model for the task of AQ inference. We implement Doubly Stochastic Variational Inference, a DGP algorithm, and show that it performs comparably to the state-of-the-art models.