Despite recent advances, sampling-based inference for Bayesian Neural Networks (BNNs) remains a significant challenge in probabilistic deep learning. While sampling-based approaches do not require a variational distribution assumption, current state-of-the-art samplers still struggle to navigate the complex and highly multimodal posteriors of BNNs. As a consequence, sampling still requires considerably longer inference times than non-Bayesian methods even for small neural networks, despite recent advances in making software implementations more efficient. Besides the difficulty of finding high-probability regions, the time until samplers provide sufficient exploration of these areas remains unpredictable. To tackle these challenges, we introduce an ensembling approach that leverages strategies from optimization and a recently proposed sampler called Microcanonical Langevin Monte Carlo (MCLMC) for efficient, robust and predictable sampling performance. Compared to approaches based on the state-of-the-art No-U-Turn Sampler, our approach delivers substantial speedups up to an order of magnitude, while maintaining or improving predictive performance and uncertainty quantification across diverse tasks and data modalities. The suggested Microcanonical Langevin Ensembles and modifications to MCLMC additionally enhance the method's predictability in resource requirements, facilitating easier parallelization. All in all, the proposed method offers a promising direction for practical, scalable inference for BNNs.
Full-Waveform Inversion (FWI) is a nonlinear iterative seismic imaging technique that, by reducing the misfit between recorded and predicted seismic waveforms, can produce detailed estimates of subsurface geophysical properties. Nevertheless, the strong nonlinearity of FWI can trap the optimization in local minima. This issue arises due to factors such as improper initial values, the absence of low frequencies in the measurements, noise, and other related considerations. To address this challenge and with the advent of advanced machine-learning techniques, data-driven methods, such as deep learning, have attracted significantly increasing attention in the geophysical community. Furthermore, the elastic wave equation should be included in FWI to represent elastic effects accurately. The intersection of data-driven techniques and elastic scattering theories presents opportunities and challenges. In this paper, by using the knowledge of elastic scattering (physics of the problem) and integrating it with machine learning techniques, we propose methods for the solution of time-harmonic FWI to enhance accuracy compared to pure data-driven and physics-based approaches. Moreover, to address uncertainty quantification, by modifying the structure of the Variational Autoencoder, we introduce a probabilistic deep learning method based on the physics of the problem that enables us to explore the uncertainties of the solution. According to the limited availability of datasets in this field and to assess the performance and accuracy of the proposed methods, we create a comprehensive dataset close to reality and conduct a comparative analysis of the presented approaches to it.
We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations. Stochastically driven flow models are pertinent to a diverse range of natural phenomena, including jets on giant planets, ocean circulation, and the variability of midlatitude weather. However, much of the recent progress in deep learning has predominantly focused on deterministic systems. The SLT comprises a stochastically-forced transformer paired with a translation-equivariant autoencoder, trained towards the Continuous Ranked Probability Score. We showcase its effectiveness by applying it to a well-researched zonal jet system, where the interaction between stochastically forced eddies and the zonal mean flow results in a rich low-frequency variability. The SLT accurately reproduces system dynamics across various integration periods, validated through quantitative diagnostics that include spectral properties and the rate of transitions between distinct states. The SLT achieves a five-order-of-magnitude speedup in emulating the zonally-averaged flow compared to direct numerical simulations. This acceleration facilitates the cost-effective generation of large ensembles, enabling the exploration of statistical questions concerning the probabilities of spontaneous transition events.
Existing regression models tend to fall short in both accuracy and uncertainty estimation when the label distribution is imbalanced. In this paper, we propose a probabilistic deep learning model, dubbed variational imbalanced regression (VIR), which not only performs well in imbalanced regression but naturally produces reasonable uncertainty estimation as a byproduct. Different from typical variational autoencoders assuming I.I.D. representations (a data point's representation is not directly affected by other data points), our VIR borrows data with similar regression labels to compute the latent representation's variational distribution; furthermore, different from deterministic regression models producing point estimates, VIR predicts the entire normal-inverse-gamma distributions and modulates the associated conjugate distributions to impose probabilistic reweighting on the imbalanced data, thereby providing better uncertainty estimation. Experiments in several real-world datasets show that our VIR can outperform state-of-the-art imbalanced regression models in terms of both accuracy and uncertainty estimation. Code will soon be available at https://github.com/Wang-ML-Lab/variational-imbalanced-regression.
This paper introduces a novel approach to probabilistic deep learning, kernel density matrices, which provide a simpler yet effective mechanism for representing joint probability distributions of both continuous and discrete random variables. In quantum mechanics, a density matrix is the most general way to describe the state of a quantum system. This work extends the concept of density matrices by allowing them to be defined in a reproducing kernel Hilbert space. This abstraction allows the construction of differentiable models for density estimation, inference, and sampling, and enables their integration into end-to-end deep neural models. In doing so, we provide a versatile representation of marginal and joint probability distributions that allows us to develop a differentiable, compositional, and reversible inference procedure that covers a wide range of machine learning tasks, including density estimation, discriminative learning, and generative modeling. The broad applicability of the framework is illustrated by two examples: an image classification model that can be naturally transformed into a conditional generative model, and a model for learning with label proportions that demonstrates the framework's ability to deal with uncertainty in the training samples. The framework is implemented as a library and is available at: https://github.com/fagonzalezo/kdm.
Data imbalance is ubiquitous when applying machine learning to real-world problems, particularly regression problems. If training data are imbalanced, the learning is dominated by the densely covered regions of the target distribution and the learned regressor tends to exhibit poor performance in sparsely covered regions. Beyond standard measures like oversampling or reweighting, there are two main approaches to handling learning from imbalanced data. For regression, recent work leverages the continuity of the distribution, while for classification, the trend has been to use ensemble methods, allowing some members to specialize in predictions for sparser regions. In our method, named UVOTE, we integrate recent advances in probabilistic deep learning with an ensemble approach for imbalanced regression. We replace traditional regression losses with negative log-likelihood, which also predicts sample-wise aleatoric uncertainty. Our experiments show that this loss function handles imbalance better. Additionally, we use the predicted aleatoric uncertainty values to fuse the predictions of different expert models in the ensemble, eliminating the need for a separate aggregation module. We compare our method with existing alternatives on multiple public benchmarks and show that UVOTE consistently outperforms the prior art, while at the same time producing better-calibrated uncertainty estimates. Our code is available at https://github.com/SherryJYC/UVOTE.
Learning-based algorithms for automated license plate recognition implicitly assume that the training and test data are well aligned. However, this may not be the case under extreme environmental conditions, or in forensic applications where the system cannot be trained for a specific acquisition device. Predictions on such out-of-distribution images have an increased chance of failing. But this failure case is oftentimes hard to recognize for a human operator or an automated system. Hence, in this work we propose to model the prediction uncertainty for license plate recognition explicitly. Such an uncertainty measure allows to detect false predictions, indicating an analyst when not to trust the result of the automated license plate recognition. In this paper, we compare three methods for uncertainty quantification on two architectures. The experiments on synthetic noisy or blurred low-resolution images show that the predictive uncertainty reliably finds wrong predictions. We also show that a multi-task combination of classification and super-resolution improves the recognition performance by 109\% and the detection of wrong predictions by 29 %.
Computed tomography has propelled scientific advances in fields from biology to materials science. This technology allows for the elucidation of 3-dimensional internal structure by the attenuation of x-rays through an object at different rotations relative to the beam. By imaging 2-dimensional projections, a 3-dimensional object can be reconstructed through a computational algorithm. Imaging at a greater number of rotation angles allows for improved reconstruction. However, taking more measurements increases the x-ray dose and may cause sample damage. Deep neural networks have been used to transform sparse 2-D projection measurements to a 3-D reconstruction by training on a dataset of known similar objects. However, obtaining high-quality object reconstructions for the training dataset requires high x-ray dose measurements that can destroy or alter the specimen before imaging is complete. This becomes a chicken-and-egg problem: high-quality reconstructions cannot be generated without deep learning, and the deep neural network cannot be learned without the reconstructions. This work develops and validates a self-supervised probabilistic deep learning technique, the physics-informed variational autoencoder, to solve this problem. A dataset consisting solely of sparse projection measurements from each object is used to jointly reconstruct all objects of the set. This approach has the potential to allow visualization of fragile samples with x-ray computed tomography. We release our code for reproducing our results at: https://github.com/vganapati/CT_PVAE .
The versatility to learn from a handful of samples is the hallmark of human intelligence. Few-shot learning is an endeavour to transcend this capability down to machines. Inspired by the promise and power of probabilistic deep learning, we propose a novel variational inference network for few-shot classification (coined as TRIDENT) to decouple the representation of an image into semantic and label latent variables, and simultaneously infer them in an intertwined fashion. To induce task-awareness, as part of the inference mechanics of TRIDENT, we exploit information across both query and support images of a few-shot task using a novel built-in attention-based transductive feature extraction module (we call AttFEX). Our extensive experimental results corroborate the efficacy of TRIDENT and demonstrate that, using the simplest of backbones, it sets a new state-of-the-art in the most commonly adopted datasets miniImageNet and tieredImageNet (offering up to 4% and 5% improvements, respectively), as well as for the recent challenging cross-domain miniImagenet --> CUB scenario offering a significant margin (up to 20% improvement) beyond the best existing cross-domain baselines. Code and experimentation can be found in our GitHub repository: https://github.com/anujinho/trident
The ability to estimate epistemic uncertainty is often crucial when deploying machine learning in the real world, but modern methods often produce overconfident, uncalibrated uncertainty predictions. A common approach to quantify epistemic uncertainty, usable across a wide class of prediction models, is to train a model ensemble. In a naive implementation, the ensemble approach has high computational cost and high memory demand. This challenges in particular modern deep learning, where even a single deep network is already demanding in terms of compute and memory, and has given rise to a number of attempts to emulate the model ensemble without actually instantiating separate ensemble members. We introduce FiLM-Ensemble, a deep, implicit ensemble method based on the concept of Feature-wise Linear Modulation (FiLM). That technique was originally developed for multi-task learning, with the aim of decoupling different tasks. We show that the idea can be extended to uncertainty quantification: by modulating the network activations of a single deep network with FiLM, one obtains a model ensemble with high diversity, and consequently well-calibrated estimates of epistemic uncertainty, with low computational overhead in comparison. Empirically, FiLM-Ensemble outperforms other implicit ensemble methods, and it and comes very close to the upper bound of an explicit ensemble of networks (sometimes even beating it), at a fraction of the memory cost.
Accurate uncertainty quantification is a major challenge in deep learning, as neural networks can make overconfident errors and assign high confidence predictions to out-of-distribution (OOD) inputs. The most popular approaches to estimate predictive uncertainty in deep learning are methods that combine predictions from multiple neural networks, such as Bayesian neural networks (BNNs) and deep ensembles. However their practicality in real-time, industrial-scale applications are limited due to the high memory and computational cost. Furthermore, ensembles and BNNs do not necessarily fix all the issues with the underlying member networks. In this work, we study principled approaches to improve uncertainty property of a single network, based on a single, deterministic representation. By formalizing the uncertainty quantification as a minimax learning problem, we first identify distance awareness, i.e., the model's ability to quantify the distance of a testing example from the training data, as a necessary condition for a DNN to achieve high-quality (i.e., minimax optimal) uncertainty estimation. We then propose Spectral-normalized Neural Gaussian Process (SNGP), a simple method that improves the distance-awareness ability of modern DNNs with two simple changes: (1) applying spectral normalization to hidden weights to enforce bi-Lipschitz smoothness in representations and (2) replacing the last output layer with a Gaussian process layer. On a suite of vision and language understanding benchmarks, SNGP outperforms other single-model approaches in prediction, calibration and out-of-domain detection. Furthermore, SNGP provides complementary benefits to popular techniques such as deep ensembles and data augmentation, making it a simple and scalable building block for probabilistic deep learning. Code is open-sourced at https://github.com/google/uncertainty-baselines
The transition to a fully renewable energy grid requires better forecasting of demand at the low-voltage level to increase efficiency and ensure reliable control. However, high fluctuations and increasing electrification cause huge forecast variability, not reflected in traditional point estimates. Probabilistic load forecasts take future uncertainties into account and thus allow more informed decision-making for the planning and operation of low-carbon energy systems. We propose an approach for flexible conditional density forecasting of short-term load based on Bernstein polynomial normalizing flows, where a neural network controls the parameters of the flow. In an empirical study with 363 smart meter customers, our density predictions compare favorably against Gaussian and Gaussian mixture densities. Also, they outperform a non-parametric approach based on the pinball loss for 24h-ahead load forecasting for two different neural network architectures.
The COVID-19 pandemic has significantly impacted the tourism and hospitality sector. Public policies such as travel restrictions and stay-at-home orders had significantly affected tourist activities and service businesses' operations and profitability. To this end, it is essential to develop an interpretable forecast model that supports managerial and organizational decision-making. We developed DemandNet, a novel deep learning framework for predicting time series data under the influence of the COVID-19 pandemic. The framework starts by selecting the top static and dynamic features embedded in the time series data. Then, it includes a nonlinear model which can provide interpretable insight into the previously seen data. Lastly, a prediction model is developed to leverage the above characteristics to make robust long-term forecasts. We evaluated the framework using daily hotel demand and revenue data from eight cities in the US. Our findings reveal that DemandNet outperforms the state-of-art models and can accurately predict the impact of the COVID-19 pandemic on hotel demand and revenues.
Neural density estimators have proven remarkably powerful in performing efficient simulation-based Bayesian inference in various research domains. In particular, the BayesFlow framework uses a two-step approach to enable amortized parameter estimation in settings where the likelihood function is implicitly defined by a simulation program. But how faithful is such inference when simulations are poor representations of reality? In this paper, we conceptualize the types of model misspecification arising in simulation-based inference and systematically investigate the performance of the BayesFlow framework under these misspecifications. We propose an augmented optimization objective which imposes a probabilistic structure on the latent data space and utilize maximum mean discrepancy (MMD) to detect potentially catastrophic misspecifications during inference undermining the validity of the obtained results. We verify our detection criterion on a number of artificial and realistic misspecifications, ranging from toy conjugate models to complex models of decision making and disease outbreak dynamics applied to real data. Further, we show that posterior inference errors increase as a function of the distance between the true data-generating distribution and the typical set of simulations in the latent summary space. Thus, we demonstrate the dual utility of MMD as a method for detecting model misspecification and as a proxy for verifying the faithfulness of amortized Bayesian inference.
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to trust the forecasts. Recently, several practical tools to estimate uncertainty have been developed in probabilistic deep learning. However, there have not been empirical applications and extensive comparisons of these tools in the domain of air quality forecasts. Therefore, this work applies state-of-the-art techniques of uncertainty quantification in a real-world setting of air quality forecasts. Through extensive experiments, we describe training probabilistic models and evaluate their predictive uncertainties based on empirical performance, reliability of confidence estimate, and practical applicability. We also propose improving these models using "free" adversarial training and exploiting temporal and spatial correlation inherent in air quality data. Our experiments demonstrate that the proposed models perform better than previous works in quantifying uncertainty in data-driven air quality forecasts. Overall, Bayesian neural networks provide a more reliable uncertainty estimate but can be challenging to implement and scale. Other scalable methods, such as deep ensemble, Monte Carlo (MC) dropout, and stochastic weight averaging-Gaussian (SWAG), can perform well if applied correctly but with different tradeoffs and slight variations in performance metrics. Finally, our results show the practical impact of uncertainty estimation and demonstrate that, indeed, probabilistic models are more suitable for making informed decisions. Code and dataset are available at \url{https://github.com/Abdulmajid-Murad/deep_probabilistic_forecast}
To validate the safety of automated vehicles (AV), scenario-based testing aims to systematically describe driving scenarios an AV might encounter. In this process, continuous inputs such as velocities result in an infinite number of possible variations of a scenario. Thus, metamodels are used to perform analyses or to select specific variations for examination. However, despite the safety criticality of AV testing, metamodels are usually seen as a part of an overall approach, and their predictions are not questioned. This paper analyzes the predictive performance of Gaussian processes (GP), deep Gaussian processes, extra-trees, and Bayesian neural networks (BNN), considering four scenarios with 5 to 20 inputs. Building on this, an iterative approach is introduced and evaluated, which allows to efficiently select test cases for common analysis tasks. The results show that regarding predictive performance, the appropriate selection of test cases is more important than the choice of metamodels. However, the choice of metamodels remains crucial: Their great flexibility allows BNNs to benefit from large amounts of data and to model even the most complex scenarios. In contrast, less flexible models like GPs convince with higher reliability. Hence, relevant test cases are best explored using scalable virtual test setups and flexible models. Subsequently, more realistic test setups and more reliable models can be used for targeted testing and validation.
Simultaneous Localization and Mapping (SLAM) system typically employ vision-based sensors to observe the surrounding environment. However, the performance of such systems highly depends on the ambient illumination conditions. In scenarios with adverse visibility or in the presence of airborne particulates (e.g. smoke, dust, etc.), alternative modalities such as those based on thermal imaging and inertial sensors are more promising. In this paper, we propose the first complete thermal-inertial SLAM system which combines neural abstraction in the SLAM front end with robust pose graph optimization in the SLAM back end. We model the sensor abstraction in the front end by employing probabilistic deep learning parameterized by Mixture Density Networks (MDN). Our key strategies to successfully model this encoding from thermal imagery are the usage of normalized 14-bit radiometric data, the incorporation of hallucinated visual (RGB) features, and the inclusion of feature selection to estimate the MDN parameters. To enable a full SLAM system, we also design an efficient global image descriptor which is able to detect loop closures from thermal embedding vectors. We performed extensive experiments and analysis using three datasets, namely self-collected ground robot and handheld data taken in indoor environment, and one public dataset (SubT-tunnel) collected in underground tunnel. Finally, we demonstrate that an accurate thermal-inertial SLAM system can be realized in conditions of both benign and adverse visibility.
NASA's Global Ecosystem Dynamics Investigation (GEDI) is a key climate mission whose goal is to advance our understanding of the role of forests in the global carbon cycle. While GEDI is the first space-based LIDAR explicitly optimized to measure vertical forest structure predictive of aboveground biomass, the accurate interpretation of this vast amount of waveform data across the broad range of observational and environmental conditions is challenging. Here, we present a novel supervised machine learning approach to interpret GEDI waveforms and regress canopy top height globally. We propose a probabilistic deep learning approach based on an ensemble of deep convolutional neural networks(CNN) to avoid the explicit modelling of unknown effects, such as atmospheric noise. The model learns to extract robust features that generalize to unseen geographical regions and, in addition, yields reliable estimates of predictive uncertainty. Ultimately, the global canopy top height estimates produced by our model have an expected RMSE of 2.7 m with low bias.
Predictive uncertainty estimation is an essential next step for the reliable deployment of deep object detectors in safety-critical tasks. In this work, we focus on estimating predictive distributions for bounding box regression output with variance networks. We show that in the context of object detection, training variance networks with negative log likelihood (NLL) can lead to high entropy predictive distributions regardless of the correctness of the output mean. We propose to use the energy score as a non-local proper scoring rule and find that when used for training, the energy score leads to better calibrated and lower entropy predictive distributions than NLL. We also address the widespread use of non-proper scoring metrics for evaluating predictive distributions from deep object detectors by proposing an alternate evaluation approach founded on proper scoring rules. Using the proposed evaluation tools, we show that although variance networks can be used to produce high quality predictive distributions, ad-hoc approaches used by seminal object detectors for choosing regression targets during training do not provide wide enough data support for reliable variance learning. We hope that our work helps shift evaluation in probabilistic object detection to better align with predictive uncertainty evaluation in other machine learning domains. Code for all models, evaluation, and datasets is available at: https://github.com/asharakeh/probdet.git.
In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the microcosmos. Meanwhile, machine learning inverse design of materials raised intensive attention, resulting in various intelligent systems for matter engineering. Here, inspired by quantum theory, we propose a probabilistic deep learning paradigm for the inverse design of functional meta-structures. Our probability-density-based neural network (PDN) can accurately capture all plausible meta-structures to meet the desired performances. Local maxima in probability density distribution correspond to the most likely candidates. We verify this approach by designing multiple meta-structures for each targeted transmission spectrum to enrich design choices.