Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture and quantify different sources of uncertainty, particularly those associated with model errors. In this work we perform toy-model and state-of-the-art model experiments to analyze to what extent artificial neural networks (ANNs) are able to model the different sources of uncertainty present in a forecast. In particular those associated with the accuracy of the initial conditions and those introduced by the model error. We also compare different training strategies: one based on a direct training using the mean and spread of an ensemble forecast as target, the other ones rely on an indirect training strategy using an analyzed state as target in which the uncertainty is implicitly learned from the data. Experiments using the Lorenz'96 model show that the ANNs are able to emulate some of the properties of ensemble forecasts like the filtering of the most unpredictable modes and a state-dependent quantification of the forecast uncertainty. Moreover, ANNs provide a reliable estimation of the forecast uncertainty in the presence of model error. Preliminary experiments conducted with a state-of-the-art forecasting system also confirm the ability of ANNs to produce a reliable quantification of the forecast uncertainty.
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Recent years have witnessed tremendously improved efficiency of Automated Machine Learning (AutoML), especially Automated Deep Learning (AutoDL) systems, but recent work focuses on tabular, image, or NLP tasks. So far, little attention has been paid to general AutoDL frameworks for time series forecasting, despite the enormous success in applying different novel architectures to such tasks. In this paper, we propose an efficient approach for the joint optimization of neural architecture and hyperparameters of the entire data processing pipeline for time series forecasting. In contrast to common NAS search spaces, we designed a novel neural architecture search space covering various state-of-the-art architectures, allowing for an efficient macro-search over different DL approaches. To efficiently search in such a large configuration space, we use Bayesian optimization with multi-fidelity optimization. We empirically study several different budget types enabling efficient multi-fidelity optimization on different forecasting datasets. Furthermore, we compared our resulting system, dubbed \system, against several established baselines and show that it significantly outperforms all of them across several datasets.
Multi-modal learning focuses on training models by equally combining multiple input data modalities during the prediction process. However, this equal combination can be detrimental to the prediction accuracy because different modalities are usually accompanied by varying levels of uncertainty. Using such uncertainty to combine modalities has been studied by a couple of approaches, but with limited success because these approaches are either designed to deal with specific classification or segmentation problems and cannot be easily translated into other tasks, or suffer from numerical instabilities. In this paper, we propose a new Uncertainty-aware Multi-modal Learner that estimates uncertainty by measuring feature density via Cross-modal Random Network Prediction (CRNP). CRNP is designed to require little adaptation to translate between different prediction tasks, while having a stable training process. From a technical point of view, CRNP is the first approach to explore random network prediction to estimate uncertainty and to combine multi-modal data. Experiments on two 3D multi-modal medical image segmentation tasks and three 2D multi-modal computer vision classification tasks show the effectiveness, adaptability and robustness of CRNP. Also, we provide an extensive discussion on different fusion functions and visualization to validate the proposed model.
The value of uncertainty quantification on predictions for trained neural networks (NNs) on quantum chemical reference data is quantitatively explored. For this, the architecture of the PhysNet NN was suitably modified and the resulting model was evaluated with different metrics to quantify calibration, quality of predictions, and whether prediction error and the predicted uncertainty can be correlated. The results from training on the QM9 database and evaluating data from the test set within and outside the distribution indicate that error and uncertainty are not linearly related. The results clarify that noise and redundancy complicate property prediction for molecules even in cases for which changes - e.g. double bond migration in two otherwise identical molecules - are small. The model was then applied to a real database of tautomerization reactions. Analysis of the distance between members in feature space combined with other parameters shows that redundant information in the training dataset can lead to large variances and small errors whereas the presence of similar but unspecific information returns large errors but small variances. This was, e.g., observed for nitro-containing aliphatic chains for which predictions were difficult although the training set contained several examples for nitro groups bound to aromatic molecules. This underlines the importance of the composition of the training data and provides chemical insight into how this affects the prediction capabilities of a ML model. Finally, the approach put forward can be used for information-based improvement of chemical databases for target applications through active learning optimization.
The algorithms available for retail forecasting have increased in complexity. Newer methods, such as machine learning, are inherently complex. The more traditional families of forecasting models, such as exponential smoothing and autoregressive integrated moving averages, have expanded to contain multiple possible forms and forecasting profiles. We question complexity in forecasting and the need to consider such large families of models. Our argument is that parsimoniously identifying suitable subsets of models will not decrease forecasting accuracy nor will it reduce the ability to estimate forecast uncertainty. We propose a framework that balances forecasting performance versus computational cost, resulting in the consideration of only a reduced set of models. We empirically demonstrate that a reduced set performs well. Finally, we translate computational benefits to monetary cost savings and environmental impact and discuss the implications of our results in the context of large retailers.
The flow-driven spectral chaos (FSC) is a recently developed method for tracking and quantifying uncertainties in the long-time response of stochastic dynamical systems using the spectral approach. The method uses a novel concept called 'enriched stochastic flow maps' as a means to construct an evolving finite-dimensional random function space that is both accurate and computationally efficient in time. In this paper, we present a multi-element version of the FSC method (the ME-FSC method for short) to tackle (mainly) those dynamical systems that are inherently discontinuous over the probability space. In ME-FSC, the random domain is partitioned into several elements, and then the problem is solved separately on each random element using the FSC method. Subsequently, results are aggregated to compute the probability moments of interest using the law of total probability. To demonstrate the effectiveness of the ME-FSC method in dealing with discontinuities and long-time integration of stochastic dynamical systems, four representative numerical examples are presented in this paper, including the Van-der-Pol oscillator problem and the Kraichnan-Orszag three-mode problem. Results show that the ME-FSC method is capable of solving problems that have strong nonlinear dependencies over the probability space, both reliably and at low computational cost.
Encouraged by decision makers' appetite for future information on topics ranging from elections to pandemics, and enabled by the explosion of data and computational methods, model based forecasts have garnered increasing influence on a breadth of decisions in modern society. Using several classic examples from fisheries management, I demonstrate that selecting the model or models that produce the most accurate and precise forecast (measured by statistical scores) can sometimes lead to worse outcomes (measured by real-world objectives). This can create a forecast trap, in which the outcomes such as fish biomass or economic yield decline while the manager becomes increasingly convinced that these actions are consistent with the best models and data available. The forecast trap is not unique to this example, but a fundamental consequence of non-uniqueness of models. Existing practices promoting a broader set of models are the best way to avoid the trap.
High-end vehicles have been furnished with a number of electronic control units (ECUs), which provide upgrading functions to enhance the driving experience. The controller area network (CAN) is a well-known protocol that connects these ECUs because of its modesty and efficiency. However, the CAN bus is vulnerable to various types of attacks. Although the intrusion detection system (IDS) is proposed to address the security problem of the CAN bus, most previous studies only provide alerts when attacks occur without knowing the specific type of attack. Moreover, an IDS is designed for a specific car model due to diverse car manufacturers. In this study, we proposed a novel deep learning model called supervised contrastive (SupCon) ResNet, which can handle multiple attack identification on the CAN bus. Furthermore, the model can be used to improve the performance of a limited-size dataset using a transfer learning technique. The capability of the proposed model is evaluated on two real car datasets. When tested with the car hacking dataset, the experiment results show that the SupCon ResNet model improves the overall false-negative rates of four types of attack by four times on average, compared to other models. In addition, the model achieves the highest F1 score at 0.9994 on the survival dataset by utilizing transfer learning. Finally, the model can adapt to hardware constraints in terms of memory size and running time.
Due to their increasing spread, confidence in neural network predictions became more and more important. However, basic neural networks do not deliver certainty estimates or suffer from over or under confidence. Many researchers have been working on understanding and quantifying uncertainty in a neural network's prediction. As a result, different types and sources of uncertainty have been identified and a variety of approaches to measure and quantify uncertainty in neural networks have been proposed. This work gives a comprehensive overview of uncertainty estimation in neural networks, reviews recent advances in the field, highlights current challenges, and identifies potential research opportunities. It is intended to give anyone interested in uncertainty estimation in neural networks a broad overview and introduction, without presupposing prior knowledge in this field. A comprehensive introduction to the most crucial sources of uncertainty is given and their separation into reducible model uncertainty and not reducible data uncertainty is presented. The modeling of these uncertainties based on deterministic neural networks, Bayesian neural networks, ensemble of neural networks, and test-time data augmentation approaches is introduced and different branches of these fields as well as the latest developments are discussed. For a practical application, we discuss different measures of uncertainty, approaches for the calibration of neural networks and give an overview of existing baselines and implementations. Different examples from the wide spectrum of challenges in different fields give an idea of the needs and challenges regarding uncertainties in practical applications. Additionally, the practical limitations of current methods for mission- and safety-critical real world applications are discussed and an outlook on the next steps towards a broader usage of such methods is given.
Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.
The demand for artificial intelligence has grown significantly over the last decade and this growth has been fueled by advances in machine learning techniques and the ability to leverage hardware acceleration. However, in order to increase the quality of predictions and render machine learning solutions feasible for more complex applications, a substantial amount of training data is required. Although small machine learning models can be trained with modest amounts of data, the input for training larger models such as neural networks grows exponentially with the number of parameters. Since the demand for processing training data has outpaced the increase in computation power of computing machinery, there is a need for distributing the machine learning workload across multiple machines, and turning the centralized into a distributed system. These distributed systems present new challenges, first and foremost the efficient parallelization of the training process and the creation of a coherent model. This article provides an extensive overview of the current state-of-the-art in the field by outlining the challenges and opportunities of distributed machine learning over conventional (centralized) machine learning, discussing the techniques used for distributed machine learning, and providing an overview of the systems that are available.
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