In this work, we introduce a novel Deep Learning-based method to perceive the environment of a vehicle based on radar scans while accounting for uncertainties in its predictions. The environment of the host vehicle is segmented into equally sized grid cells which are classified individually. Complementary to the segmentation output, our Deep Learning-based algorithm is capable of differentiating uncertainties in its predictions as being related to an inadequate model (epistemic uncertainty) or noisy data (aleatoric uncertainty). To this end, weights are described as probability distributions accounting for uncertainties in the model parameters. Distributions are learned in a supervised fashion using gradient descent. We prove that uncertainties in the model output correlate with the precision of its predictions. Compared to previous concepts, we show superior performance of our approach to reliably perceive the environment of a vehicle.
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Deep-learning models for traffic data prediction can have superior performance in modeling complex functions using a multi-layer architecture. However, a major drawback of these approaches is that most of these approaches do not offer forecasts with uncertainty estimates, which are essential for traffic operations and control. Without uncertainty estimates, it is difficult to place any level of trust to the model predictions, and operational strategies relying on overconfident predictions can lead to worsening traffic conditions. In this study, we propose a Bayesian recurrent neural network framework for uncertainty quantification in traffic prediction with higher generalizability by introducing spectral normalization to its hidden layers. In our paper, we have shown that normalization alters the training process of deep neural networks by controlling the model's complexity and reducing the risk of overfitting to the training data. This, in turn, helps improve the generalization performance of the model on out-of-distribution datasets. Results demonstrate that spectral normalization improves uncertainty estimates and significantly outperforms both the layer normalization and model without normalization in single-step prediction horizons. This improved performance can be attributed to the ability of spectral normalization to better localize the feature space of the data under perturbations. Our findings are especially relevant to traffic management applications, where predicting traffic conditions across multiple locations is the goal, but the availability of training data from multiple locations is limited. Spectral normalization, therefore, provides a more generalizable approach that can effectively capture the underlying patterns in traffic data without requiring location-specific models.
Model-based control requires an accurate model of the system dynamics for precisely and safely controlling the robot in complex and dynamic environments. Moreover, in the presence of variations in the operating conditions, the model should be continuously refined to compensate for dynamics changes. In this paper, we present a self-supervised learning approach that actively models the dynamics of nonlinear robotic systems. We combine offline learning from past experience and online learning from current robot interaction with the unknown environment. These two ingredients enable a highly sample-efficient and adaptive learning process, capable of accurately inferring model dynamics in real-time even in operating regimes that greatly differ from the training distribution. Moreover, we design an uncertainty-aware model predictive controller that is heuristically conditioned to the aleatoric (data) uncertainty of the learned dynamics. This controller actively chooses the optimal control actions that (i) optimize the control performance and (ii) improve the efficiency of online learning sample collection. We demonstrate the effectiveness of our method through a series of challenging real-world experiments using a quadrotor system. Our approach showcases high resilience and generalization capabilities by consistently adapting to unseen flight conditions, while it significantly outperforms classical and adaptive control baselines.
How can we quantify uncertainty if our favorite computational tool - be it a numerical, a statistical, or a machine learning approach, or just any computer model - provides single-valued output only? In this article, we introduce the Easy Uncertainty Quantification (EasyUQ) technique, which transforms real-valued model output into calibrated statistical distributions, based solely on training data of model output-outcome pairs, without any need to access model input. In its basic form, EasyUQ is a special case of the recently introduced Isotonic Distributional Regression (IDR) technique that leverages the pool-adjacent-violators algorithm for nonparametric isotonic regression. EasyUQ yields discrete predictive distributions that are calibrated and optimal in finite samples, subject to stochastic monotonicity. The workflow is fully automated, without any need for tuning. The Smooth EasyUQ approach supplements IDR with kernel smoothing, to yield continuous predictive distributions that preserve key properties of the basic form, including both, stochastic monotonicity with respect to the original model output, and asymptotic consistency. For the selection of kernel parameters, we introduce multiple one-fit grid search, a computationally much less demanding approximation to leave-one-out cross-validation. We use simulation examples and forecast data from weather prediction to illustrate the techniques. In a study of benchmark problems from machine learning, we show how EasyUQ and Smooth EasyUQ can be integrated into the workflow of neural network learning and hyperparameter tuning, and find EasyUQ to be competitive with conformal prediction, as well as more elaborate input-based approaches.
Clustering is an important task in many areas of knowledge: medicine and epidemiology, genomics, environmental science, economics, visual sciences, among others. Methodologies to perform inference on the number of clusters have often been proved to be inconsistent, and introducing a dependence structure among the clusters implies additional difficulties in the estimation process. In a Bayesian setting, clustering is performed by considering the unknown partition as a random object and define a prior distribution on it. This prior distribution may be induced by models on the observations, or directly defined for the partition. Several recent results, however, have shown the difficulties in consistently estimating the number of clusters, and, therefore, the partition. The problem itself of summarising the posterior distribution on the partition remains open, given the large dimension of the partition space. This work aims at reviewing the Bayesian approaches available in the literature to perform clustering, presenting advantages and disadvantages of each of them in order to suggest future lines of research.
Bayesian inference is often utilized for uncertainty quantification tasks. A recent analysis by Xu and Raginsky 2022 rigorously decomposed the predictive uncertainty in Bayesian inference into two uncertainties, called aleatoric and epistemic uncertainties, which represent the inherent randomness in the data-generating process and the variability due to insufficient data, respectively. They analyzed those uncertainties in an information-theoretic way, assuming that the model is well-specified and treating the model's parameters as latent variables. However, the existing information-theoretic analysis of uncertainty cannot explain the widely believed property of uncertainty, known as the sensitivity between the test and training data. It implies that when test data are similar to training data in some sense, the epistemic uncertainty should become small. In this work, we study such uncertainty sensitivity using our novel decomposition method for the predictive uncertainty. Our analysis successfully defines such sensitivity using information-theoretic quantities. Furthermore, we extend the existing analysis of Bayesian meta-learning and show the novel sensitivities among tasks for the first time.
Autonomous robotic tasks require actively perceiving the environment to achieve application-specific goals. In this paper, we address the problem of positioning an RGB camera to collect the most informative images to represent an unknown scene, given a limited measurement budget. We propose a novel mapless planning framework to iteratively plan the next best camera view based on collected image measurements. A key aspect of our approach is a new technique for uncertainty estimation in image-based neural rendering, which guides measurement acquisition at the most uncertain view among view candidates, thus maximising the information value during data collection. By incrementally adding new measurements into our image collection, our approach efficiently explores an unknown scene in a mapless manner. We show that our uncertainty estimation is generalisable and valuable for view planning in unknown scenes. Our planning experiments using synthetic and real-world data verify that our uncertainty-guided approach finds informative images leading to more accurate scene representations when compared against baselines.
The generalization mystery in deep learning is the following: Why do over-parameterized neural networks trained with gradient descent (GD) generalize well on real datasets even though they are capable of fitting random datasets of comparable size? Furthermore, from among all solutions that fit the training data, how does GD find one that generalizes well (when such a well-generalizing solution exists)? We argue that the answer to both questions lies in the interaction of the gradients of different examples during training. Intuitively, if the per-example gradients are well-aligned, that is, if they are coherent, then one may expect GD to be (algorithmically) stable, and hence generalize well. We formalize this argument with an easy to compute and interpretable metric for coherence, and show that the metric takes on very different values on real and random datasets for several common vision networks. The theory also explains a number of other phenomena in deep learning, such as why some examples are reliably learned earlier than others, why early stopping works, and why it is possible to learn from noisy labels. Moreover, since the theory provides a causal explanation of how GD finds a well-generalizing solution when one exists, it motivates a class of simple modifications to GD that attenuate memorization and improve generalization. Generalization in deep learning is an extremely broad phenomenon, and therefore, it requires an equally general explanation. We conclude with a survey of alternative lines of attack on this problem, and argue that the proposed approach is the most viable one on this basis.
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.
We present self-supervised geometric perception (SGP), the first general framework to learn a feature descriptor for correspondence matching without any ground-truth geometric model labels (e.g., camera poses, rigid transformations). Our first contribution is to formulate geometric perception as an optimization problem that jointly optimizes the feature descriptor and the geometric models given a large corpus of visual measurements (e.g., images, point clouds). Under this optimization formulation, we show that two important streams of research in vision, namely robust model fitting and deep feature learning, correspond to optimizing one block of the unknown variables while fixing the other block. This analysis naturally leads to our second contribution -- the SGP algorithm that performs alternating minimization to solve the joint optimization. SGP iteratively executes two meta-algorithms: a teacher that performs robust model fitting given learned features to generate geometric pseudo-labels, and a student that performs deep feature learning under noisy supervision of the pseudo-labels. As a third contribution, we apply SGP to two perception problems on large-scale real datasets, namely relative camera pose estimation on MegaDepth and point cloud registration on 3DMatch. We demonstrate that SGP achieves state-of-the-art performance that is on-par or superior to the supervised oracles trained using ground-truth labels.
A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty. The past decade has seen major advances in many perception tasks such as visual object recognition and speech recognition using deep learning models. For higher-level inference, however, probabilistic graphical models with their Bayesian nature are still more powerful and flexible. In recent years, Bayesian deep learning has emerged as a unified probabilistic framework to tightly integrate deep learning and Bayesian models. In this general framework, the perception of text or images using deep learning can boost the performance of higher-level inference and in turn, the feedback from the inference process is able to enhance the perception of text or images. This survey provides a comprehensive introduction to Bayesian deep learning and reviews its recent applications on recommender systems, topic models, control, etc. Besides, we also discuss the relationship and differences between Bayesian deep learning and other related topics such as Bayesian treatment of neural networks.
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