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Outcomes of data-driven AI models cannot be assumed to be always correct. To estimate the uncertainty in these outcomes, the uncertainty wrapper framework has been proposed, which considers uncertainties related to model fit, input quality, and scope compliance. Uncertainty wrappers use a decision tree approach to cluster input quality related uncertainties, assigning inputs strictly to distinct uncertainty clusters. Hence, a slight variation in only one feature may lead to a cluster assignment with a significantly different uncertainty. Our objective is to replace this with an approach that mitigates hard decision boundaries of these assignments while preserving interpretability, runtime complexity, and prediction performance. Five approaches were selected as candidates and integrated into the uncertainty wrapper framework. For the evaluation based on the Brier score, datasets for a pedestrian detection use case were generated using the CARLA simulator and YOLOv3. All integrated approaches achieved a softening, i.e., smoothing, of uncertainty estimation. Yet, compared to decision trees, they are not so easy to interpret and have higher runtime complexity. Moreover, some components of the Brier score impaired while others improved. Most promising regarding the Brier score were random forests. In conclusion, softening hard decision tree boundaries appears to be a trade-off decision.

Deraining is a significant and fundamental computer vision task, aiming to remove the rain streaks and accumulations in an image or video captured under a rainy day. Existing deraining methods usually make heuristic assumptions of the rain model, which compels them to employ complex optimization or iterative refinement for high recovery quality. This, however, leads to time-consuming methods and affects the effectiveness for addressing rain patterns deviated from from the assumptions. In this paper, we propose a simple yet efficient deraining method by formulating deraining as a predictive filtering problem without complex rain model assumptions. Specifically, we identify spatially-variant predictive filtering (SPFilt) that adaptively predicts proper kernels via a deep network to filter different individual pixels. Since the filtering can be implemented via well-accelerated convolution, our method can be significantly efficient. We further propose the EfDeRain+ that contains three main contributions to address residual rain traces, multi-scale, and diverse rain patterns without harming the efficiency. First, we propose the uncertainty-aware cascaded predictive filtering (UC-PFilt) that can identify the difficulties of reconstructing clean pixels via predicted kernels and remove the residual rain traces effectively. Second, we design the weight-sharing multi-scale dilated filtering (WS-MS-DFilt) to handle multi-scale rain streaks without harming the efficiency. Third, to eliminate the gap across diverse rain patterns, we propose a novel data augmentation method (i.e., RainMix) to train our deep models. By combining all contributions with sophisticated analysis on different variants, our final method outperforms baseline methods on four single-image deraining datasets and one video deraining dataset in terms of both recovery quality and speed.

In model-free deep reinforcement learning (RL) algorithms, using noisy value estimates to supervise policy evaluation and optimization is detrimental to the sample efficiency. As this noise is heteroscedastic, its effects can be mitigated using uncertainty-based weights in the optimization process. Previous methods rely on sampled ensembles, which do not capture all aspects of uncertainty. We provide a systematic analysis of the sources of uncertainty in the noisy supervision that occurs in RL, and introduce inverse-variance RL, a Bayesian framework which combines probabilistic ensembles and Batch Inverse Variance weighting. We propose a method whereby two complementary uncertainty estimation methods account for both the Q-value and the environment stochasticity to better mitigate the negative impacts of noisy supervision. Our results show significant improvement in terms of sample efficiency on discrete and continuous control tasks.

Managing a large-scale portfolio with many assets is one of the most challenging tasks in the field of finance. It is partly because estimation of either covariance or precision matrix of asset returns tends to be unstable or even infeasible when the number of assets $p$ exceeds the number of observations $n$. For this reason, most of the previous studies on portfolio management have focused on the case of $p < n$. To deal with the case of $p > n$, we propose to use a new Bayesian framework based on adaptive graphical LASSO for estimating the precision matrix of asset returns in a large-scale portfolio. Unlike the previous studies on graphical LASSO in the literature, our approach utilizes a Bayesian estimation method for the precision matrix proposed by Oya and Nakatsuma (2020) so that the positive definiteness of the precision matrix should be always guaranteed. As an empirical application, we construct the global minimum variance portfolio of $p=100$ for various values of $n$ with the proposed approach as well as the non-Bayesian graphical LASSO approach, and compare their out-of-sample performance with the equal weight portfolio as the benchmark. We also compare them with portfolios based on random matrix theory filtering and Ledoit-Wolf shrinkage estimation which were used by Torri et al. (2019). In this comparison, the proposed approach produces more stable results than the non-Bayesian approach and the other comparative approaches in terms of Sharpe ratio, portfolio composition and turnover even if $n$ is much smaller than $p$.

In this work we use variational inference to quantify the degree of uncertainty in deep learning model predictions of radio galaxy classification. We show that the level of model posterior variance for individual test samples is correlated with human uncertainty when labelling radio galaxies. We explore the model performance and uncertainty calibration for a variety of different weight priors and suggest that a sparse prior produces more well-calibrated uncertainty estimates. Using the posterior distributions for individual weights, we show that we can prune 30% of the fully-connected layer weights without significant loss of performance by removing the weights with the lowest signal-to-noise ratio (SNR). We demonstrate that a larger degree of pruning can be achieved using a Fisher information based ranking, but we note that both pruning methods affect the uncertainty calibration for Fanaroff-Riley type I and type II radio galaxies differently. Finally we show that, like other work in this field, we experience a cold posterior effect, whereby the posterior must be down-weighted to achieve good predictive performance. We examine whether adapting the cost function to accommodate model misspecification can compensate for this effect, but find that it does not make a significant difference. We also examine the effect of principled data augmentation and find that this improves upon the baseline but also does not compensate for the observed effect. We interpret this as the cold posterior effect being due to the overly effective curation of our training sample leading to likelihood misspecification, and raise this as a potential issue for Bayesian deep learning approaches to radio galaxy classification in future.

This dissertation studies a fundamental open challenge in deep learning theory: why do deep networks generalize well even while being overparameterized, unregularized and fitting the training data to zero error? In the first part of the thesis, we will empirically study how training deep networks via stochastic gradient descent implicitly controls the networks' capacity. Subsequently, to show how this leads to better generalization, we will derive {\em data-dependent} {\em uniform-convergence-based} generalization bounds with improved dependencies on the parameter count. Uniform convergence has in fact been the most widely used tool in deep learning literature, thanks to its simplicity and generality. Given its popularity, in this thesis, we will also take a step back to identify the fundamental limits of uniform convergence as a tool to explain generalization. In particular, we will show that in some example overparameterized settings, {\em any} uniform convergence bound will provide only a vacuous generalization bound. With this realization in mind, in the last part of the thesis, we will change course and introduce an {\em empirical} technique to estimate generalization using unlabeled data. Our technique does not rely on any notion of uniform-convergece-based complexity and is remarkably precise. We will theoretically show why our technique enjoys such precision. We will conclude by discussing how future work could explore novel ways to incorporate distributional assumptions in generalization bounds (such as in the form of unlabeled data) and explore other tools to derive bounds, perhaps by modifying uniform convergence or by developing completely new tools altogether.

Deep neural networks have significantly contributed to the success in predictive accuracy for classification tasks. However, they tend to make over-confident predictions in real-world settings, where domain shifting and out-of-distribution (OOD) examples exist. Most research on uncertainty estimation focuses on computer vision because it provides visual validation on uncertainty quality. However, few have been presented in the natural language process domain. Unlike Bayesian methods that indirectly infer uncertainty through weight uncertainties, current evidential uncertainty-based methods explicitly model the uncertainty of class probabilities through subjective opinions. They further consider inherent uncertainty in data with different root causes, vacuity (i.e., uncertainty due to a lack of evidence) and dissonance (i.e., uncertainty due to conflicting evidence). In our paper, we firstly apply evidential uncertainty in OOD detection for text classification tasks. We propose an inexpensive framework that adopts both auxiliary outliers and pseudo off-manifold samples to train the model with prior knowledge of a certain class, which has high vacuity for OOD samples. Extensive empirical experiments demonstrate that our model based on evidential uncertainty outperforms other counterparts for detecting OOD examples. Our approach can be easily deployed to traditional recurrent neural networks and fine-tuned pre-trained transformers.

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.

The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this work, we show that it suffices to perform inference over a small subset of model weights in order to obtain accurate predictive posteriors. The other weights are kept as point estimates. This subnetwork inference framework enables us to use expressive, otherwise intractable, posterior approximations over such subsets. In particular, we implement subnetwork linearized Laplace: We first obtain a MAP estimate of all weights and then infer a full-covariance Gaussian posterior over a subnetwork. We propose a subnetwork selection strategy that aims to maximally preserve the model's predictive uncertainty. Empirically, our approach is effective compared to ensembles and less expressive posterior approximations over full networks.

Data augmentation has been widely used for training deep learning systems for medical image segmentation and plays an important role in obtaining robust and transformation-invariant predictions. However, it has seldom been used at test time for segmentation and not been formulated in a consistent mathematical framework. In this paper, we first propose a theoretical formulation of test-time augmentation for deep learning in image recognition, where the prediction is obtained through estimating its expectation by Monte Carlo simulation with prior distributions of parameters in an image acquisition model that involves image transformations and noise. We then propose a novel uncertainty estimation method based on the formulated test-time augmentation. Experiments with segmentation of fetal brains and brain tumors from 2D and 3D Magnetic Resonance Images (MRI) showed that 1) our test-time augmentation outperforms a single-prediction baseline and dropout-based multiple predictions, and 2) it provides a better uncertainty estimation than calculating the model-based uncertainty alone and helps to reduce overconfident incorrect predictions.