Structured uncertainty prediction networks

This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to predict a full Gaussian covariance matrix for each reconstruction, which permits efficient sampling and likelihood evaluation. We demonstrate that our model can accurately reconstruct ground truth correlated residual distributions for synthetic datasets and generate plausible high frequency samples for real face images. We also illustrate the use of these predicted covariances for structure preserving image denoising

Reliable Multimodal Trajectory Prediction via Error Aligned Uncertainty Optimization

Reliable uncertainty quantification in deep neural networks is very crucial in safety-critical applications such as automated driving for trustworthy and informed decision-making. Assessing the quality of uncertainty estimates is challenging as ground truth for uncertainty estimates is not available. Ideally, in a well-calibrated model, uncertainty estimates should perfectly correlate with model error. We propose a novel error aligned uncertainty optimization method and introduce a trainable loss function to guide the models to yield good quality uncertainty estimates aligning with the model error. Our approach targets continuous structured prediction and regression tasks, and is evaluated on multiple datasets including a large-scale vehicle motion prediction task involving real-world distributional shifts. We demonstrate that our method improves average displacement error by 1.69% and 4.69%, and the uncertainty correlation with model error by 17.22% and 19.13% as quantified by Pearson correlation coefficient on two state-of-the-art baselines.Comment: Accepted to ECCV 2022 workshop - Safe Artificial Intelligence for Automated Drivin

A New PHO-rmula for Improved Performance of Semi-Structured Networks

Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural networks (SSNs). We show that techniques to properly identify the contributions of the different model components in SSNs, however, lead to suboptimal network estimation, slower convergence, and degenerated or erroneous predictions. In order to solve these problems while preserving favorable model properties, we propose a non-invasive post-hoc orthogonalization (PHO) that guarantees identifiability of model components and provides better estimation and prediction quality. Our theoretical findings are supported by numerical experiments, a benchmark comparison as well as a real-world application to COVID-19 infections.Comment: ICML 202

Improving Uncertainty Quantification of Variance Networks by Tree-Structured Learning

To improve uncertainty quantification of variance networks, we propose a novel tree-structured local neural network model that partitions the feature space into multiple regions based on uncertainty heterogeneity. A tree is built upon giving the training data, whose leaf nodes represent different regions where region-specific neural networks are trained to predict both the mean and the variance for quantifying uncertainty. The proposed Uncertainty-Splitting Neural Regression Tree (USNRT) employs novel splitting criteria. At each node, a neural network is trained on the full data first, and a statistical test for the residuals is conducted to find the best split, corresponding to the two sub-regions with the most significant uncertainty heterogeneity. USNRT is computationally friendly because very few leaf nodes are sufficient and pruning is unnecessary. On extensive UCI datasets, in terms of both calibration and sharpness, USNRT shows superior performance compared to some recent popular methods for variance prediction, including vanilla variance network, deep ensemble, dropout-based methods, tree-based models, etc. Through comprehensive visualization and analysis, we uncover how USNRT works and show its merits

Uncertainty Quantification over Graph with Conformalized Graph Neural Networks

Graph Neural Networks (GNNs) are powerful machine learning prediction models on graph-structured data. However, GNNs lack rigorous uncertainty estimates, limiting their reliable deployment in settings where the cost of errors is significant. We propose conformalized GNN (CF-GNN), extending conformal prediction (CP) to graph-based models for guaranteed uncertainty estimates. Given an entity in the graph, CF-GNN produces a prediction set/interval that provably contains the true label with pre-defined coverage probability (e.g. 90%). We establish a permutation invariance condition that enables the validity of CP on graph data and provide an exact characterization of the test-time coverage. Moreover, besides valid coverage, it is crucial to reduce the prediction set size/interval length for practical use. We observe a key connection between non-conformity scores and network structures, which motivates us to develop a topology-aware output correction model that learns to update the prediction and produces more efficient prediction sets/intervals. Extensive experiments show that CF-GNN achieves any pre-defined target marginal coverage while significantly reducing the prediction set/interval size by up to 74% over the baselines. It also empirically achieves satisfactory conditional coverage over various raw and network features.Comment: Published at NeurIPS 202