The novel Bayesian loss described in formula 7 can be computed in closed form. For vector datasets, all models share an architecture of 3 linear layers with Relu activation. For PostNet, we used a 1D batch normalization after the encoder. All metrics have been scaled by 100 . We obtain numbers in [0, 100] for all scores instead of [0, 1].

Based on R1's comments we also evaluated the models based on mutual Theoretically, the two metrics bring similar information [C]. For these reasons, we decided to use APR. We attribute the strong performance of PostNet to the dim. Similar conclusions have been drawn in [E]. In our paper we use 5 random splits (60%, 20%, 20%).

The novel Bayesian loss described in formula 7 can be computed in closed form. For vector datasets, all models share an architecture of 3 linear layers with Relu activation. For PostNet, we used a 1D batch normalization after the encoder. All metrics have been scaled by 100 . We obtain numbers in [0, 100] for all scores instead of [0, 1].

This paper explores a modern predictive uncertainty estimation approach, called evidential deep learning (EDL), in which a single neural network model is trained to learn a meta distribution over the predictive distribution by minimizing a specific objective function. Despite their strong empirical performance, recent studies by Bengs et al. identify a fundamental pitfall of the existing methods: the learned epistemic uncertainty may not vanish even in the infinite-sample limit. We corroborate the observation by providing a unifying view of a class of widely used objectives from the literature. Our analysis reveals that the EDL methods essentially train a meta distribution by minimizing a certain divergence measure between the distribution and a sample-size-independent target distribution, resulting in spurious epistemic uncertainty. Grounded in theoretical principles, we propose learning a consistent target distribution by modeling it with a mixture of Dirichlet distributions and learning via variational inference. Afterward, a final meta distribution model distills the learned uncertainty from the target model. Experimental results across various uncertainty-based downstream tasks demonstrate the superiority of our proposed method, and illustrate the practical implications arising from the consistency and inconsistency of learned epistemic uncertainty.

In this paper, we propose a differentiable WORLD synthesizer and demonstrate its use in end-to-end audio style transfer tasks such as (singing) voice conversion and the DDSP timbre transfer task. Accordingly, our baseline differentiable synthesizer has no model parameters, yet it yields adequate synthesis quality. We can extend the baseline synthesizer by appending lightweight black-box postnets which apply further processing to the baseline output in order to improve fidelity. An alternative differentiable approach considers extraction of the source excitation spectrum directly, which can improve naturalness albeit for a narrower class of style transfer applications. The acoustic feature parameterization used by our approaches has the added benefit that it naturally disentangles pitch and timbral information so that they can be modeled separately. Moreover, as there exists a robust means of estimating these acoustic features from monophonic audio sources, it allows for parameter loss terms to be added to an end-to-end objective function, which can help convergence and/or further stabilize (adversarial) training.

Accurate estimation of aleatoric and epistemic uncertainty is crucial to build safe and reliable systems. Traditional approaches, such as dropout and ensemble methods, estimate uncertainty by sampling probability predictions from different submodels, which leads to slow uncertainty estimation at inference time. Recent works address this drawback by directly predicting parameters of prior distributions over the probability predictions with a neural network. While this approach has demonstrated accurate uncertainty estimation, it requires defining arbitrary target parameters for in-distribution data and makes the unrealistic assumption that out-of-distribution (OOD) data is known at training time. In this work we propose the Posterior Network (PostNet), which uses Normalizing Flows to predict an individual closed-form posterior distribution over predicted probabilites for any input sample. The posterior distributions learned by PostNet accurately reflect uncertainty for in- and out-of-distribution data -- without requiring access to OOD data at training time. PostNet achieves state-of-the art results in OOD detection and in uncertainty calibration under dataset shifts.