Large transformer-based foundation models have been commonly used as pre-trained models that can be adapted to different challenging datasets and settings with state-of-the-art generalization performance.

Multi-label active learning is a crucial yet challenging area in contemporary machine learning, often complicated by a large and sparse label space.

Large transformer-based foundation models have been commonly used as pre-trained models that can be adapted to different challenging datasets and settings with state-of-the-art generalization performance.

Deterministic neural networks (NNs) are increasingly being deployed in safety critical domains, where calibrated, robust, and efficient measures of uncertainty are crucial.

Conformal prediction (CP) is a popular frequentist framework for representing uncertainty by providing prediction sets that guarantee coverage of the true label with a user-adjustable probability. In most applications, CP operates on confidence scores coming from a standard (first-order) probabilistic predictor (e.g., softmax outputs). Second-order predictors, such as credal set predictors or Bayesian models, are also widely used for uncertainty quantification and are known for their ability to represent both aleatoric and epistemic uncertainty. Despite their popularity, there is still an open question on ``how they can be incorporated into CP''. In this paper, we discuss the desiderata for CP when valid second-order predictions are available. We then introduce Bernoulli prediction sets (BPS), which produce the smallest prediction sets that ensure conditional coverage in this setting. When given first-order predictions, BPS reduces to the well-known adaptive prediction sets (APS). Furthermore, when the validity assumption on the second-order predictions is compromised, we apply conformal risk control to obtain a marginal coverage guarantee while still accounting for epistemic uncertainty.

In the early stages of drug discovery, decisions regarding which experiments to pursue can be influenced by computational models. These decisions are critical due to the time-consuming and expensive nature of the experiments. Therefore, it is becoming essential to accurately quantify the uncertainty in machine learning predictions, such that resources can be used optimally and trust in the models improves. While computational methods for drug discovery often suffer from limited data and sparse experimental observations, additional information can exist in the form of censored labels that provide thresholds rather than precise values of observations. However, the standard approaches that quantify uncertainty in machine learning cannot fully utilize censored labels. In this work, we adapt ensemble-based, Bayesian, and Gaussian models with tools to learn from censored labels by using the Tobit model from survival analysis. Our results demonstrate that despite the partial information available in censored labels, they are essential to accurately and reliably model the real pharmaceutical setting.

The Evidential Regression Network (ERN) represents a novel approach that integrates deep learning with Dempster-Shafer's theory to predict a target and quantify the associated uncertainty. Guided by the underlying theory, specific activation functions must be employed to enforce non-negative values, which is a constraint that compromises model performance by limiting its ability to learn from all samples. This paper provides a theoretical analysis of this limitation and introduces an improvement to overcome it. Initially, we define the region where the models can't effectively learn from the samples. Following this, we thoroughly analyze the ERN and investigate this constraint. Leveraging the insights from our analysis, we address the limitation by introducing a novel regularization term that empowers the ERN to learn from the whole training set. Our extensive experiments substantiate our theoretical findings and demonstrate the effectiveness of the proposed solution.

High-fidelity computational simulations and physical experiments of hypersonic flows are resource intensive. Training scientific machine learning (SciML) models on limited high-fidelity data offers one approach to rapidly predict behaviors for situations that have not been seen before. However, high-fidelity data is itself in limited quantity to validate all outputs of the SciML model in unexplored input space. As such, an uncertainty-aware SciML model is desired. The SciML model's output uncertainties could then be used to assess the reliability and confidence of the model's predictions. In this study, we extend a deep operator network (Deep-ONet) using three different uncertainty quantification mechanisms: mean-variance estimation (MVE), evidential uncertainty, and ensembling. The uncertainty aware DeepONet models are trained and evaluated on the hypersonic flow around a blunt cone object with data generated via computational fluid dynamics over a wide range of Mach numbers and altitudes. We find that ensembling outperforms the other two uncertainty models in terms of minimizing error and calibrating uncertainty in both interpolative and extrapolative regimes.

Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant evidential models can quantify fine-grained uncertainty using the learned evidence. To ensure theoretically sound evidential models, the evidence needs to be non-negative, which requires special activation functions for model training and inference. This constraint often leads to inferior predictive performance compared to standard softmax models, making it challenging to extend them to many large-scale datasets. To unveil the real cause of this undesired behavior, we theoretically investigate evidential models and identify a fundamental limitation that explains the inferior performance: existing evidential activation functions create zero evidence regions, which prevent the model to learn from training samples falling into such regions. A deeper analysis of evidential activation functions based on our theoretical underpinning inspires the design of a novel regularizer that effectively alleviates this fundamental limitation. Extensive experiments over many challenging real-world datasets and settings confirm our theoretical findings and demonstrate the effectiveness of our proposed approach.