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Neural ordinary differential equations (ODEs) are an emerging class of deep learning models for dynamical systems. They are particularly useful for learning an ODE vector field from observed trajectories (i.e., inverse problems). We here…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
Neural networks are among the most accurate supervised learning methods in use today, but their opacity makes them difficult to trust in critical applications, especially when conditions in training differ from those in test. Recent work on…
A Bayesian treatment of deep learning allows for the computation of uncertainties associated with the predictions of deep neural networks. We show how the concept of Errors-in-Variables can be used in Bayesian deep regression to also…
Uncertainty estimation aims to evaluate the confidence of a trained deep neural network. However, existing uncertainty estimation approaches rely on low-dimensional distributional assumptions and thus suffer from the high dimensionality of…
Data-driven forecasts of air quality have recently achieved more accurate short-term predictions. Despite their success, most of the current data-driven solutions lack proper quantifications of model uncertainty that communicate how much to…
This paper proposes a paradigm of uncertainty injection for training deep learning model to solve robust optimization problems. The majority of existing studies on deep learning focus on the model learning capability, while assuming the…
Approximate Bayesian inference for the class of latent Gaussian models can be achieved efficiently with integrated nested Laplace approximations (INLA). Based on recent reformulations in the INLA methodology, we propose a further extension…
Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…
Deep learning methods employ multiple processing layers to learn hierarchical representations of data and have produced state-of-the-art results in many domains. Recently, a variety of model designs and methods have blossomed in the context…
Machine learning is finding increasingly broad application in the physical sciences. This most often involves building a model relationship between a dependent, measurable output and an associated set of controllable, but complicated,…
The optimization foundations of deep linear networks have recently received significant attention. However, due to their inherent non-convexity and hierarchical structure, analyzing the loss functions of deep linear networks remains a…
Existing deep active learning algorithms achieve impressive sampling efficiency on natural language processing tasks. However, they exhibit several weaknesses in practice, including (a) inability to use uncertainty sampling with black-box…
Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…
Approximate Bayesian inference typically revolves around computing the posterior parameter distribution. In practice, however, the main object of interest is often a model's predictions rather than its parameters. In this work, we propose…
There has been a recent push in making machine learning models more interpretable so that their performance can be trusted. Although successful, these methods have mostly focused on the deep learning methods while the fundamental…
The integrated nested Laplace approximations (INLA) method has become a widely utilized tool for researchers and practitioners seeking to perform approximate Bayesian inference across various fields of application. To address the growing…
Deep learning is a topic of considerable current interest. The availability of massive data collections and powerful software resources has led to an impressive amount of results in many application areas that reveal essential but hidden…
Traditional deep neural nets (NNs) have shown the state-of-the-art performance in the task of classification in various applications. However, NNs have not considered any types of uncertainty associated with the class probabilities to…
Deep Neural Networks (DNNs) have achieved state-of-the-art accuracy performance in many tasks. However, recent works have pointed out that the outputs provided by these models are not well-calibrated, seriously limiting their use in…