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In this study, we prove rigourous bounds on the error and stability analysis of deep learning methods for the nonstationary Magneto-hydrodynamics equations. We obtain the approximate ability of the neural network by the convergence of a…
Deep learning models have significantly improved prediction accuracy in various fields, gaining recognition across numerous disciplines. Yet, an aspect of deep learning that remains insufficiently addressed is the assessment of prediction…
Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…
Although treatment effects can be estimated from observed outcome distributions obtained from proper randomization in clinical trials, covariate adjustment is recommended to increase precision. For important treatment effects, such as odds…
Event datasets are sequences of events of various types occurring irregularly over the time-line, and they are increasingly prevalent in numerous domains. Existing work for modeling events using conditional intensities rely on either using…
In this paper, we propose a new deep learning approach, called neural association model (NAM), for probabilistic reasoning in artificial intelligence. We propose to use neural networks to model association between any two events in a…
We present neural frailty machine (NFM), a powerful and flexible neural modeling framework for survival regressions. The NFM framework utilizes the classical idea of multiplicative frailty in survival analysis to capture unobserved…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…
The ratio of the hazard functions of two populations or two strata of a single population plays an important role in time-to-event analysis. Cox regression is commonly used to estimate the hazard ratio under the assumption that it is…
Deep neural networks (DNN) have been used successfully in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. In this paper, we…
Survival analysis aims at modeling the relationship between covariates and event occurrence with some untracked (censored) samples. In implementation, existing methods model the survival distribution with strong assumptions or in a discrete…
We introduce new approaches for forecasting IBNR (Incurred But Not Reported) frequencies by leveraging individual claims data, which includes accident date, reporting delay, and possibly additional features for every reported claim. A key…
Survival analysis is a critical tool for the modelling of time-to-event data, such as life expectancy after a cancer diagnosis or optimal maintenance scheduling for complex machinery. However, current neural network models provide an…
Recent developments on deep learning established some theoretical properties of deep neural networks estimators. However, most of the existing works on this topic are restricted to bounded loss functions or (sub)-Gaussian or bounded input.…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…
Classical deep learning typically operates on individual cases. Despite its success, real-world usage often requires repeated inference to estimate statistical quantities for complex decision-making tasks involving uncertainty or…
The hazard ratio from the Cox proportional hazards model is a ubiquitous summary of treatment effect. However, when hazards are non-proportional, the hazard ratio can lose a stable causal interpretation and become study-dependent because it…
Auxiliary information can be exploited in machine learning models using the paradigm of evidence based conditional inference. Multi-modal techniques in Deep Neural Networks (DNNs) can be seen as perturbing the latent feature representation…
This paper establishes statistical properties of deep neural network (DNN) estimators under dependent data. Two general results for nonparametric sieve estimators directly applicable to DNN estimators are given. The first establishes rates…