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We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

Undirected graphical models are powerful tools for uncovering complex relationships among high-dimensional variables. This paper aims to fully recover the structure of an undirected graphical model when the data naturally take matrix form,…

The aim of this paper is to propose a suitable method for constructing prediction intervals for the output of neural network models. To do this, we adapt the extremely randomized trees method originally developed for random forests to…

Estimating causal effects from observational data informs us about which factors are important in an autonomous system, and enables us to take better decisions. This is important because it has applications in selecting a treatment in…

Consider the problem of estimating average treatment effects when a large number of covariates are used to adjust for possible confounding through outcome regression and propensity score models. The conventional approach of model building…

To have a superior generalization, a deep learning neural network often involves a large size of training sample. With increase of hidden layers in order to increase learning ability, neural network has potential degradation in accuracy.…

We present a new and general method of weighted least square univariate regression where the dependent variable is expanded as a series of suitably chosen functions of the independent variables. Each term of the series is obtained by an…

Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As…

Regression methods assume that accurate labels are available for training. However, in certain scenarios, obtaining accurate labels may not be feasible, and relying on multiple specialists with differing opinions becomes necessary. Existing…

Researchers now routinely use AI or other machine learning methods to estimate latent variables of economic interest, then plug-in the estimates as covariates in a regression. We show both theoretically and empirically that naively treating…

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design…

Deep neural networks tend to underestimate uncertainty and produce overly confident predictions. Recently proposed solutions, such as MC Dropout and SDENet, require complex training and/or auxiliary out-of-distribution data. We propose a…

Symbolic regression via genetic programming is a flexible approach to machine learning that does not require up-front specification of model structure. However, traditional approaches to symbolic regression require the use of protected…

In engineering, models are often used to represent the behavior of a system. Estimators are then needed to approximate the values of the model's parameters based on observations. This approximation implies a difference between the values…

In regression modelling approach, the main step is to fit the regression line as close as possible to the target variable. In this process most algorithms try to fit all of the data in a single line and hence fitting all parts of target…

A prediction interval covers a future observation from a random process in repeated sampling, and is typically constructed by identifying a pivotal quantity that is also an ancillary statistic. Analogously, a tolerance interval covers a…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of…

There is significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware neural networks (NNs), based on learning…

We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…