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Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…
Identifying dynamical system (DS) is a vital task in science and engineering. Traditional methods require numerous calls to the DS solver, rendering likelihood-based or least-squares inference frameworks impractical. For efficient parameter…
A practical approach to evaluate performance of a Gaussian process regression models (GPR) for irregularly sampled sparse time-series is introduced. The approach entails construction of a secondary autoregressive model using the fine scale…
In data analysis, contamination caused by outliers is inevitable, and robust statistical methods are strongly demanded. In this paper, our concern is to develop a new approach for robust data analysis based on scoring rules. The scoring…
Out-of-distribution (OOD) detection is an important task in machine learning systems for ensuring their reliability and safety. Deep probabilistic generative models facilitate OOD detection by estimating the likelihood of a data sample.…
Local Polynomial Regression (LPR) is a widely used nonparametric method for modeling complex relationships due to its flexibility and simplicity. It estimates a regression function by fitting low-degree polynomials to localized subsets of…
Modeling epidemic spread is critical for informing policy decisions aimed at mitigation. Accordingly, in this work we present a new data-driven method based on Gaussian process regression (GPR) to model epidemic spread through the…
Gaussian process regression (GPR) is a powerful machine learning method which has recently enjoyed wider use, in particular in physical sciences. In its original formulation, GPR uses a square matrix of covariances among training data and…
Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the…
Gaussian processes (GP) are a widely used model for regression problems in supervised machine learning. Implementation of GP regression typically requires $O(n^3)$ logic gates. We show that the quantum linear systems algorithm [Harrow et…
Gaussian process (GP) methods have been widely studied recently, especially for large-scale systems with big data and even more extreme cases when data is sparse. Key advantages of these methods consist in: 1) the ability to provide…
Linear regression with the classical normality assumption for the error distribution may lead to an undesirable posterior inference of regression coefficients due to the potential outliers. This paper considers the finite mixture of two…
Sure Independence Screening is a fast procedure for variable selection in ultra-high dimensional regression analysis. Unfortunately, its performance greatly deteriorates with increasing dependence among the predictors. To solve this issue,…
Multi-output regression seeks to borrow strength and leverage commonalities across different but related outputs in order to enhance learning and prediction accuracy. A fundamental assumption is that the output/group membership labels for…
The performance of Gaussian Process (GP) regression is often hampered by the curse of dimensionality, which inflates computational cost and reduces predictive power in high-dimensional problems. Variable selection is thus crucial for…
When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that…
Almost all scientific data have uncertainties originating from different sources. Gaussian process regression (GPR) models are a natural way to model data with Gaussian-distributed uncertainties. GPR also has the benefit of reducing I/O…
Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…
Outliers in discrete choice response data may result from misclassification and misreporting of the response variable and from choice behaviour that is inconsistent with modelling assumptions (e.g. random utility maximisation). In the…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…