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This paper considers generalized linear models using rule-based features, also referred to as rule ensembles, for regression and probabilistic classification. Rules facilitate model interpretation while also capturing nonlinear dependences…

The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model (GLM) for the outcome variable, and a working…

We study low-rank matrix regression in settings where matrix-valued predictors and scalar responses are observed across multiple individuals. Rather than assuming a fully homogeneous coefficient matrices across individuals, we accommodate…

We propose a supervised principal component regression method for relating functional responses with high dimensional predictors. Unlike the conventional principal component analysis, the proposed method builds on a newly defined expected…

Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…

In categorical data analysis, several regression models have been proposed for hierarchically-structured response variables, e.g. the nested logit model. But they have been formally defined for only two or three levels in the hierarchy.…

Mixtures of Linear Regressions (MLR) is an important mixture model with many applications. In this model, each observation is generated from one of the several unknown linear regression components, where the identity of the generated…

Extending generalized estimating equations (GEE) to ordinal response data requires a conversion of the ordinal response to a vector of binary category indicators. That leads to a rather complicated association structure, and the…

Relational logistic regression (RLR) is a representation of conditional probability in terms of weighted formulae for modelling multi-relational data. In this paper, we develop a learning algorithm for RLR models. Learning an RLR model from…

Regression is a fundamental tool in scientific research. Ordinary least squares (OLS), one of the most widely used regression methods, enjoys several desirable properties, including the best linear unbiased estimator (BLUE) property. It is…

Standard Gaussian Process (GP) regression, a powerful machine learning tool, is computationally expensive when it is applied to large datasets, and potentially inaccurate when data points are sparsely distributed in a high-dimensional…

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among…

In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (a) p-values from a previous study, (b) a summary of prior information, and (c) omics…

The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…

Local regression is widely used to explore spatial heterogeneity, but anisotropic or effectively low-dimensional neighborhoods can produce ill-conditioned local solves, causing coefficient variation driven by numerical artifacts rather than…

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…

Clinical and epidemiological studies encode participant information in multivariate vectors with mixed type variables on continuous, truncated, ordinal, and binary scales. Semiparametric Gaussian Copula (SGC) assumes that observed data is…

We consider the problem of learning Relational Logistic Regression (RLR). Unlike standard logistic regression, the features of RLRs are first-order formulae with associated weight vectors instead of scalar weights. We turn the problem of…

Partial least squares (PLS) regression combines dimensionality reduction and prediction using a latent variable model. Since partial least squares regression (PLS-R) does not require matrix inversion or diagonalization, it can be applied to…

We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression matrix by elaborately adding more rows.…