Related papers: Model Selection for independent not identically di…
When performing regression or classification, we are interested in the conditional probability distribution for an outcome or class variable Y given a set of explanatoryor input variables X. We consider Bayesian models for this task. In…
We propose an empirical likelihood ratio test for nonparametric model selection, where the competing models may be nested, nonnested, overlapping, misspecified, or correctly specified. It compares the squared prediction errors of models…
Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another…
The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable than ever. Notwithstanding its…
Log-linear models are a well-established method for describing statistical dependencies among a set of n random variables. The observed frequencies of the n-tuples are explained by a joint probability such that its logarithm is a sum of…
A common problem in physics is to fit regression data by a parametric class of functions, and to decide whether a certain functional form allows for a good fit of the data. Common goodness of fit methods are based on the calculation of the…
Model selection is basically a process of finding the best model from the subset of models in which the explanatory variables are effective on the response variable. The log likelihood function for the lack of fit term and a specified…
Multi-model mimicry (MMM) is a flexible model selection technique for comparison of multiple, non-nested models on any desired goodness-of-fit criteria. Applicable to any set of candidate models that are 1) able to be fit to observed data,…
We consider the problem of model selection in a high-dimensional sparse linear regression model under privacy constraints. We propose a differentially private (DP) best subset selection method with strong statistical utility properties by…
Mathematical models are invaluable for understanding and predicting how biological systems behave, although their construction requires specifying mechanisms and relationships that are often not perfectly known. In the presence of multiple…
In a regression model, prediction is typically performed after model selection. The large variability in the model selection makes the prediction unstable. Thus, it is essential to reduce the variability in model selection and improve…
Subset selection in multiple linear regression aims to choose a subset of candidate explanatory variables that tradeoff fitting error (explanatory power) and model complexity (number of variables selected). We build mathematical programming…
We propose novel methodology for testing equality of model parameters between two high-dimensional populations. The technique is very general and applicable to a wide range of models. The method is based on sample splitting: the data is…
In today's modern era of Big data, computationally efficient and scalable methods are needed to support timely insights and informed decision making. One such method is sub-sampling, where a subset of the Big data is analysed and used as…
In machine learning, privacy requirements at inference or deployment time often evolve due to changing policies, regulations, or user preferences. In this work, we aim to construct a magnitude of models to satisfy any target differential…
Penalized regression models are popularly used in high-dimensional data analysis to conduct variable selection and model fitting simultaneously. Whereas success has been widely reported in literature, their performances largely depend on…
In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory…
Using a recently proposed privacy definition of R\'enyi Differential Privacy (RDP), we re-examine the inherent privacy of releasing a single sample from a posterior distribution. We exploit the impact of the prior distribution in mitigating…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…
In regression with random design, we study the problem of selecting a model that performs well for out-of-sample prediction. We do not assume that any of the candidate models under consideration are correct. Our analysis is based on…