Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regression modelling with I-priors   We introduce the I-prior methodology as a unifying framework for estimating a
variety of regression models, including varying coefficient, multilevel,
longitudinal models, and models with functional covariates and responses. It
can also be used for multi-class classification, with low or high dimensional
covariates.
  The I-prior is generally defined as a maximum entropy prior. For a regression
function, the I-prior is Gaussian with covariance kernel proportional to the
Fisher information on the regression function, which is estimated by its
posterior distribution under the I-prior. The I-prior has the intuitively
appealing property that the more information is available on a linear
functional of the regression function, the larger the prior variance, and the
smaller the influence of the prior mean on the posterior distribution.
  Advantages compared to competing methods, such as Gaussian process regression
or Tikhonov regularization, are ease of estimation and model comparison. In
particular, we develop an EM algorithm with a simple E and M step for
estimating hyperparameters, facilitating estimation for complex models. We also
propose a novel parsimonious model formulation, requiring a single scale
parameter for each (possibly multidimensional) covariate and no further
parameters for interaction effects. This simplifies estimation because fewer
hyperparameters need to be estimated, and also simplifies model comparison of
models with the same covariates but different interaction effects; in this
case, the model with the highest estimated likelihood can be selected.
  Using a number of widely analyzed real data sets we show that predictive
performance of our methodology is competitive. An R-package implementing the
methodology is available (Jamil, 2019).

33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph