2 research outputs found
LMLFM: Longitudinal Multi-Level Factorization Machine
We consider the problem of learning predictive models from longitudinal data,
consisting of irregularly repeated, sparse observations from a set of
individuals over time. Such data often exhibit {\em longitudinal correlation}
(LC) (correlations among observations for each individual over time), {\em
cluster correlation} (CC) (correlations among individuals that have similar
characteristics), or both. These correlations are often accounted for using
{\em mixed effects models} that include {\em fixed effects} and {\em random
effects}, where the fixed effects capture the regression parameters that are
shared by all individuals, whereas random effects capture those parameters that
vary across individuals. However, the current state-of-the-art methods are
unable to select the most predictive fixed effects and random effects from a
large number of variables, while accounting for complex correlation structure
in the data and non-linear interactions among the variables. We propose
Longitudinal Multi-Level Factorization Machine (LMLFM), to the best of our
knowledge, the first model to address these challenges in learning predictive
models from longitudinal data. We establish the convergence properties, and
analyze the computational complexity, of LMLFM. We present results of
experiments with both simulated and real-world longitudinal data which show
that LMLFM outperforms the state-of-the-art methods in terms of predictive
accuracy, variable selection ability, and scalability to data with large number
of variables. The code and supplemental material is available at
\url{https://github.com/junjieliang672/LMLFM}.Comment: Thirty-Fourth AAAI Conference on Artificial Intelligence, accepte
Latent Sparse Modeling of Longitudinal Multi-Dimensional Data
We propose a tensor-based approach to analyze multi-dimensional data describing sample subjects. It simultaneously discovers patterns in features and reveals past temporal points that have impact on current outcomes. The model coefficient, a k-mode tensor, is decomposed into a summation of k tensors of the same dimension. To accomplish feature selection, we introduce the tensor '"atent LF,1 norm" as a grouped penalty in our formulation. Furthermore, the proposed model takes into account within-subject correlations by developing a tensor-based quadratic inference function. We provide an asymptotic analysis of our model when the sample size approaches to infinity. To solve the corresponding optimization problem, we develop a linearized block coordinate descent algorithm and prove its convergence for a fixed sample size. Computational results on synthetic datasets and real-file fMRI and EEG problems demonstrate the superior performance of the proposed approach over existing techniques