arXiv subjects

Adam Lund

Publications and source records attributed to Adam Lund.

3 recordsLinked to original sources

arXiv2018

Soft Maximin Estimation for Heterogeneous Data

Extracting a common robust signal from data divided into heterogeneous groups can be difficult when each group -- in addition to the signal -- can contain large, unique variation components. Previously, maximin estimation has been proposed as a robust estimation method in the presence of heterogeneous noise. We propose soft maximin estimation as a computationally attractive alternative aimed at striking a balance between pooled estimation and (hard) maximin estimation. The soft maximin method provides a range of estimators, controlled by a parameter $\zeta>0$, that interpolates pooled least squares estimation and maximin estimation. By establishing relevant theoretical properties we argue that the soft maximin method is both statistically sensibel and computationally attractive. We also demonstrate, on real and simulated data, that the soft maximin estimator can offer improvements over both pooled OLS and hard maximin in terms of predictive performance and computational complexity. A time and memory efficient implementation is provided in the R package \verb+SMME+ available on CRAN.

stat.ME↗

arXiv2018

Sparse Network Estimation for Dynamical Spatio-temporal Array Models

Neural field models represent neuronal communication on a population level via synaptic weight functions. Using voltage sensitive dye (VSD) imaging it is possible to obtain measurements of neural fields with a relatively high spatial and temporal resolution. The synaptic weight functions represent functional connectivity in the brain and give rise to a spatio-temporal dependence structure. We present a stochastic functional differential equation for modeling neural fields, which leads to a vector autoregressive model of the data via basis expansions of the synaptic weight functions and time and space discretization. Fitting the model to data is a pratical challenge as this represents a large scale regression problem. By using a 1-norm penalty in combination with localized basis functions it is possible to learn a sparse network representation of the functional connectivity of the brain, but still, the explicit construction of a design matrix can be computationally prohibitive. We demonstrate that by using tensor product basis expansions, the computation of the penalized estimator via a proximal gradient algorithm becomes feasible. It is crucial for the computations that the data is organized in an array as is the case for the three dimensional VSD imaging data. This allows for the use of array arithmetic that is both memory and time efficient.The proposed method is implemented and showcased in the R package dynamo available from CRAN.

stat.ME↗

arXiv2015

Penalized estimation in large-scale generalized linear array models

Large-scale generalized linear array models (GLAMs) can be challenging to fit. Computation and storage of its tensor product design matrix can be impossible due to time and memory constraints, and previously considered design matrix free algorithms do not scale well with the dimension of the parameter vector. A new design matrix free algorithm is proposed for computing the penalized maximum likelihood estimate for GLAMs, which, in particular, handles nondifferentiable penalty functions. The proposed algorithm is implemented and available via the R package \verb+glamlasso+. It combines several ideas -- previously considered separately -- to obtain sparse estimates while at the same time efficiently exploiting the GLAM structure. In this paper the convergence of the algorithm is treated and the performance of its implementation is investigated and compared to that of \verb+glmnet+ on simulated as well as real data. It is shown that the computation time for

stat.CO↗