2 research outputs found
Direct Estimation of Differential Functional Graphical Models
We consider the problem of estimating the difference between two functional
undirected graphical models with shared structures. In many applications, data
are naturally regarded as high-dimensional random function vectors rather than
multivariate scalars. For example, electroencephalography (EEG) data are more
appropriately treated as functions of time. In these problems, not only can the
number of functions measured per sample be large, but each function is itself
an infinite dimensional object, making estimation of model parameters
challenging. We develop a method that directly estimates the difference of
graphs, avoiding separate estimation of each graph, and show it is consistent
in certain high-dimensional settings. We illustrate finite sample properties of
our method through simulation studies. Finally, we apply our method to EEG data
to uncover differences in functional brain connectivity between alcoholics and
control subjects.Comment: 21 pages, 3 figures, to be published in NeurIPS 2019; added link to
cod
Constrained High Dimensional Statistical Inference
In typical high dimensional statistical inference problems, confidence
intervals and hypothesis tests are performed for a low dimensional subset of
model parameters under the assumption that the parameters of interest are
unconstrained. However, in many problems, there are natural constraints on
model parameters and one is interested in whether the parameters are on the
boundary of the constraint or not. e.g. non-negativity constraints for
transmission rates in network diffusion. In this paper, we provide algorithms
to solve this problem of hypothesis testing in high-dimensional statistical
models under constrained parameter space. We show that following our testing
procedure we are able to get asymptotic designed Type I error under the null.
Numerical experiments demonstrate that our algorithm has greater power than the
standard algorithms where the constraints are ignored. We demonstrate the
effectiveness of our algorithms on two real datasets where we have
{\emph{intrinsic}} constraint on the parameters