1,504 research outputs found
Greedy low-rank algorithm for spatial connectome regression
Recovering brain connectivity from tract tracing data is an important
computational problem in the neurosciences. Mesoscopic connectome
reconstruction was previously formulated as a structured matrix regression
problem (Harris et al., 2016), but existing techniques do not scale to the
whole-brain setting. The corresponding matrix equation is challenging to solve
due to large scale, ill-conditioning, and a general form that lacks a
convergent splitting. We propose a greedy low-rank algorithm for connectome
reconstruction problem in very high dimensions. The algorithm approximates the
solution by a sequence of rank-one updates which exploit the sparse and
positive definite problem structure. This algorithm was described previously
(Kressner and Sirkovi\'c, 2015) but never implemented for this connectome
problem, leading to a number of challenges. We have had to design judicious
stopping criteria and employ efficient solvers for the three main sub-problems
of the algorithm, including an efficient GPU implementation that alleviates the
main bottleneck for large datasets. The performance of the method is evaluated
on three examples: an artificial "toy" dataset and two whole-cortex instances
using data from the Allen Mouse Brain Connectivity Atlas. We find that the
method is significantly faster than previous methods and that moderate ranks
offer good approximation. This speedup allows for the estimation of
increasingly large-scale connectomes across taxa as these data become available
from tracing experiments. The data and code are available online
On the causal interpretation of acyclic mixed graphs under multivariate normality
In multivariate statistics, acyclic mixed graphs with directed and bidirected
edges are widely used for compact representation of dependence structures that
can arise in the presence of hidden (i.e., latent or unobserved) variables.
Indeed, under multivariate normality, every mixed graph corresponds to a set of
covariance matrices that contains as a full-dimensional subset the covariance
matrices associated with a causally interpretable acyclic digraph. This digraph
generally has some of its nodes corresponding to hidden variables. We seek to
clarify for which mixed graphs there exists an acyclic digraph whose hidden
variable model coincides with the mixed graph model. Restricting to the
tractable setting of chain graphs and multivariate normality, we show that
decomposability of the bidirected part of the chain graph is necessary and
sufficient for equality between the mixed graph model and some hidden variable
model given by an acyclic digraph
Low thrust interplanetary trajectory open loop error analysis, volume 1 Final report
Computer program for open-loop error analysis of low thrust interplanetary trajectorie
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