7 research outputs found
Consistency of Maximum Likelihood for Continuous-Space Network Models
Network analysis needs tools to infer distributions over graphs of arbitrary
size from a single graph. Assuming the distribution is generated by a
continuous latent space model which obeys certain natural symmetry and
smoothness properties, we establish three levels of consistency for
non-parametric maximum likelihood inference as the number of nodes grows: (i)
the estimated locations of all nodes converge in probability on their true
locations; (ii) the distribution over locations in the latent space converges
on the true distribution; and (iii) the distribution over graphs of arbitrary
size converges.Comment: 21 page
Non-Parametric Manifold Learning
We introduce an estimator for distances in a compact Riemannian manifold M
based on graph Laplacian estimates of the Laplace-Beltrami operator. We upper
bound the l2-loss for the ratio of the estimator over the true manifold
distance, or more precisely an approximation of manifold distance in
non-commutative geometry (cf. [Connes and Suijelekom, 2020]), in terms of
spectral errors in the graph Laplacian estimates and, implicitly, several
geometric properties of the manifold. We consequently obtain a consistency
result for the estimator for samples equidistributed from a strictly positive
density on M and graph Laplacians which spectrally converge, in a suitable
sense, to the Laplace-Beltrami operator. The estimator resembles, and in fact
its convergence properties are derived from, a special case of the Kontorovic
dual reformulation of Wasserstein distance known as Connes' Distance Formula
Novel genetic loci associated with hippocampal volume
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg =-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness
Novel genetic loci associated with hippocampal volume
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg=-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness
Novel genetic loci associated with hippocampal volume
The hippocampal formation is a brain structure integrally involved in episodic memory, spatial navigation, cognition and stress responsiveness. Structural abnormalities in hippocampal volume and shape are found in several common neuropsychiatric disorders. To identify the genetic underpinnings of hippocampal structure here we perform a genome-wide association study (GWAS) of 33,536 individuals and discover six independent loci significantly associated with hippocampal volume, four of them novel. Of the novel loci, three lie within genes (ASTN2, DPP4 and MAST4) and one is found 200 kb upstream of SHH. A hippocampal subfield analysis shows that a locus within the MSRB3 gene shows evidence of a localized effect along the dentate gyrus, subiculum, CA1 and fissure. Further, we show that genetic variants associated with decreased hippocampal volume are also associated with increased risk for Alzheimer's disease (rg=-0.155). Our findings suggest novel biological pathways through which human genetic variation influences hippocampal volume and risk for neuropsychiatric illness