1,701 research outputs found
Covariate-assisted spectral clustering
Biological and social systems consist of myriad interacting units. The
interactions can be represented in the form of a graph or network. Measurements
of these graphs can reveal the underlying structure of these interactions,
which provides insight into the systems that generated the graphs. Moreover, in
applications such as connectomics, social networks, and genomics, graph data
are accompanied by contextualizing measures on each node. We utilize these node
covariates to help uncover latent communities in a graph, using a modification
of spectral clustering. Statistical guarantees are provided under a joint
mixture model that we call the node-contextualized stochastic blockmodel,
including a bound on the mis-clustering rate. The bound is used to derive
conditions for achieving perfect clustering. For most simulated cases,
covariate-assisted spectral clustering yields results superior to regularized
spectral clustering without node covariates and to an adaptation of canonical
correlation analysis. We apply our clustering method to large brain graphs
derived from diffusion MRI data, using the node locations or neurological
region membership as covariates. In both cases, covariate-assisted spectral
clustering yields clusters that are easier to interpret neurologically.Comment: 28 pages, 4 figures, includes substantial changes to theoretical
result
When Social Influence Meets Item Inference
Research issues and data mining techniques for product recommendation and
viral marketing have been widely studied. Existing works on seed selection in
social networks do not take into account the effect of product recommendations
in e-commerce stores. In this paper, we investigate the seed selection problem
for viral marketing that considers both effects of social influence and item
inference (for product recommendation). We develop a new model, Social Item
Graph (SIG), that captures both effects in form of hyperedges. Accordingly, we
formulate a seed selection problem, called Social Item Maximization Problem
(SIMP), and prove the hardness of SIMP. We design an efficient algorithm with
performance guarantee, called Hyperedge-Aware Greedy (HAG), for SIMP and
develop a new index structure, called SIG-index, to accelerate the computation
of diffusion process in HAG. Moreover, to construct realistic SIG models for
SIMP, we develop a statistical inference based framework to learn the weights
of hyperedges from data. Finally, we perform a comprehensive evaluation on our
proposals with various baselines. Experimental result validates our ideas and
demonstrates the effectiveness and efficiency of the proposed model and
algorithms over baselines.Comment: 12 page
Deep Learning in a Generalized HJM-type Framework Through Arbitrage-Free Regularization
We introduce a regularization approach to arbitrage-free factor-model
selection. The considered model selection problem seeks to learn the closest
arbitrage-free HJM-type model to any prespecified factor-model. An asymptotic
solution to this, a priori computationally intractable, problem is represented
as the limit of a 1-parameter family of optimizers to computationally tractable
model selection tasks. Each of these simplified model-selection tasks seeks to
learn the most similar model, to the prescribed factor-model, subject to a
penalty detecting when the reference measure is a local martingale-measure for
the entire underlying financial market. A simple expression for the penalty
terms is obtained in the bond market withing the affine-term structure setting,
and it is used to formulate a deep-learning approach to arbitrage-free affine
term-structure modelling. Numerical implementations are also performed to
evaluate the performance in the bond market.Comment: 23 Pages + Reference
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