8,640 research outputs found
Minimum Average Deviance Estimation for Sufficient Dimension Reduction
Sufficient dimension reduction reduces the dimensionality of data while
preserving relevant regression information. In this article, we develop Minimum
Average Deviance Estimation (MADE) methodology for sufficient dimension
reduction. It extends the Minimum Average Variance Estimation (MAVE) approach
of Xia et al. (2002) from continuous responses to exponential family
distributions to include Binomial and Poisson responses. Local likelihood
regression is used to learn the form of the regression function from the data.
The main parameter of interest is a dimension reduction subspace which projects
the covariates to a lower dimension while preserving their relationship with
the outcome. To estimate this parameter within its natural space, we consider
an iterative algorithm where one step utilizes a Stiefel manifold optimizer. We
empirically evaluate the performance of three prediction methods, two that are
intrinsic to local likelihood estimation and one that is based on the
Nadaraya-Watson estimator. Initial results show that, as expected, MADE can
outperform MAVE when there is a departure from the assumption of additive
errors
Dimension Estimation Using Random Connection Models
Information about intrinsic dimension is crucial to perform dimensionality
reduction, compress information, design efficient algorithms, and do
statistical adaptation. In this paper we propose an estimator for the intrinsic
dimension of a data set. The estimator is based on binary neighbourhood
information about the observations in the form of two adjacency matrices, and
does not require any explicit distance information. The underlying graph is
modelled according to a subset of a specific random connection model, sometimes
referred to as the Poisson blob model. Computationally the estimator scales
like n log n, and we specify its asymptotic distribution and rate of
convergence. A simulation study on both real and simulated data shows that our
approach compares favourably with some competing methods from the literature,
including approaches that rely on distance information
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