1,202 research outputs found
Prototype selection for parameter estimation in complex models
Parameter estimation in astrophysics often requires the use of complex
physical models. In this paper we study the problem of estimating the
parameters that describe star formation history (SFH) in galaxies. Here,
high-dimensional spectral data from galaxies are appropriately modeled as
linear combinations of physical components, called simple stellar populations
(SSPs), plus some nonlinear distortions. Theoretical data for each SSP is
produced for a fixed parameter vector via computer modeling. Though the
parameters that define each SSP are continuous, optimizing the signal model
over a large set of SSPs on a fine parameter grid is computationally infeasible
and inefficient. The goal of this study is to estimate the set of parameters
that describes the SFH of each galaxy. These target parameters, such as the
average ages and chemical compositions of the galaxy's stellar populations, are
derived from the SSP parameters and the component weights in the signal model.
Here, we introduce a principled approach of choosing a small basis of SSP
prototypes for SFH parameter estimation. The basic idea is to quantize the
vector space and effective support of the model components. In addition to
greater computational efficiency, we achieve better estimates of the SFH target
parameters. In simulations, our proposed quantization method obtains a
substantial improvement in estimating the target parameters over the common
method of employing a parameter grid. Sparse coding techniques are not
appropriate for this problem without proper constraints, while constrained
sparse coding methods perform poorly for parameter estimation because their
objective is signal reconstruction, not estimation of the target parameters.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS500 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Minimax Estimation of Distances on a Surface and Minimax Manifold Learning in the Isometric-to-Convex Setting
We start by considering the problem of estimating intrinsic distances on a
smooth surface. We show that sharper estimates can be obtained via a
reconstruction of the surface, and discuss the use of the tangential Delaunay
complex for that purpose. We further show that the resulting approximation rate
is in fact optimal in an information-theoretic (minimax) sense. We then turn to
manifold learning and argue that a variant of Isomap where the distances are
instead computed on a reconstructed surface is minimax optimal for the problem
of isometric manifold embedding
Representation Learning via Manifold Flattening and Reconstruction
This work proposes an algorithm for explicitly constructing a pair of neural
networks that linearize and reconstruct an embedded submanifold, from finite
samples of this manifold. Our such-generated neural networks, called Flattening
Networks (FlatNet), are theoretically interpretable, computationally feasible
at scale, and generalize well to test data, a balance not typically found in
manifold-based learning methods. We present empirical results and comparisons
to other models on synthetic high-dimensional manifold data and 2D image data.
Our code is publicly available.Comment: 44 pages, 19 figure
- …