Automatic Derivation of Statistical Data Analysis Algorithms: Planetary Nebulae and Beyond

Fischer, Bernd

doi:10.1063/1.1751372

Cited by 7 publications

(7 citation statements)

References 17 publications

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“…In this section, we focus on four classic real-world datasets with ground truth clustering: abalone, digits, iris, and movement libras. abalone, iris, and movement libras have been used in various works (see [46,47,49,50,89] for example) and are available online at the UCI Machine learning repository [78].…”

Section: Setupmentioning

confidence: 99%

On the Local Structure of Stable Clustering Instances

Cohen-Addad¹,

Schwiegelshohn²

2017

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)

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We study the classic k-median and k-means clustering objectives in the beyond-worst-case scenario. We consider three well-studied notions of structured data that aim at characterizing real-world inputs:• Distribution Stability (introduced by Awasthi, Blum, and Sheffet, FOCS 2010)• Spectral Separability (introduced by Kumar and Kannan, FOCS 2010)• Perturbation Resilience (introduced by Bilu and Linial, ICS 2010) We prove structural results showing that inputs satisfying at least one of the conditions are inherently "local". Namely, for any such input, any local optimum is close both in term of structure and in term of objective value to the global optima.As a corollary we obtain that the widely-used Local Search algorithm has strong performance guarantees for both the tasks of recovering the underlying optimal clustering and obtaining a clustering of small cost. This is a significant step toward understanding the success of local search heuristics in clustering applications. *

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Section: Setupmentioning

confidence: 99%

On the Local Structure of Stable Clustering Instances

Cohen-Addad¹,

Schwiegelshohn²

2017

2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)

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“…IBPES search is also implemented using simplex search in AutoBayes [6]. When initialized to the FastSES solution, simplex produces results similar to gradient descent.…”

Section: Discussionmentioning

confidence: 99%

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Huyser¹

2004

AIP Conference Proceedings

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Abstract.Astronomical objects known as planetary nebulae (PNe) consist of a shell of gas expelled by an aging star. In cases where the gas shell can be assumed to be ellipsoidal, the PN can be easily modeled in three spatial dimensions. We utilize a model that joins the physics of PNe to this geometry and generates simulated nebular images. Hubble Space Telescope images of actual PNe provide data with which the model images may be compared. We employ Bayesian model estimation and search the parameter space for values that generate a match between observed and model images. The forward model is characterized by thirteen parameters; consequently model estimation requires the search of a 13-dimensional parameter space. The 'curse of dimensionality,' compounded by a computationally intense forward problem, makes forward searches extremely time-consuming and frequently causes them to become trapped in a local solution. We find that both the speed and quality of the search can be improved by reducing the dimensionality of the search space.Our basic approach utilizes a hierarchy of models of increasing complexity. Earlier studies establish that a hierarchical sequence converges more quickly, and to a better solution, than a search relying only on the most complex model. Here we report results for a hierarchy of five models. The first three models treat the nebula as a 2D image, estimating its position, angular size, orientation and rim thickness. The last two models explore its characteristics as a 3D object and enable us to characterize the physics of the nebula. This five-model hierarchy is applied to real ellipsoidal PNe to estimate their geometric properties and gas density profiles.

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“…In both cases, the generated code is based on Kalman filter algorithms, which make extensive use of matrix operations. The other two examples are AUTOBAYES specifications which are part of a more comprehensive analysis of planetary nebula images taken by the Hubble Space Telescope (see [5,8] for more details). segm describes an image segmentation problem for which an iterative (numerical) statistical clustering algorithm is synthesized.…”

Section: Program Corpusmentioning

confidence: 99%

Using Automated Theorem Provers to Certify Auto-generated Aerospace Software

Denney¹,

Fischer

Schumann

2004

Automated Reasoning

Self Cite

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We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). For full automation, however, the obligations must be aggressively preprocessed and simplified. We discuss the unique requirements this application places on the ATPs and demonstrate how the individual simplification stages, which are implemented by rewriting, influence the ability of the ATPs to solve the proof tasks. Our results are based on 13 certification experiments that lead to more than 25,000 proof tasks which have each been attempted by Vampire, Spass, and e-setheo.

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Automatic Derivation of Statistical Data Analysis Algorithms: Planetary Nebulae and Beyond

Cited by 7 publications

References 17 publications

On the Local Structure of Stable Clustering Instances

On the Local Structure of Stable Clustering Instances

Discovering Planetary Nebula Geometries: Explorations with a Hierarchy of Models

Using Automated Theorem Provers to Certify Auto-generated Aerospace Software

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