Heuristic Classifier Performance Bounds in High Dimensional Settings

2002 ◽  
Author(s):  
Paul M. Baggenstoss
Keyword(s):  
High Dimensional ◽  
Performance Bounds ◽  
Classifier Performance

Visualizing High Dimensional Classifier Performance Data

2009 ◽  
pp. 105-129
Author(s):  
Rocio Alaiz-Rodríguez ◽  
Nathalie Japkowicz ◽  
Peter Tischer
Keyword(s):  
Performance Data ◽  
High Dimensional ◽  
Classifier Performance

scholarly journals Phase transitions of spectral initialization for high-dimensional non-convex estimation

2019 ◽  
Vol 9 (3) ◽  
pp. 507-541 ◽  
Author(s):  
Yue M Lu ◽  
Gen Li
Keyword(s):  
Spectral Method ◽  
Phase Retrieval ◽  
Worked Examples ◽  
Asymptotic Formulas ◽  
High Dimensional ◽  
Performance Bounds ◽  
Actual Performance ◽  
Retrieval Problem ◽  
Two Phases

Abstract We study a spectral initialization method that serves a key role in recent work on estimating signals in non-convex settings. Previous analysis of this method focuses on the phase retrieval problem and provides only performance bounds. In this paper, we consider arbitrary generalized linear sensing models and present a precise asymptotic characterization of the performance of the method in the high-dimensional limit. Our analysis also reveals a phase transition phenomenon that depends on the ratio between the number of samples and the signal dimension. When the ratio is below a minimum threshold, the estimates given by the spectral method are no better than random guesses drawn from a uniform distribution on the hypersphere, thus carrying no information; above a maximum threshold, the estimates become increasingly aligned with the target signal. The computational complexity of the method, as measured by the spectral gap, is also markedly different in the two phases. Worked examples and numerical results are provided to illustrate and verify the analytical predictions. In particular, simulations show that our asymptotic formulas provide accurate predictions for the actual performance of the spectral method even at moderate signal dimensions.

scholarly journals On landmark selection and sampling in high-dimensional data analysis

2009 ◽  
Vol 367 (1906) ◽  
pp. 4295-4312 ◽  
Author(s):  
Mohamed-Ali Belabbas ◽  
Patrick J. Wolfe
Keyword(s):  
Spectral Analysis ◽  
Partial Information ◽  
Selection Process ◽  
High Dimensional Data ◽  
Video Data ◽  
High Dimensional ◽  
Dimensional Manifold ◽  
Performance Bounds ◽  
Landmark Selection ◽  
Low Dimensional

In recent years, the spectral analysis of appropriately defined kernel matrices has emerged as a principled way to extract the low-dimensional structure often prevalent in high-dimensional data. Here, we provide an introduction to spectral methods for linear and nonlinear dimension reduction, emphasizing ways to overcome the computational limitations currently faced by practitioners with massive datasets. In particular, a data subsampling or landmark selection process is often employed to construct a kernel based on partial information, followed by an approximate spectral analysis termed the Nyström extension. We provide a quantitative framework to analyse this procedure, and use it to demonstrate algorithmic performance bounds on a range of practical approaches designed to optimize the landmark selection process. We compare the practical implications of these bounds by way of real-world examples drawn from the field of computer vision, whereby low-dimensional manifold structure is shown to emerge from high-dimensional video data streams.

High-Dimensional Probability

2018 ◽  
Author(s):  
Roman Vershynin
Keyword(s):  
High Dimensional

The Semantic Credentials of High-Dimensional Memory Models

2014 ◽  
Author(s):  
Curt Burgess ◽  
Sarah Maples
Keyword(s):  
Memory Models ◽  
High Dimensional
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