Reconstructing Algebraic Functions from Mixed Data

The authors consider the task of reconstructing algebraic functions given by black boxes. Unlike traditional settings, they are interested in black boxes which represent several algebraic functions-f/sub 1/, .. ., f/sub k/, where at each input x, the box arbitarrily chooses a subset of f/sub 1/(x), .. ., f/sub k/(x) to output. They show how to reconstruct the functions f/sub 1/, .. ., f/sub k/ from the black box. This allows them to group the same points into sets, such that for each set, all outputs to points in the set are from the same algebraic function. The methods are robust in the presence of errors in the black box. The model and techniques can be applied in the areas of computer vision, machine learning, curve fitting and polynomial approximation, self-correcting programs and bivariate polynomial factorization. >

Authors

• Sigal Ar
• Richard J. Lipton
• Ronitt Rubinfeld
• Madhu Sudan 0001

Keywords

• Image edge detection
• Polynomials
• Computer vision
• Image reconstruction
• Information technology
• Robot vision systems
• Layout
• Detection algorithms
• Computer errors
• Application software
• Algebraic Function
• Methods Section
• High Probability
• Learning Models
• Black Box
• General Case
• Part Of Research
• Edge Detection
• Polynomial Of Degree
• Real Variables
• Real-valued Function
• Polynomial-time Algorithm
• Finite Field
• Discrete Domain
• Rational Function
• Boolean Variable
• Output Error
• Multivariate Function