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Transforms of pseudo-Boolean random variables |
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| Authors: | Guoli Ding Jianhua Chen |
| Institution: | a Department of Mathematics, LSU, Baton Rouge, LA 70803, United States b Department of Computer Science, 298 Coates Hall, LSU, Baton Rouge, LA 70803, United States c Department of Experimental Statistics, LSU, Baton Rouge, LA 70803, United States |
| Abstract: | As in earlier works, we consider {0,1}n as a sample space with a probability measure on it, thus making pseudo-Boolean functions into random variables. Under the assumption that the coordinate random variables are independent, we show it is very easy to give an orthonormal basis for the space of pseudo-Boolean random variables of degree at most k. We use this orthonormal basis to find the transform of a given pseudo-Boolean random variable and to answer various least squares minimization questions. |
| Keywords: | Pseudo-Boolean function Probability measure Orthonormal basis Transform |
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