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Implement a variant of Polynomial::evaluate_mle() for "long zero tail" polynomials, i.e., polynomials with all zero coefficients from a given index (bound). This method is meant for polynomials where at least half of the last coefficients are zero. Assuming that bound <= 2^k and size of polynomial is 2^n, then we can fold over k dimensions and finally multiply the result with (1 - challenge) for all the challenges at higher dimensions.
Namely, all monomials containing terms X_{k+1}, ....X_n have zero coefficients and all the monomials with non-zero coefficients contain the term (1-X_{k+1}) * (1-X_{k+2}) * ..... * (1-X_n).
Therefore, we perform a standard mle in dimension k and the result is multiplied by (1-u_{k+1}) * (1-u{k+2}) * ...(1-u_n) where u_i's denote the challenges.
The text was updated successfully, but these errors were encountered:
Implement a variant of Polynomial::evaluate_mle() for "long zero tail" polynomials, i.e., polynomials with all zero coefficients from a given index (bound). This method is meant for polynomials where at least half of the last coefficients are zero. Assuming that bound <= 2^k and size of polynomial is 2^n, then we can fold over k dimensions and finally multiply the result with (1 - challenge) for all the challenges at higher dimensions.
Namely, all monomials containing terms X_{k+1}, ....X_n have zero coefficients and all the monomials with non-zero coefficients contain the term (1-X_{k+1}) * (1-X_{k+2}) * ..... * (1-X_n).
Therefore, we perform a standard mle in dimension k and the result is multiplied by (1-u_{k+1}) * (1-u{k+2}) * ...(1-u_n) where u_i's denote the challenges.
The text was updated successfully, but these errors were encountered: