Random Discriminants

Iterated discriminants

It is shown that the discriminant of a discriminant has the same irreducible factors as the product of seven polynomials which are defined as the GCD of the generators of an elimination ideal. Under tame conditions of genericity, three of these polynomials are irreducible and generate the corresponding elimination ideal, while the four other are equal to one. Moreover the factors of two of thes...

Mixed Discriminants

The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plücker coordinates of a mixed Grassmannian. An explicit degree formula i...

On Associated Discriminants 3

In this note we introduce a family i ; i = 0; : : : ; n ? 2 of discriminants in the space P n of polynomials of degree n in one variable and study some of their algebraic and topological properties following Ar]-Va] and GKZ]. The discriminant i consists of all polynomials p such that some nontrivial linear combination 0 p+ 1 p 0 + + i p (i) has a zero of multiplicity greater or equal i+2. In pa...

Low Frequency Discriminants 4

Boosted Dyadic Kernel Discriminants

We introduce a novel learning algorithm for binary classification with hyperplane discriminants based on pairs of training points from opposite classes (dyadic hypercuts). This algorithm is further extended to nonlinear discriminants using kernel functions satisfying Mercer’s conditions. An ensemble of simple dyadic hypercuts is learned incrementally by means of a confidence-rated version of Ad...