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Tensor decomposition for learning Gaussian mixtures from moments
In data processing and machine learning, an important challenge is to recover and exploit models that can represent accurately the data.
Computing real radicals by moment optimization
A truncated positive generic linear functional vanishing on the generators of is computed solving a Moment Optimization Problem (MOP).
Commutative Algebra Algebraic Geometry Optimization and Control
Exact Moment Representation in Polynomial Optimization
We also bound theorder of the relaxation at which flat truncation holds. As corollaries, we conclude that flat truncation holds:$\bullet$ when regularity conditions, known as Boundary Hessian Conditions, hold: this resultimplies that flat truncation and MoM exactness holds generically;$\bullet$ when the support of the quadratic module Q is zero-dimensional;$\bullet$ in singular cases, flat truncation holds for the MoM relaxation extended with the polarconstraints when the real variety of polar points is finite. Effective numerical computations illustrate these flat truncation properties.
Commutative Algebra Algebraic Geometry Optimization and Control
