Testing Algebraic Complete Intersections
A theoretical research paper on statistical testing of algebraic complete intersections. It proposes a scheme for testing whether a high-dimensional data distribution concentrates near an algebraic complete intersection, using quantitative geometric estimates for regular polynomial systems to convert the geometric test into a tractable auxiliary optimization problem.
Timeline (last 90 days)
The paper "Testing Algebraic Complete Intersections" studies the statistical problem of testing, given independent and identically distributed samples from a probability distribution on a high-dimensional real space, whether that distribution is concentrated near an algebraic complete intersection.
The learning procedure designed in the paper has two outputs: under the premise of a controlled relaxation of the approximation threshold, certifying that no algebraic complete intersection satisfying the conditions exists, or returning a candidate regression manifold with controlled geometric complexity.
The authors developed a data-driven algorithm to solve the auxiliary optimization problem and gave explicit bounds on sample complexity and arithmetic complexity.
All Facts (3)
The paper "Testing Algebraic Complete Intersections" studies the statistical problem of testing, given independent and identically distributed samples from a probability distribution on a high-dimensional real space, whether that distribution is concentrated near an algebraic complete intersection.
50%UnverifiedThe learning procedure designed in the paper has two outputs: under the premise of a controlled relaxation of the approximation threshold, certifying that no algebraic complete intersection satisfying the conditions exists, or returning a candidate regression manifold with controlled geometric complexity.
50%UnverifiedThe authors developed a data-driven algorithm to solve the auxiliary optimization problem and gave explicit bounds on sample complexity and arithmetic complexity.
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