11 papers
Kernel Density Estimation by Spectral Decomposition: Data-Driven Tapering and Superposition
Mitchell A. Thornton
Kernel density estimation depends largely on one choice, the smoothing bandwidth. We treat bandwidth selection and density estimation in the characteristic-function domain, where t…
Algebraic Diversity: Group-Theoretic Spectral Estimation from Single Observations
Mitchell A. Thornton
We establish that temporal averaging over multiple observations is the degenerate case of algebraic group action with the trivial group . A General Replacement Theorem pro…
Matched Generators for the Karhunen--Loève Transform: A Double-Commutator Eigenvalue Theory
Mitchell A. Thornton
The Karhunen--Loève transform (KLT) diagonalizes the covariance of a second-order process and is optimal for mean-square truncation. Which classical transform it reduces to is gov…
Unification of Signal Transform Theory
Mitchell A. Thornton
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Loève transform (KLT), and several others along with their c…
Blind Symmetry Matching in Quantum States with Application to Shot-Count Reduction
Mitchell A. Thornton
Measuring a quantum computation in a basis adapted to a symmetry it carries reduces the repeated measurements, commonly referred to as ``shots'', needed to read a statistical answe…
Quantum Algebraic Diversity: Single-Copy Density Matrix Estimation via Group-Structured Measurements
Mitchell A. Thornton
We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The Quantum Algebraic Diversity (QAD) Theorem establishes that a gr…