7 papers
A Version Space Approach for Digital Circuit Analysis
Mitchell A. Thornton
Many questions about a digital circuit take the same form. A hidden object is consistent with a set of observations, and one wants to know how many remain consistent and which obse…
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…
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 gove…
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…
Symmetry-Aware Convex Shrinkage for High-Dimensional Covariance Estimation
Mitchell A. Thornton
We develop a class of data-adaptive shrinkage estimators for high-dimensional covariance estimation in which the shrinkage target is a Reynolds projection of the sample covariance…
Continuous Algebraic Diversity: Unifying Spectral, Wavelet, and Time-Frequency Analysis via Lie Group Actions
Mitchell A. Thornton
We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2…