Dmitry Panchenko

Permutation tests for classification

We describe a permutation procedure used extensively in classification problems in computational biology and medical imaging. We empirically study the procedure on simulated data and real examples from neuroimaging studies and DNA microarray analysis. A theoretical analysis is also suggested to assess the asymptotic behavior of the test. An interesting observation is that concentration of the permutation procedure is controlled by a Rademacher average which also controls the concentration of empirical errors to expected errors.

The Parisi formula for mixed

The Parisi formula for the free energy in the Sherrington-Kirkpatrick and mixed

p

p

-spin models

-spin models for even

Log-Concavity Property of the Error Probability With Application to Local Bounds for Wireless Communications

p\geq2

Complexities of convex combinations and bounding the generalization error in classification

was proved in the seminal work of Michel Talagrand [Ann. of Math. (2) 163 (2006) 221-263]. In this paper we prove the Parisi formula for general mixed

Spin glass models from the point of view of spin distributions

p

On the overlap in the multiple spherical SK models

-spin models which also include

The free energy in a multi-species Sherrington–Kirkpatrick model

p

A connection between the Ghirlanda–Guerra identities and ultrametricity

-spin interactions for odd