Related papers: Spectral Thresholds for Identifiability and Stabil…
We study the following question in the context of imitation learning for continuous control: how are the underlying stability properties of an expert policy reflected in the sample-complexity of an imitation learning task? We provide the…
For estimating the unknown parameters in an unstable autoregressive AR(p), the paper proposes sequential least squares estimates with a special stopping time defined by the trace of the observed Fisher information matrix. The limiting…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
We study the linear stability of inviscid steady parallel flow of an ideal gas in a channel of finite width. Compressible isothermal two-dimensional monochromatic perturbations are considered. The eigenvalue problem governing density and…
The Whitham equation is a model for the evolution of small-amplitude, unidirectional waves of all wavelengths on shallow water. It has been shown to accurately model the evolution of waves in laboratory experiments. We compute…
We analyze a numerical instability that occurs in the well-known split-step Fourier method on the background of a soliton. This instability is found to be very sensitive to small changes of the parameters of both the numerical grid and the…
A generalized spiked Fisher matrix is considered in this paper. We establish a criterion for the description of the support of the limiting spectral distribution of high-dimensional generalized Fisher matrix and study the almost sure limits…
The main challenge that sets transfer learning apart from traditional supervised learning is the distribution shift, reflected as the shift between the source and target models and that between the marginal covariate distributions. In this…
The aim of this work is to design an explicit finite dimensional boundary feedback controller for locally exponentially stabilizing the equilibrium solutions to Fisher's equation in both $L^2(0,1)$ and $H^1(0,1)$. The feedback controller is…
Spectroscopy detected in the time domain entails many techniques, such as FTIR, pump-probe, FT-Raman, and 2DES, and applications, such as molecule characterization, excited state dynamics studies, or spectra classifications. Surprisingly,…
The Saffman-Taylor instability occurs when a less viscous fluid is displacing a more viscous one in a rectangular Hele-Shaw cell. A surface tension on the interface between the two fluids is improving the stability. The multi-layer Hele -…
Calibrated probability outputs of trained classifiers are increasingly used as inputs to downstream regression estimands such as effects, prevalences, or disparities for a latent group observed only on a small labelled subset. A standard…
The Fisher information theory sets a fundamental bound on the minimum measurement error achievable from independent and identically distributed (i.i.d.) measurement events. The assumption of identical and independent distribution often…
Numerically solving the 2D Helmholtz equation is widely known to be very difficult largely due to its highly oscillatory solution, which brings about the pollution effect. A very fine mesh size is necessary to deal with a large wavenumber…
We study the stability and instability of the Gaussian logarithmic Sobolev inequality, in terms of covariance, Wasserstein distance and Fisher information, addressing several open questions in the literature. We first establish an improved…
Random Fisher matrices arise naturally in multivariate statistical analysis and understanding the properties of its eigenvalues is of primary importance for many hypothesis testing problems like testing the equality between two multivariate…
Fisher zeros are the zeros of the partition function in the complex beta=2N_c/g^2 plane. When they pinch the real axis, finite size scaling allows one to distinguish between first and second order transition and to estimate exponents. On…
The error threshold transition in a stochastic (i.e. finite population) version of the quasispecies model of molecular evolution is studied using finite-size scaling. For the single-sharp-peak replication landscape, the deterministic model…
We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in…
We study a hypothesis testing problem in the context of high-dimensional changepoint detection. Given a matrix $X \in \R^{p \times n}$ with independent Gaussian entries, the goal is to determine whether or not a sparse, non-null fraction of…