Nonasymptotic upper bounds for the reconstruction error of PCA
نویسندگان
چکیده
منابع مشابه
Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms∗
MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. ...
متن کاملNonasymptotic bounds on the estimation error of MCMC algorithms
We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is non-asymptotic. We first establish a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a possibly unbounded target function f. The bound is sharp in the sense that the leading term is exactly σ as(P, f)/n, where σ 2 as(P, f) is the CLT asymptoti...
متن کاملAn Approximate Inference Approach for the PCA Reconstruction Error
The problem of computing a resample estimate for the reconstruction error in PCA is reformulated as an inference problem with the help of the replica method. Using the expectation consistent (EC) approximation, the intractable inference problem can be solved efficiently with two variational parameters. A perturbative correction to the result is computed and an alternative simplified derivation ...
متن کاملNonasymptotic Bounds for Autoregressive Time Series Modeling
The subject of this paper is autoregressive (AR) modeling of a stationary, Gaussian discrete time process, based on a finite sequence of observations. The process is assumed to admit an AR(∞) representation with exponentially decaying coefficients. We adopt the nonparametric minimax framework and study how well the process can be approximated by a finiteorder AR model. A lower bound on the accu...
متن کاملUpper and lower bounds for numerical radii of block shifts
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2020
ISSN: 0090-5364
DOI: 10.1214/19-aos1839