相关论文: High-probability bounds for the reconstruction err…

We present a framework for upper bounding the number of iterations required by first-order optimization algorithms implementing constrained LQR controllers. We derive new bounds for the condition number and extremal eigenvalues of the…

We study the statistical limits of testing and estimation for a rank one deformation of a Gaussian random tensor. We compute the sharp thresholds for hypothesis testing and estimation by maximum likelihood and show that they are the same.…

In this paper we give a criterion to prove boundedness results for several operators from $H^1((0,\infty),\gamma_\alpha)$ to $L^1((0,\infty),\gamma_\alpha)$ and also from $L^\infty((0,\infty),\gamma_\alpha)$ to…

This paper studies the least upper bounds on coverage probabilities of the empirical likelihood ratio confidence regions based on estimating equations. The implications of the bounds on empirical likelihood inference are also discussed.

In this paper, we revisit approximation properties of piecewise polynomial spaces, which contain more than ${\cal P}_{r-1}$ but not ${\cal P}_r$. We develop more accurate upper and lower error bounds that are sharper than those used in…

What property of the data distribution determines the excess risk of principal component analysis? In this paper, we provide a precise answer to this question. We establish a central limit theorem for the error of the principal subspace…

Error bounds are a requisite for trusting or distrusting solutions in an informed way. Until recently, provable error bounds in the absence of constraint qualifications were unattainable for many classes of cones that do not admit…

We deal with several pcf problems; we characterize another version of exponentiation: number of kappa-branches in a tree with lambda nodes, deal with existence of independent sets in stable theories, possible cardinality of ultraproduct,…

We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…

In this paper upper and lower bounds on the probability of decoding failure under maximum likelihood decoding are derived for different (nonbinary) Raptor code constructions. In particular four different constructions are considered; (i)…

When an eigenvector of a semi-bounded operator is positive, we show that a remarkably simple argument allows to obtain upper and lower bounds for its associated eigenvalue. This theorem is a substantial generalization of Barta-like…

We consider the integration of two-dimensional, piecewise constant functions with respect to copulas. By drawing a connection to linear assignment problems, we can give optimal upper and lower bounds for such integrals and construct the…

Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued…

We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…

We obtain tight upper and lower bounds to the eigenvalues of an anharmonic oscillator with a rational potential. We compare our bounds with results given by other approaches.

We prove an upper bound for the volume-normalized second nonzero eigenvalue of the Laplace operator on closed Riemannian manifold, in terms of the conformal volume. This bound provides effective upper bound for a large class of manifolds,…

We show that the eigenvalues of the Neumann-Poincar\'e operator on analytic boundaries of simply connected bounded planar domains tend to zero exponentially fast, and the exponential convergence rate is determined by the maximal Grauert…

We obtain new recurrence relations, an explicit formula, and convolution identities for higher order geometric polynomials. These relations generalize known results for geometric polynomials, and lead to congruences for higher order…

In this note, we investigate the performance of the PCM scheme with linear quantization rule for quantizing unit-norm tight frame expansions for ${\mathbb R}^d$ without the White Noise Hypothesis. In \cite{WX}, Wang and Xu showed that for…

We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design covariance $\Sigma$ directly but incorporates it into empirical…