Related papers: Restriction estimates using polynomial partitionin…
The statistical problem of estimating the effective dimension-reduction (EDR) subspace in the multi-index regression model with deterministic design and additive noise is considered. A new procedure for recovering the directions of the EDR…
We prove an effective version of the Oppenheim conjecture with a polynomial error rate. The proof is based on an effective equidistribution theorem which in turn relies on recent progress towards restricted projection problem.
In this paper, we investigate the possibility of improvement of the widely-used filtering algorithm for the linear constraints in constraint satisfaction problems in the presence of the alldifferent constraints. In many cases, the fact that…
Polynomial convergence bounds are considered for left, right, and split preconditioned GMRES. They include the cases of Weighted and Deflated GMRES for a linear system Ax = b. In particular, the case of positive definite A is considered.…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
We apply the Bennett-Carbery-Tao multilinear restriction estimate in order to bound restriction operators and more general oscillatory integral operators. We get improved L^p estimates in the Stein restriction problem for dimension at least…
A linear restriction of a function is the same function with its domain restricted to points on a given line. This paper addresses the problem of computing a succinct representation for a linear restriction of a piecewise-linear neural…
We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present…
We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained…
We consider the robust version of items selection problem, in which the goal is to choose representatives from a family of sets, preserving constraints on the allowed items' combinations. We prove NP-hardness of the deterministic version,…
The restricted strong convexity is an effective tool for deriving globally linear convergence rates of descent methods in convex minimization. Recently, the global error bound and quadratic growth properties appeared as new competitors. In…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
We give a lower bound for the degree of an irreducible factor of a given polynomial. This improves and generalizes the results obtained in [4, On the irreducible factors of a polynomial, Proc. Amer. Math. Soc., 148 (2020] 1429 -- 1437].
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ continuous derivatives. The construction is based on polynomial extension from neighboring elements…
Let $S \subset \Bbb R^n$ be a smooth compact hypersurface with a strictly positive second fundamental form, $E$ be the Fourier extension operator on $S$, and $X$ be a Lebesgue measurable subset of $\Bbb R^n$. If $X$ contains a ball of each…
We analyze Kumar's recent quadratic algebraic branching program size lower bound proof method (CCC 2017) for the power sum polynomial. We present a refinement of this method that gives better bounds in some cases. The lower bound relies on…
We consider the communication complexity of some fundamental convex optimization problems in the point-to-point (coordinator) and blackboard communication models. We strengthen known bounds for approximately solving linear regression,…
Firstly, bilinear Fourier Restriction estimates --which are well-known for free waves-- are extended to adapted spaces of functions of bounded quadratic variation, under quantitative assumptions on the phase functions. This has applications…