Related papers: General Lower Bounds based on Computer Generated H…
We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…
$f,g_1,...,g_m$ be elements of the polynomial ring $\mathbb{R}[x_1,...,x_n]$. The paper deals with the general problem of computing a lower bound for $f$ on the subset of $\mathbb{R}^n$ defined by the inequalities $g_i\ge 0$, $i=1,...,m$.…
This paper is concerned with the computable error estimates for the eigenvalue problem which is solved by the general conforming finite element methods on the general meshes. Based on the computable error estimate, we can give an…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…
An efficient algorithm for computing lower bounds on the global linear complexity of nonlinearly filtered PN-sequences is presented. The technique here developed is based exclusively on the realization of bit wise logic operations, which…
The methods commonly used for numerical differentiation, such as the "center-difference formula" and "four-points formula" are unusable in simulations or real-time data analysis because they require knowledge of the future. In Bard'11, an…
Easily computable lower and upper bounds are found for the sum of Catalan numbers. The lower bound is proven to be tighter than the upper bound, which previously was declared to be only an asymptotic. The average of these bounds is proven…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
We deal with a problem of finding maximum of a function from the Holder class on a quantum computer. We show matching lower and upper bounds on the complexity of this problem. We prove upper bounds by constructing an algorithm that uses the…
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…
We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…
We describe discrete restricted Boltzmann machines: probabilistic graphical models with bipartite interactions between visible and hidden discrete variables. Examples are binary restricted Boltzmann machines and discrete naive Bayes models.…
How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…
Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general…
Many practitioners who use the EM algorithm complain that it is sometimes slow. When does this happen, and what can be done about it? In this paper, we study the general class of bound optimization algorithms - including…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
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…