Related papers: On the approximation gain for abc-triples
Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
The probabilistic abstract interpretation framework of neural network analysis analyzes a neural network by analyzing its density distribution flow of all possible inputs. The grids approximation is one of abstract domains the framework…
One field of particular interest in Number Theory concerns the gaps between consecutive primes. Within the last few years, very important results have been achieved on how small these gaps can be. The strongest of these results were…
This paper develops the proximal method of multipliers for a class of nonsmooth convex optimization. The method generates a sequence of minimization problems (subproblems). We show that the sequence of approximations to the solutions of the…
Bayesian inference is often used in cosmology and astrophysics to derive constraints on model parameters from observations. This approach relies on the ability to compute the likelihood of the data given a choice of model parameters. In…
In this note we present a refinement of the AM-GM inequality, and then we estimate in a special case the typical size of the improvement.
We provide a geometric proof that the random proposer mechanism is a $4$-approximation to the first-best gains from trade in bilateral exchange. We then refine this geometric analysis to recover the state-of-the-art approximation ratio of…
Let $\boldsymbol{\alpha}\in \mathbb{R}^N$ and $Q\geq 1$. We consider the sum $\sum_{\boldsymbol{q}\in [-Q,Q]^N\cap\mathbb{Z}^N\backslash\{\boldsymbol{0}\}}\|\boldsymbol{\alpha}\cdot\boldsymbol{q}\|^{-1}$. Sharp upper bounds are known when…
We present a novel approximation algorithm for $k$-median that achieves an approximation guarantee of $1+\sqrt{3}+\epsilon$, improving upon the decade-old ratio of $3+\epsilon$. Our approach is based on two components, each of which, we…
Approximate Bayesian computation (ABC) is an approach for sampling from an approximate posterior distribution in the presence of a computationally intractable likelihood function. A common implementation is based on simulating model,…
In order to involve user knowledge in determining equality of sets, which may not be equal in the mathematical sense, three types of approximate (rough) equalities were introduced by Novotny and Pawlak ([8, 9, 10]). These notions were…
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity…
We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…
How can heuristic strategies emerge from smaller building blocks? We propose Approximate Bayesian Computation as a computational solution to this problem. As a first proof of concept, we demonstrate how a heuristic decision strategy such as…
An ultrametric defined on a subset S of a metric space X can be extended to X while roughly preserving distances between pairs in S x X.
We study fairness in the context of classification where the performance is measured by the area under the curve (AUC) of the receiver operating characteristic. AUC is commonly used to measure the performance of prediction models. The same…
The Collatz and $abc$ conjectures, both well known and thoroughly studied, appear to be largely unrelated at first sight. We show that assuming the $abc$ conjecture true is helpful to improve the lower bound of integers initiating a…
In the present paper, we study the existence of best proximity pair in ultrametric spaces. We show, under suitable assumptions, that the proximinal pair $(A,B)$ has a best proximity pair. As a consequence we generalize a well known best…
In recent years, fairness in machine learning has emerged as a critical concern to ensure that developed and deployed predictive models do not have disadvantageous predictions for marginalized groups. It is essential to mitigate…
We consider list versions of sparse approximation problems, where unlike the existing results in sparse approximation that consider situations with unique solutions, we are interested in multiple solutions. We introduce these problems and…