Related papers: Speculate-Correct Error Bounds for k-Nearest Neigh…

Local model interpretation methods explain individual predictions by assigning an importance value to each input feature. This value is often determined by measuring the change in confidence when a feature is removed. However, the…

The $k$-Opt and Lin-Kernighan algorithm are two of the most important local search approaches for the Metric TSP. Both start with an arbitrary tour and make local improvements in each step to get a shorter tour. We show that for any fixed…

The edit distance is a metric of dissimilarity between strings, widely applied in computational biology, speech recognition, and machine learning. Let $e_k(n)$ denote the average edit distance between random, independent strings of $n$…

We introduce a novel \textit{k}-nearest neighbor (\textit{k}-NN) regression method for joint estimation of the conditional mean and variance. The proposed algorithm preserves the computational efficiency and manifold-learning capabilities…

We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…

We derive various error exponents in the bee identification problem under two different decoding rules. Under na\"ive decoding, which decodes each bee independently of the others, we analyze a general discrete memoryless channel and a…

Classical probabilistic rounding error analysis is particularly well suited to stochastic rounding (SR), and it yields strong results when dealing with floating-point algorithms that rely heavily on summation. For many numerical linear…

In this paper we give local error estimates in Sobolev norms for the Galerkin method applied to strongly elliptic pseudodifferential equations on a polygon. By using the K-operator, an operator which averages the values of the Galerkin…

Score function estimation is the cornerstone of both training and sampling from diffusion generative models. Despite this fact, the most commonly used estimators are either biased neural network approximations or high variance Monte Carlo…

This paper proposes a new probabilistic classification algorithm using a Markov random field approach. The joint distribution of class labels is explicitly modelled using the distances between feature vectors. Intuitively, a class label…

We analyse the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We derive new tighter deterministic and probabilistic bounds that we use to…

In the realm of machine learning, the KNN classification algorithm is widely recognized for its simplicity and efficiency. However, its sensitivity to the K value poses challenges, especially with small sample sizes or outliers, impacting…

In this paper we present a new error bound on sampling algorithms for frequent itemsets mining. We show that the new bound is asymptotically tighter than the state-of-art bounds, i.e., given the chosen samples, for small enough error…

We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informative explicit expressions, and new deterministic and…

In this paper, we establish improved effective irrationality measures for certain numbers of the form $\sqrt[3]{n}$, using approximations obtained from hypergeometric functions. These results are very close to the best possible using this…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

We prove risk bounds for binary classification in high-dimensional settings when the sample size is allowed to be smaller than the dimensionality of the training set observations. In particular, we prove upper bounds for both 'compressive…

Motivated by the mode estimation problem of an unknown multivariate probability density function, we study the problem of identifying the point with the minimum k-th nearest neighbor distance for a given dataset of n points. We study the…

We derive a posteriori error estimators for an optimal control problem governed by a convection-reaction-diffusion equation; control constraints are also considered. We consider a family of low-order stabilized finite element methods to…

Let $k$ and $n$ be positive integers, $n>k$. Define $r(n,k)$ to be the minimum positive value of $$ |\sqrt{a_1} + ... + \sqrt{a_k} - \sqrt{b_1} - >... -\sqrt{b_k} | $$ where $ a_1, a_2, ..., a_k, b_1, b_2, ..., b_k $ are positive integers…