Related papers: Near-optimal sample compression for nearest neighb…
Convex sample approximations of chance-constrained optimization problems are considered, in which chance constraints are replaced by sets of sampled constraints. We propose a randomized sample selection strategy that allows tight bounds to…
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…
In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…
Compressing word embeddings is important for deploying NLP models in memory-constrained settings. However, understanding what makes compressed embeddings perform well on downstream tasks is challenging---existing measures of compression…
Motivated by applications in machine learning, such as subset selection and data summarization, we consider the problem of maximizing a monotone submodular function subject to mixed packing and covering constraints. We present a tight…
Motivated by safety-critical applications, test-time attacks on classifiers via adversarial examples has recently received a great deal of attention. However, there is a general lack of understanding on why adversarial examples arise;…
We introduce in this paper a new summarization method for large graphs. Our summarization approach retains only a user-specified proportion of the neighbors of each node in the graph. Our main aim is to simplify large graphs so that they…
Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…
A novel and intuitive nearest neighbours based clustering algorithm is introduced, in which a cluster is defined in terms of an equilibrium condition which balances its size and cohesiveness. The formulation of the equilibrium condition…
We consider the problem of approximating a function in general nonlinear subsets of $L^2$ when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
In regression analysis one wants to estimate the regression function from a data. In this paper we consider the rate of convergence for the nearest neighbor estimator in case that the regression function is $(p,C)$-smooth. It is an open…
Nearest neighbor (NN) algorithms have been extensively used for missing data problems in recommender systems and sequential decision-making systems. Prior theoretical analysis has established favorable guarantees for NN when the underlying…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
We propose the first adversarially robust algorithm for monotone submodular maximization under single and multiple knapsack constraints with scalable implementations in distributed and streaming settings. For a single knapsack constraint,…
We study the consistency of the $k$-nearest neighbor regressor under complex survey designs. While consistency results for this algorithm are well established for independent and identically distributed data, corresponding results for…
The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces…
The $k$-nearest neighbor ($k$-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the number of neighbors $k$. This parameter exerts a direct impact on…
We consider the problem of approximating a function in a general nonlinear subset of $L^2$, when only a weighted Monte Carlo estimate of the $L^2$-norm can be computed. Of particular interest in this setting is the concept of sample…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
Deep nets generalize well despite having more parameters than the number of training samples. Recent works try to give an explanation using PAC-Bayes and Margin-based analyses, but do not as yet result in sample complexity bounds better…