Related papers: PolyFit: Polynomial-based Indexing Approach for Fa…
Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…
Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…
We want to recover the regression function in the single-index model. Using an aggregation algorithm with local polynomial estimators, we answer in particular to the second part of Question~2 from Stone (1982) on the optimal convergence…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
The growing demands of processing massive datasets have promoted irresistible trends of running machine learning applications on MapReduce. When processing large input data, it is often of greater values to produce fast and accurate enough…
Ranking data represent a peculiar form of multivariate ordinal data taking values in the set of permutations. Despite the numerous methodological contributions to increase the flexibility of ranked data modeling, the application of more…
While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse…
The ability to handle large scale graph data is crucial to an increasing number of applications. Much work has been dedicated to supporting basic graph operations such as subgraph matching, reachability, regular expression matching, etc. In…
Range-filtered approximate nearest neighbor (RFANN) search is a fundamental operation in modern data systems. Given a set of objects, each with a vector and a numerical attribute, an RFANN query retrieves the nearest neighbors to a query…
With the continued digitization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when…
In this paper, we propose a new algorithm to speed-up the convergence of accelerated proximal gradient (APG) methods. In order to minimize a convex function $f(\mathbf{x})$, our algorithm introduces a simple line search step after each…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
A method for approximating continuous functions $\mathbb{Z}_{p}^{n}\rightarrow\mathbb{Z}_{p}$ by a linear superposition of continuous functions $\mathbb{Z}_{p}\rightarrow\mathbb{Z}_{p}$ is presented and a polynomial regression model is…
Distribution-free uncertainty estimation for ensemble methods is increasingly desirable due to the widening deployment of multi-modal black-box predictive models. Conformal prediction is one approach that avoids such distributional…
Fast Nearest Neighbor (NN) search is a fundamental challenge in large-scale data processing and analytics, particularly for analyzing multimedia contents which are often of high dimensionality. Instead of using exact NN search, extensive…
Width-based search algorithms seek plans by prioritizing states according to a suitably defined measure of novelty, that maps states into a set of novelty categories. Space and time complexity to evaluate state novelty is known to be…
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…
Highly efficient and even nearly optimal algorithms have been developed for the classical problem of univariate polynomial root-finding (see, e.g., \cite{P95}, \cite{P02}, \cite{MNP13}, and the bibliography therein), but this is still an…
Conformal prediction constructs a set of labels instead of a single point prediction, while providing a probabilistic coverage guarantee. Beyond the coverage guarantee, adaptiveness to example difficulty is an important property. It means…
It has been known in potential theory that, for some kernels matrices corresponding to well-separated point sets, fast analytical low-rank approximation can be achieved via the use of proxy points. This proxy point method gives a…