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In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…
According to the probability ranking principle, the document set with the highest values of probability of relevance optimizes information retrieval effectiveness given the probabilities are estimated as accurately as possible. The key…
This paper deals with the clustering of univariate observations: given a set of observations coming from $K$ possible clusters, one has to estimate the cluster means. We propose an algorithm based on the minimization of the "KP" criterion…
We consider data in the form of pairwise comparisons of n items, with the goal of precisely identifying the top k items for some value of k < n, or alternatively, recovering a ranking of all the items. We analyze the Copeland counting…
In this paper, we consider the weighted online set k-multicover problem. In this problem, we have a universe V of elements, a family S of subsets of V with a positive real cost for every set in S and a "coverage factor" (positive integer)…
A common problem in machine learning is to rank a set of n items based on pairwise comparisons. Here ranking refers to partitioning the items into sets of pre-specified sizes according to their scores, which includes identification of the…
We introduce an online version of the multiselection problem, in which q selection queries are requested on an unsorted array of n elements. We provide the first online algorithm that is 1-competitive with Kaligosi et al. [ICALP 2005] in…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
This paper presents the first convergence result for random search algorithms to a subset of the Pareto set of given maximum size k with bounds on the approximation quality. The core of the algorithm is a new selection criterion based on a…
Query re-optimization is an adaptive query processing technique that re-invokes the optimizer at certain points in query execution. The goal is to dynamically correct the cardinality estimation errors using the statistics collected at…
We present scalable parallel algorithms with sublinear per-processor communication volume and low latency for several fundamental problems related to finding the most relevant elements in a set, for various notions of relevance: We begin…
We initiate a study of a query-driven approach to designing partition trees for range-searching problems. Our model assumes that a data structure is to be built for an unknown query distribution that we can access through a sampling oracle,…
We consider robust combinatorial optimization problems where the decision maker can react to a scenario by choosing from a finite set of $k$ solutions. This approach is appropriate for decision problems under uncertainty where the…
The analysis of algorithms mostly relies on counting classic elementary operations like additions, multiplications, comparisons, swaps etc. This approach is often sufficient to quantify an algorithm's efficiency. In some cases, however,…
We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…
Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…
We consider the Top-$K$ selection problem, which aims to identify the largest $K$ elements in an array. Top-$K$ selection arises in many machine learning algorithms and often becomes a bottleneck on accelerators, which are optimized for…
Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…
We present an approximate sampling framework and discuss how risk-limiting audits can compensate for these approximations, while maintaining their "risk-limiting" properties. Our framework is general and can compensate for counting mistakes…