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Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy…
Motivated by applications in machine learning and statistics, we study distributed optimization problems over a network of processors, where the goal is to optimize a global objective composed of a sum of local functions. In these problems,…
This is the first study on crowdsourcing Pareto-optimal object finding, which has applications in public opinion collection, group decision making, and information exploration. Departing from prior studies on crowdsourcing skyline and…
Consensus clustering (or clustering aggregation) inputs $k$ partitions of a given ground set $V$, and seeks to create a single partition that minimizes disagreement with all input partitions. State-of-the-art algorithms for consensus…
The min-knapsack problem with compactness constraints extends the classical knapsack problem, in the case of ordered items, by introducing a restriction ensuring that they cannot be too far apart. This problem has applications in…
A well-known but rarely used approach to text categorization uses conditional entropy estimates computed using data compression tools. Text affinity scores derived from compressed sizes can be used for classification and ranking tasks, but…
Ensemble methods have been widely applied in Reinforcement Learning (RL) in order to enhance stability, increase convergence speed, and improve exploration. These methods typically work by employing an aggregation mechanism over actions of…
The input data features set for many data driven tasks is high-dimensional while the intrinsic dimension of the data is low. Data analysis methods aim to uncover the underlying low dimensional structure imposed by the low dimensional hidden…
We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
In this contribution, the clustering procedure based on K-Means algorithm is studied as an inverse problem, which is a special case of the illposed problems. The attempts to improve the quality of the clustering inverse problem drive to…
Quality assessments of models in unsupervised learning and clustering verification in particular have been a long-standing problem in the machine learning research. The lack of robust and universally applicable cluster validity scores often…
Partisan gerrymandering is a major cause for voter disenfranchisement in United States. However, convincing US courts to adopt specific measures to quantify gerrymandering has been of limited success to date. Recently, Stephanopoulos and…
We develop an algorithm that finds the consensus of many different clustering solutions of a graph. We formulate the problem as a median set partitioning problem and propose a greedy optimization technique. Unlike other approaches that find…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
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…
Modeling of aggregation processes in space-inhomogeneous systems is extremely numerically challenging since complicated aggregation equations -- Smoluchowski equations are to be solved at each space point along with the computation of…
The $k$-Means clustering problem on $n$ points is NP-Hard for any dimension $d\ge 2$, however, for the 1D case there exists exact polynomial time algorithms. Previous literature reported an $O(kn^2)$ time dynamic programming algorithm that…
An important way to make large training sets is to gather noisy labels from crowds of non experts. We propose a method to aggregate noisy labels collected from a crowd of workers or annotators. Eliciting labels is important in tasks such as…
Low-rank decomposition plays a central role in accelerating convolutional neural network (CNN), and the rank of decomposed kernel-tensor is a key parameter that determines the complexity and accuracy of a neural network. In this paper, we…