A novel weighted rank aggregation algorithm with applications in gene prioritization

We propose a new family of algorithms for bounding/approximating the optimal solution of rank aggregation problems based on weighted Kendall distances. The algorithms represent linear programming relaxations of integer programs that involve variables reflecting partial orders of three or more candidates. Our simulation results indicate that the linear programs give near-optimal performance for a number of important voting parameters, and outperform methods based on PageRank and Weighted Bipartite Matching. Finally, we illustrate the performance of the aggregation method on a set of test genes pertaining to the Bardet-Biedl syndrome, schizophrenia, and HIV and show that the combinatorial method matches or outperforms state-of-the art algorithms such as ToppGene

Combinatorial Optimization

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Reduced-Dimension Linear Transform Coding of Correlated Signals in Networks

A model, called the linear transform network (LTN), is proposed to analyze the compression and estimation of correlated signals transmitted over directed acyclic graphs (DAGs). An LTN is a DAG network with multiple source and receiver nodes. Source nodes transmit subspace projections of random correlated signals by applying reduced-dimension linear transforms. The subspace projections are linearly processed by multiple relays and routed to intended receivers. Each receiver applies a linear estimator to approximate a subset of the sources with minimum mean squared error (MSE) distortion. The model is extended to include noisy networks with power constraints on transmitters. A key task is to compute all local compression matrices and linear estimators in the network to minimize end-to-end distortion. The non-convex problem is solved iteratively within an optimization framework using constrained quadratic programs (QPs). The proposed algorithm recovers as special cases the regular and distributed Karhunen-Loeve transforms (KLTs). Cut-set lower bounds on the distortion region of multi-source, multi-receiver networks are given for linear coding based on convex relaxations. Cut-set lower bounds are also given for any coding strategy based on information theory. The distortion region and compression-estimation tradeoffs are illustrated for different communication demands (e.g. multiple unicast), and graph structures.Comment: 33 pages, 7 figures, To appear in IEEE Transactions on Signal Processin

A Mathematical Programming Approach for Imputation of Unknown Journal Ratings in a Combined Journal Quality List

The quality of faculty scholarship and productivity is one of the primary measures for faculty evaluation in most academic institutions. Due to the diversity and interdisciplinary nature of modern academic research fields, it is increasingly important to use journal quality lists, with journal ratings, that offer credible measures of the worth of faculty scholarship. Despite the existence of such metrics, journal lists, by their very nature, exclude some well‐recognized journals. Consequently, academic institutions expend inordinate resources to assess the quality of unrated journals appropriately and equitably across disciplines. The current research proposes mathematical programming models as a path to determining unknown ratings of multiple journal quality lists, using only their known rating information. The objective of the models is to minimize the total number of instances where two journals are rated in opposite order by two different journal quality lists. Computational results based on journal quality list data in https://harzing.com/ indicate that the proposed methods outperform existing imputation algorithms with most realistic test data sets in terms of accuracy, root mean square error, and mean absolute deviation