Data-Mining – Page 3 – Optimization Online

Unbiased Subdata Selection for Fair Classification: A Unified Framework and Scalable Algorithms

Published: 2020/12/22, Updated: 2020/12/23

(Mixed) Integer Nonlinear Programming, Data-Mining

As an important problem in modern data analytics, classification has witnessed varieties of applications from different domains. Different from conventional classification approaches, fair classification concerns the issues of unintentional biases against the sensitive features (e.g., gender, race). Due to high nonconvexity of fairness measures, existing methods are often unable to model exact fairness, which can … Read more

A dynamic programming approach to segmented isotonic regression

Published: 2020/12/08

Data-Mining, Dynamic Programming, Energy cardinality-constrained shortest path problem, consumers' price-response, data clustering, inverse problems, isotonic regression, segmented regression

This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on … Read more

Accuracy and fairness trade-offs in machine learning: A stochastic multi-objective approach

Published: 2020/08/03, Updated: 2020/09/03

Suyun Liu

Luis Nunes Vicente

Data-Mining, Multi-Criteria Optimization, Stochastic Programming disparate impact, equal opportunity, fairness, machine learning, multi-objective optimization, nonconvex optimization, pareto fronts, sensitive/protected attributes, stochastic approximation, supervised learning

In the application of machine learning to real life decision-making systems, e.g., credit scoring and criminal justice, the prediction outcomes might discriminate against people with sensitive attributes, leading to unfairness. The commonly used strategy in fair machine learning is to include fairness as a constraint or a penalization term in the minimization of the prediction … Read more

The block mutual coherence property condition for signal recovery

Published: 2020/07/10

Data-Mining, Nonsmooth Optimization, Statistics

Compressed sensing shows that a sparse signal can stably be recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the $\ell_2/\ell_1-\alpha\ell_2$ minimization method for the stable recovery of block-sparse signals is investigated. … Read more

The block mutual coherence property condition for signal recovery

Published: 2020/06/10

Data-Mining, Nonlinear Optimization

Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks

Published: 2020/05/22, Updated: 2022/05/06

(Mixed) Integer Nonlinear Programming, Data-Mining, Network Optimization bayesian networks, consistency, directed acyclic graphs, early stopping criterion, mixed-integer conic programming

Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge discovery. We study the problem of learning the sparse DAG structure of a BN from continuous observational data. The central problem can be modeled as … Read more

The high-order block RIP for non-convex block-sparse compressed sensing

Published: 2020/03/07

Data-Mining, Statistics

This paper concentrates on the recovery of block-sparse signals, which is not only sparse but also nonzero elements are arrayed into some blocks (clusters) rather than being arbitrary distributed all over the vector, from linear measurements. We establish high-order sufficient conditions based on block RIP to ensure the exact recovery of every block $s$-sparse signal … Read more

Best Principal Submatrix Selection for the Maximum Entropy Sampling Problem: Scalable Algorithms and Performance Guarantees

Published: 2020/01/23, Updated: 2023/05/01

Yongchun Li

Weijun Xie

Data-Mining

This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix with a given size out of a covariance matrix from a system. MESP has been widely applied to many areas, including healthcare, power system, manufacturing, data science, etc. Investigating its Lagrangian dual and primal characterization, we … Read more

The perturbation analysis of nonconvex low-rank matrix robust recovery

Published: 2019/12/25

Jianwen Huang

Wang Wendong

Feng Zhang

Applications - Science and Engineering, Data-Mining

In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees … Read more

Online matrix factorization for Markovian data and applications to Network Dictionary Learning

Published: 2019/11/11

Laura Balzano

Hanbaek Lyu

Deanna Needell

Data-Mining, Nonlinear Optimization convergence analysis, dictionary learning, markovian data, non-negative matrix factorization, online matrix factorization

Online Matrix Factorization (OMF) is a fundamental tool for dictionary learning problems, giving an approximate representation of complex data sets in terms of a reduced number of extracted features. Convergence guarantees for most of the OMF algorithms in the literature assume independence between data matrices, and the case of a dependent data stream remains largely … Read more