Outlier Detection in Time Series via Mixed-Integer Conic Quadratic Optimization

Gómez, Andrés

doi:10.1137/19m1306233

Cited by 12 publications

(9 citation statements)

References 81 publications

(80 reference statements)

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“…where a 1 , a 2 > 0 are constants. While we refer the reader to [29] for details on the derivation of cl conv(X T ), we point out that it can in fact be described by lifted supermodular inequalities. Indeed, in this case, function g α is given by…”

Section: Previous Results As Lifted Supermodular Inequalitiesmentioning

confidence: 99%

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Supermodularity and valid inequalities for quadratic optimization with indicators

Atamtürk¹,

Gómez²

2020

Preprint

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We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult, the specific set function for the rank-one quadratic can be minimized in linear time. We show that the convex hull of the epigraph of the quadratic can be obtaining from inequalities for the underlying supermodular set function by lifting them into nonlinear inequalities in the original space of variables. Explicit forms of the convex-hull description are given, both in the original space of variables and in an extended formulation via conic quadraticrepresentable inequalities, along with a polynomial separation algorithm. Computational experiments indicate that the lifted supermodular inequalities in conic quadratic form are quite effective in reducing the integrality gap for quadratic optimization with indicators.

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Section: Previous Results As Lifted Supermodular Inequalitiesmentioning

confidence: 99%

“…Outlier detection with temporal data. In the context of outlier detection with temporal data, Gómez [29] studies the set…”

Section: Previous Results As Lifted Supermodular Inequalitiesmentioning

confidence: 99%

Supermodularity and valid inequalities for quadratic optimization with indicators

Atamtürk¹,

Gómez²

2020

Preprint

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“…Moreover, formulations with tight LO relaxations, referred to as strong formulations, are also desirable as they produce higher quality lower bounds which lead to a faster pruning of the search space, ultimately reducing the number of LO problems to be solved. Indeed, a recent research thrust focuses on devising strong formulations for inference problems (Dong et al 2015, Atamtürk et al 2018, Bienstock et al 2018, Xie and Deng 2018, Gómez 2019, Anderson et al 2020, Bertsimas et al 2020, Hazimeh et al 2020.…”

Section: Discussionmentioning

confidence: 99%

Strong Optimal Classification Trees

Aghaei¹,

Gómez²,

Vayanos³

2021

Preprint

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Decision trees are among the most popular machine learning models and are used routinely in applications ranging from revenue management and medicine to bioinformatics. In this paper, we consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixedinteger optimization (MIO) technology. Yet, existing MIO-based approaches from the literature do not leverage the power of MIO to its full extent: they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose an intuitive flow-based MIO formulation for learning optimal binary classification trees. Our formulation can accommodate side constraints to enable the design of interpretable and fair decision trees. Moreover, we show that our formulation has a stronger linear optimization relaxation than existing methods. We exploit the decomposable structure of our formulation and max-flow/min-cut duality to derive a Benders' decomposition method to speed-up computation. We propose a tailored procedure for solving each decomposed subproblem that provably generates facets of the feasible set of the MIO as constraints to add to the main problem. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 31 times faster than state-of-the art MIO-based techniques and improve out of sample performance by up to 8%.

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“…In Formula (1-3), m , n and p are the fuzzy universe of M , N and P respectively; ( ) M x , ( ) N x and ( ) P x are the mapping functions of M , N and P respectively [9]. The automatic monitoring functions of M , N and P are deduced as follows:…”

Section: Design Of Online Automatic Monitoring Methods For Internet O...mentioning

confidence: 99%

Online process automatic monitoring technology of Internet of Things card life cycle based on time series optimization

Huai-jun¹,

Lü²,

Yang³

et al. 2022

6th International Workshop on Advanced Algorithms and Control Engineering (IWAACE 2022)

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Aiming at the problem of poor real-time monitoring performance of the Internet of Things (IoT) card, an online automatic monitoring method based on the optimized time series is designed. Based on the concept of time series, the automatic monitoring function of the life cycle of the Internet of Things card is deduced. On the basis of this function, the online process automatic monitoring model is constructed to shorten the time of data transmission in the monitoring process, to realize the online process real-time monitoring of the life cycle of the Internet of Things card. In this paper, the performance of the design method is analyzed by means of comparative experiments. The data transmission time of this automatic monitoring method is all below 0.40ms, and the transmission time of business statistical analysis is the highest, and reached 2.7ms. Therefore, the method effectively reduces the transmission time of monitoring process data and improves the monitoring efficiency.

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Outlier Detection in Time Series via Mixed-Integer Conic Quadratic Optimization

Cited by 12 publications

References 81 publications

Supermodularity and valid inequalities for quadratic optimization with indicators

Supermodularity and valid inequalities for quadratic optimization with indicators

Strong Optimal Classification Trees

Online process automatic monitoring technology of Internet of Things card life cycle based on time series optimization

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