Maximization of AUC and Buffered AUC in binary classification

Norton, Matthew; Uryasev, Stan

doi:10.1007/s10107-018-1312-2

Cited by 47 publications

(34 citation statements)

References 20 publications

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“…Similar to the superquantile, bPOE is a more robust measure of tail risk, as it considers not only the probability that events/losses will exceed the threshold x, but also the magnitude of these potential events. Also, much like the superquantile, bPOE can be represented as the unique minimum of a one-dimensional convex optimization problem with the formulas given by Norton and Uryasev (2016); as follows, where [·] + = max{·, 0}.…”

Section: Background and Notationmentioning

confidence: 99%

“…While the superquantile has risen in popularity over the past decade, a related characteristic called Buffered Probability of Exceedance (bPOE) has recently been introduced, first by Rockafellar and Royset (2010) in the context of Buffered Failure Probability and then generalized by . This concept has grown in popularity within the risk management community with application in finance, logistics, analysis of natural disasters, statistics, stochastic programming, and machine learning (Shang et al (2018); Uryasev (2014); Davis and Uryasev (2016); ; Norton et al (2017); Norton and Uryasev (2016). Specifically, bPOE is the inverse of the superquantile in the same way that the CDF is the inverse of the quantile.…”

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confidence: 99%

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Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation

Norton

Khokhlov²,

Uryasev

2019

Ann Oper Res

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Conditional Value-at-Risk (CVaR) and Value-at-Risk (VaR), also called the superquantile and quantile, are frequently used to characterize the tails of probability distribution's and are popular measures of risk in applications where the distribution represents the magnitude of a potential loss. Buffered Probability of Exceedance (bPOE) is a recently introduced characterization of the tail which is the inverse of CVaR, much like the CDF is the inverse of the quantile. These quantities can prove very useful as the basis for a variety of risk-averse parametric engineering approaches. Their use, however, is often made difficult by the lack of well-known closed-form equations for calculating these quantities for commonly used probability distribution's. In this paper, we derive formulas for the superquantile and bPOE for a variety of common univariate probability distribution's. Besides providing a useful collection within a single reference, we use these formulas to incorporate the superquantile and bPOE into parametric procedures. In particular, we consider two: portfolio optimization and density estimation. First, when portfolio returns are assumed to follow particular distribution families, we show that finding the optimal portfolio via minimization of bPOE has advantages over superquantile minimization. We show that, given a fixed threshold, a single portfolio is the minimal bPOE portfolio for an entire class of distribution's simultaneously. Second, we apply our formulas to parametric density estimation and propose the method of superquantile's (MOS), a simple variation of the method of moment's (MM) where moment's are replaced by superquantile's at different confidence levels. With the freedom to select various combinations of confidence levels, MOS allows the user to focus the fitting procedure on different portions of the distribution, such as the tail when fitting heavy-tailed asymmetric data.

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Section: Background and Notationmentioning

confidence: 99%

mentioning

confidence: 99%

Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation

Norton

Khokhlov²,

Uryasev

2019

Ann Oper Res

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“…The bAUC concept is based on the so-called Buffered Probability of Exceedance (bPOE), defined in Norton and Uryasev (2016), and also in . For references to several papers using bPOE concept in various areas, see Davis and Uryasev (2016) For τ ∈ (0, 1), the τth quantile q τ (X) of X is defined by…”

Section: Bauc and Optimizationmentioning

confidence: 99%

“…for z ∈ R such that E[X] < z < sup X. Formula (10) is considered in Norton and Uryasev (2016) and as a property of bPOE, but it is convenient to use it as a definition. Further on, Upper bPOE will be called bPOE (without mentioning that it is Upper bPOE).…”

Section: Bauc and Optimizationmentioning

confidence: 99%

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Peer-To-Peer Lending: Classification in the Loan Application Process

Wei

Gotoh

Uryasev

2018

Risks

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This paper studies the peer-to-peer lending and loan application processing of LendingClub. We tried to reproduce the existing loan application processing algorithm and find features used in this process. Loan application processing is considered a binary classification problem. We used the area under the ROC curve (AUC) for evaluation of algorithms. Features were transformed with splines for improving the performance of algorithms. We considered three classification algorithms: logistic regression, buffered AUC (bAUC) maximization, and AUC maximization.With only three features, Debt-to-Income Ratio, Employment Length, and Risk Score, we obtained an AUC close to 1. We have done both in-sample and out-of-sample evaluations. The codes for cross-validation and solving problems in a Portfolio Safeguard (PSG) format are in the Appendix. The calculation results with the data and codes are posted on the website and are available for downloading.

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