Constructing Optimal Sparse Portfolios Using Regularization Methods

Fastrich, Bjoern; Paterlini, Sandra; Winker, Peter

doi:10.2139/ssrn.2169062

Cited by 33 publications

(54 citation statements)

References 38 publications

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“…(This would typically be added to a traditional quadratic risk measure.) This term is a weighted 1 -norm of the deviation from the weights, and encourages weights that deviate sparsely from the benchmark, i.e., weights with some or many entries equal to those of the benchmark [26,34,41].…”

Section: Forecast Error Riskmentioning

confidence: 99%

Multi-Period Trading via Convex Optimization

Boyd

2017

FNT in Optimization

106

139

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We consider a basic model of multi-period trading, which can be used to evaluate the performance of a trading strategy. We describe a framework for single-period optimization, where the trades in each period are found by solving a convex optimization problem that trades off expected return, risk, transaction cost and holding cost such as the borrowing cost for shorting assets. We then describe a multi-period version of the trading method, where optimization is used to plan a sequence of trades, with only the first one executed, using estimates of future quantities that are unknown when the trades are chosen. The singleperiod method traces back to Markowitz; the multi-period methods trace back to model predictive control. Our contribution is to describe the single-period and multi-period methods in one simple framework, giving a clear description of the development and the approximations made. In this paper we do not address a critical component in a trading algorithm, the predictions or forecasts of future quantities. The methods we describe in this paper can be thought of as good ways to exploit predictions, no matter how they are made. We have also developed a companion open-source software library that implements many of the ideas and methods described in the paper.

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Section: Forecast Error Riskmentioning

confidence: 99%

Multi-Period Trading via Convex Optimization

Boyd

2017

FNT in Optimization

106

139

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“…These two assumptions are not necessarily justified with fingerprinting-based positioning. It is difficult to find a proper value of the hyper-parameter of LASSO-based feature selection, which makes the feature selection unstable (Fastrich et al 2015). Finally, this feature selection algorithm is prone to overfitting.…”

Section: Selection Of Relevant Featuresmentioning

confidence: 99%

Modified Jaccard index analysis and adaptive feature selection for location fingerprinting with limited computational complexity

Zhou

2019

Journal of Location Based Services

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We propose an approach for fingerprinting-based positioning which reduces the data requirements and computational complexity of the online positioning stage. It is based on a segmentation of the entire region of interest into subregions, identification of candidate subregions during the online-stage, and position estimation using a preselected subset of relevant features. The subregion selection uses a modified Jaccard index which quantifies the similarity between the features observed by the user and those available within the reference fingerprint map. The adaptive feature selection is achieved using an adaptive forward-backward greedy search which determines a subset of features for each subregion, relevant with respect to a given fingerprinting-based positioning method. In an empirical study using signals of opportunity for fingerprinting the proposed subregion and feature selection reduce the processing time during the online-stage by a factor of about 10 while the positioning accuracy does not deteriorate significantly. In fact, in one of the two study cases the 90 th percentile of the circular error increased by 7.5% while in the other study case we even found a reduction of the corresponding circular error by 30%. KEYWORDSfingerprinting-based indoor positioning, adaptive forward-backward greedy algorithm, feature selection, modified Jaccard index, subregion selection, signals of opportunity. Torres-Sospedra et al. 2015;Xie et al. 2016), or RSS of cellular towers (Driusso et al. 2016). Such signals are location dependent features, many of which can easily be measured using a variety of mobile devices (e.g., smart phones or tablets). FIPSs are therefore also called feature-based indoor positioning systems (Kasprzak et al. 2013). The attainable quality of the position estimation using FIPS mainly depends on the spatial gradient of the features and on their stability or predictability over time (Niedermayr et al. 2014).Key challenges of FIPS, especially the ones using RSS readings from WLAN APs, are discussed e.g., in (Kushki et al. 2007) and more recently in (He and Chan 2016;Yassin et al. 2017). The former publication focuses on four challenges of FIPS utilizing vectors of RSS from WLAN AP as features. In particular, the paper addresses i) the generation of a fingerprint database to provide a reference fingerprint map (RFM) for positioning, ii) pre-processing of fingerprints for reducing computational complexity and enhancing accuracy, iii) selection of APs for positioning, and iv) estimation of the distance between a fingerprint measured by the user and the fingerprints represented within in the reference database. Extensions to large indoor regions and handling of variations of observable features caused by the changes of indoor environments or signal sources of the features (e.g., replacement of broken APs) are addressed in (He and Chan 2016).Regarding generation of the RFM, various approaches have been proposed (He and Chan 2016). Initially, the features were mapped by dedicated surveying measurements (...

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“…However, the results are affected by the choice of λ and the optimum choice depends on the data. So, feature selection based on LASSO with any fixed priorly chosen value λ is unstable [Fastrich et al, 2015]. In order to get an appropriate fixed value of λ , we use cross validation.…”

Section: Feature Selection Using Randomized Lassomentioning

confidence: 99%

Jaccard Analysis and LASSO-Based Feature Selection for Location Fingerprinting with Limited Computational Complexity

Zhou

2017

Lecture Notes in Geoinformation and Cartography

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We propose an approach to reduce both computational complexity and data storage requirements for the online positioning stage of a fingerprinting-based indoor positioning system (FIPS) by introducing segmentation of the region of interest (RoI) into sub-regions, sub-region selection using a modified Jaccard index, and feature selection based on randomized least absolute shrinkage and selection operator (LASSO). We implement these steps into a Bayesian framework of position estimation using the maximum a posteriori (MAP) principle. An additional benefit of these steps is that the time for estimating the position, and the required data storage are virtually independent of the size of the RoI and of the total number of available features within the RoI. Thus the proposed steps facilitate application of FIPS to large areas. Results of an experimental analysis using real data collected in an office building using a Nexus 6P smart phone as user device and a total station for providing position ground truth corroborate the expected performance of the proposed approach. The positioning accuracy obtained by only processing 10 automatically identified features instead of all available ones and limiting position estimation to 10 automatically identified sub-regions instead of the entire RoI is equivalent to processing all available data. In the chosen example, 50% of the errors are less than 1.8 m and 90% are less than 5 m. However, the computation time using the automatically identified subset of data is only about 1% of that required for processing the entire data set.

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Constructing Optimal Sparse Portfolios Using Regularization Methods

Cited by 33 publications

References 38 publications

Multi-Period Trading via Convex Optimization

Multi-Period Trading via Convex Optimization

Modified Jaccard index analysis and adaptive feature selection for location fingerprinting with limited computational complexity

Jaccard Analysis and LASSO-Based Feature Selection for Location Fingerprinting with Limited Computational Complexity

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