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Mode hunting through active information. (English) Zbl 1436.62030

Summary: We propose a new method to find modes based on active information. We develop an algorithm called active information mode hunting (AIMH) that, when applied to the whole space, will say whether there are any modes present and where they are. We show AIMH is consistent and, given that information increases where probability decreases, it helps to overcome issues with the curse of dimensionality. The AIMH also reduces the dimensionality with no resource to principal components. We illustrate the method in three ways: with a theoretical example (showing how it performs better than other mode hunting strategies), a real dataset business application, and a simulation.

MSC:

62B10 Statistical aspects of information-theoretic topics
62H25 Factor analysis and principal components; correspondence analysis
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References:

[1] HallP, MinotteMC, ZhangC. Bump hunting with non‐Gaussian kernels. Ann Stat. 2004;32:2124‐2141. · Zbl 1056.62049
[2] MostatE. Mode Hunting and Density Estimation With the Focussed Information Criterion [master’s thesis]. Oslo, Norway: University of Oslo; 2013.
[3] OoiH. Density visualization and mode hunting using trees. J Comput Graph Statist. 2002;11(2):328‐347.
[4] SommerfeldM, HeoG, KimP, RushST, MarronJS. Bump hunting by topological data analysis. Stat. 2017;6:462‐471.
[5] IzbickiR, LeeAB. Converting high‐dimensional regression to high‐dimensional conditional density estimation. Electron J Stat. 2017;11:2800‐2831. · Zbl 1366.62078
[6] Díaz‐PachónDA, DazardJE, RaoJS. Unsupervised bump hunting using principal components. In: AhmedSE (ed.), ed. Big and Complex Data Analysis: Methodologies and Applications. New York, NY: Springer; 2016.
[7] HadiS, LingRF. Some cautionary notes on the use of principal components regression. Am Stat. 1998;52(1):15‐19.
[8] JoliffeI. A note on the use of principal components in regression. J R Stat Soc Ser C Appl Stat. 1982;31(3):300‐303.
[9] FriedmanJH, FisherNI. Bump hunting in high‐dimensional data. Stat Comput. 1999;9:123‐143.
[10] PolonikW, WangZ. PRIM analysis. J Multivar Anal. 2010;101(3):525‐540. · Zbl 1186.62132
[11] DazardJE, RaoJS. Local sparse bump hunting. J Comput Graph Stat. 2010;19(4):900‐929.
[12] WolpertDH, MacReadyWG. No Free Lunch Theorems for Search. Technical Report SFI‐TR‐95‐02‐010. Santa Fe, NM: Santa Fe Institute; 1995.
[13] WolpertDH, MacReadyWG. No free lunch theorems for optimization. IEEE Trans Evol Comput. 1997;1(1):67‐82.
[14] DembskiWA, MarksRJ. Bernoulli’s principle of insufficient reason and conservation of information in computer search. In: Proceedings of the 2009 IEEE International Conference on Systems, Man, and Cybernetics; 2009; San Antonio, TX.
[15] DembskiWA, MarksRJ. Conservation of information in search measuring the cost of success. IEEE Trans Syst Man Cybern A Syst Hum. 2009;5(5):1051‐1061.
[16] MarksRJ, DembskiWA, EwertW. Introduction to Evolutionary Informatics. Singapore: World Scientific; 2017.
[17] Díaz‐PachónDA, MarksRJ. Maximum entropy and active information. 2017. Submitted.
[18] HastieT, TibshiraniR, FriedmanJ. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York, NY: Springer Science; 2009. · Zbl 1273.62005
[19] LamidiA. Predicting the success of Kickstarter campaigns. 2017. https://towardsdatascience.com/predicting-the-success-of-kickstarter-campaigns-3f4a976419b9
[20] BarbiM, BigelliM. Crowdfunding practices in and outside the US. Res Int Bus Finance. 2017;42:208‐223.
[21] KaurH, GeraJ. Effect of social media connectivity on success of crowdfunding campaigns. Inf Technol Quant Manag. 2017;122:767‐774.
[22] ZvilichovskyD, DanzigerS, SteinhartY. Making‐the‐product‐happen: a driver of crowdfunding participation. J Interact Mark. 2018;41:81‐93.
[23] KuppuswamyV, BayusBL. Does my contribution to your crowdfunding project matter?J Bus Ventur. 2017;32:72‐89.
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