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Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien, Departments 4 D4.4.00810:30 - 11:45

Type Lecture / discussion
SpeakerTorsten Hothorn (Epidemiology, Biostatistics and Prevention Institute, University of Zurich)
Organizer Institut für Statistik und Mathematik

Tor­sten Ho­thorn (Epidemi­ology, Bio­s­tat­ist­ics and Pre­ven­tion In­sti­tute, Uni­versity of Zurich) about "Trans­form­a­tion Forests"

The In­sti­tute for Stat­ist­ics and Mathem­at­ics (De­part­ment of Fin­ance, Ac­count­ing and Stat­ist­ics) cor­di­ally in­vites every­one in­ter­ested to at­tend the talks in our Re­search Sem­inar Ser­ies, where in­ter­na­tion­ally renowned schol­ars from lead­ing uni­versit­ies present and dis­cuss their (work­ing) pa­pers.

The list of talks for the win­ter term 2018/19 is avail­able via the fol­low­ing link: ht­tps://­math/ressem­inar

Re­gres­sion mod­els for su­per­vised learn­ing prob­lems with a con­tinu­ous re­sponse are com­monly un­der­stood as mod­els for the con­di­tional mean of the re­sponse given pre­dict­ors. This no­tion is sim­ple and there­fore ap­peal­ing for in­ter­pret­a­tion and visu­al­isa­tion. In­form­a­tion about the whole un­derly­ing con­di­tional dis­tri­bu­tion is, however, not avail­able from these mod­els. A more gen­eral un­der­stand­ing of re­gres­sion mod­els as mod­els for con­di­tional dis­tri­bu­tions al­lows much broader in­fer­ence from such mod­els, for example the com­pu­ta­tion of pre­dic­tion in­ter­vals. Several ran­dom forest-­type al­gorithms aim at es­tim­at­ing con­di­tional dis­tri­bu­tions, most prom­in­ently quantile re­gres­sion forests (Mein­shausen, 2006, JMLR). We pro­pose a novel ap­proach based on a para­met­ric fam­ily of dis­tri­bu­tions char­ac­ter­ised by their trans­form­a­tion func­tion. A ded­ic­ated novel “trans­form­a­tion tree” al­gorithm able to de­tect dis­tri­bu­tional changes is developed. Based on these trans­form­a­tion trees, we in­tro­duce “trans­form­a­tion forests” as an ad­apt­ive local like­li­hood es­tim­ator of con­di­tional dis­tri­bu­tion func­tions. The res­ult­ing pre­dict­ive dis­tri­bu­tions are fully para­met­ric yet very gen­eral and al­low in­fer­ence pro­ced­ures, such as like­li­hood-­based vari­able im­port­ances, to be ap­plied in a straight­for­ward way. The pro­ced­ure al­lows gen­eral trans­form­a­tion mod­els to be es­tim­ated without the ne­ces­sity of a pri­ori spe­cify­ing the de­pend­ency struc­ture of para­met­ers. Ap­plic­a­tions in­clude the com­pu­ta­tion of prob­ab­il­istic fore­casts, mod­el­ling dif­fer­en­tial treat­ment ef­fects, or the de­riv­a­tion of coun­ter­fac­tural dis­tri­bu­tions for all types of re­sponse vari­ables.

Kindly note that on Oc­to­ber 12 two talks are sched­uled at our in­sti­tute:
9:00  Wal­ter Far­kas
10:30  Tor­sten Ho­thorn

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