Research Seminar Series in Statistics and Mathematics

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

Art Vortrag/Diskussion
Vortragende/rTorsten Hothorn (Epidemiology, Biostatistics and Prevention Institute, University of Zurich)
Veranstalter Institut für Statistik und Mathematik
Kontakt katrin.artner@wu.ac.at

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://www.wu.ac.at/en/stat­math/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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