Research

Research Interests

• Relational Data Analysis (especially in connection with Formal Concept Analysis and the application of Vapnik-Chervonenkis theory in discrete settings)
• Stochastic Partial Ordering
• Inference with Deficient Data
• Partial Identification
• Theories of Imprecise Probabilities
• Decision Theory under imprecise probabilities and non-cardinal utility

Publications

Work in Progress

 

Papers

• Risk Aversion over Finite Domains (together with Jean Baccelli and Christoph Jansen)
• Schollmeyer, G. (2019): A Short Note on the Equivalence of the Ontic and the Epistemic View on Data Imprecision for the Case of Stochastic Dominance for Interval-Valued Data. In: De Bock, J.; de Campos, C.; de Cooman, G.; Quaeghebeur, E.; Wheeler, G. (eds): Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in PMLR, Volume 103 of Proceedings of Machine Learning Research, pages 330-337
• Fuetterer, C.; Schollmeyer, G.; Augustin, T. (2019): Constructing Simulation Data with Dependency Structure for Unreliable Single-Cell RNA-Sequencing Data Using Copulas. In: De Bock, J.; de Campos, C.; de Cooman, G.; Quaeghebeur, E.; Wheeler, G. (eds): Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, in PMLR, Volume 103 of Proceedings of Machine Learning Research, pages 216-224
• Jansen, C.; Schollmeyer, G.; Augustin, T. (2018): Concepts for decision making under severe uncertainty with partial ordinal and partial cardinal preferences. International Journal of Approximate Reasoning, 98: 112–131.
• Jansen, C.; Schollmeyer, G.; Augustin, T. (2018): A probabilistic evaluation framework for preference aggregation reflecting group homogeneity. Mathematical Social Sciences, 96: 49-62.
• Jansen, C.; Schollmeyer, G.; Augustin, T. (2017): Quantifying degrees of E-admissibility in decision making with imprecise probabilities. To appear in: Theory and Decision Library A, Springer.
• Jansen, C.; Schollmeyer, G.; Augustin, T. (2017): Concepts for decision making under severe uncertainty with partial ordinal and partial cardinal preferences. In: Antonucci, A.; Corani, G.; Couso, I.; Destercke, S. (eds): Proceedings of the Tenth International Symposium on Imprecise Probability: Theories and Applications, Volume 62 of Proceedings of Machine Learning Research, pages 253–264, PMLR.
• Jansen, C.; Augustin, T.; Schollmeyer, G. (2017): Decision theory meets linear optimization beyond computation. In: Antonucci, A.; Cholvy, L.; Papini, O. (eds): Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2017. Lecture Notes in Computer Science, vol 10369. Springer.
• Plass, J., Cattaneo, M., Schollmeyer, G., Augustin, T. (2017): On the testability of coarsening assumptions: A hypothesis test for subgroup independence. International Journal of Approximate Reasoning, 90:292-306.
• Plass, J., Cattaneo, M., Schollmeyer, G., Augustin, T. (2016): Testing of coarsening mechanisms: Coarsening at random versus subgroup independence. In Maria Brigida Ferraro, Paolo Giordani, Barbara Vantaggi, Marek Gagolewski, Maria Angeles Gil, Przemyslaw Grzegorzewski, Olgierd Hryniewicz, editors, Advances in Intelligent Systems and Computing, pages 415 to 422. SMPS, 2016.
• Schollmeyer, G. (2015): On the Number and Characterization of the Extreme Points of the Core of Necessity Measures on Finite Spaces ISIPTA '15, Proceedings of the Ninth International Symposium on Imprecise Probability: Theories and Applications
• Plass, J. and Augustin, T. and Cattaneo, M. and Schollmeyer, G. (2015): Statistical modelling under epistemic data imprecision: Some results on estimating multinomial distributions and logistic regression for coarse categorical data. In Thomas Augustin, Serena Doria, Enrique Miranda, and Erik Quaeghebeur, editors, ISIPTA '15, Proceedings of the Ninth International Symposium on Imprecise Probability: Theories and Applications, pages 247 to 256. SIPTA.
• Schollmeyer, G., Augustin, T. (2015): Statistical modeling under partial identification: Distinguishing three types of identification regions in regression analysis with interval dataInternational Journal of Approximate Reasoning, 56: 224-248.
• Schollmeyer, G., Augustin, T. (2013): On Sharp Identification Regions for Regression Under Interval Data. (with Thomas Augustin) ISIPTA '13, Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications

Reports

• Schollmeyer, G., Jansen, C., Augustin, T. (2017): A simple descriptive method for multidimensional item response theory based on stochastic dominance Technical Report 210, Department of Statistics, LMU Munich.
• Schollmeyer, G., Jansen, C., Augustin, T. (2017): Detecting stochastic dominance for poset-valued random variables as an example of linear programming on closure systems.Technical Report 209, Department of Statistics, LMU Munich.
• Schollmeyer, G., Jansen, C., Augustin, T. (2017): Application of lower quantiles for complete lattices to ranking data: Analyzing outlyingness of preference orderings.Technical Report 208, Department of Statistics, LMU Munich.
• Schollmeyer, G. (2017): Lower Quantiles for Complete Lattices.Technical Report 207, Department of Statistics, LMU Munich.
• Jansen, C., Schollmeyer,G., Augustin, T. (2016): Probabilistic Evaluation of Preference Aggregation Functions: A Statistical Approach in Social Choice Theory. Department of Statistics: Technical Reports, No. 193
• Schollmeyer, G., Augustin, T. (2013): On Sharp Identification Regions for Regression Under Interval Data Technical Report 143, Department of Statistics, LMU Munich.

Theses

• Dissertation: "Reliable statistical modeling of weakly structured information: contributions to partial identification, stochastic partial ordering and imprecise probabilities"
• Diploma Thesis: "Modellierung unsicheren Wissens durch kohärente Prävisionen"

Presentations

• Relational data analysis for weakly structured information: Utilizing linear and binary programming for computing supremum statistics on closure systems ECDA 2018
• Classification with stylized betweenness-relations allowing for regularization with uniform Vapnik-Chervonenkis-guarantees, DAGStat 2019.
• Decision making under severe uncertainty with partial ordinal and partial cardinal preferences, ISIPTA 2017
• Quantile constructions for complete lattices, DAGStat 2016.
• Simple multivariate Kolmogorov-Smirnov type tests based on lattice-valued quantiles, 12th German Probability and Statistics Days 2016.
• Partial identification in linear models: Regression with interval-valued data, CM Statistics (ERCIM 2015), London, 12-14 December 2015.
• On the Number and Characterization of the Extreme Points of the Core of Necessity Measures on Finite Spaces, Pescara, Italy, 23 July 2015.
• Conceptual Issues in the Analysis of Interval Data - Different Concepts of Identification Regions. Statistische Woche, Hannover, Germany, 17 September 2014.
• Utilizing Support Functions and Monotone Location Estimators for the Estimation of Partially Identified Regression Models. LMU Munich, München, Germany, 05 May 2014.
• Quantiles for Complete Lattices LMU Munich, München, Germany, 18 November 2013.
• On Sharp Identification Regions for Regression under Interval DataISIPTA '13, Compiègne, France, 2 July 2013.
• A Note On Sharp Identification RegionsLMU Munich, München, Germany, 28 January 2012.
• Recent Developments in the Statistical Analysis of Interval Data — The case of regression (with T. Augustin, M.E.G.V.  Cattaneo, U. Pötter, G. and A. Wiencierz). Applied Statistics 2012, Ribno, Slovenia, 23 September 2012.
• Evaluation and Comparison of Set-valued Estimators: Empirical and Structural AspectsWPMSIIP 2012, München, Germany, 12 September 2012.
• Linear Models and Partial Identification: Imprecise Linear Regression With Interval Data WPMSIIP 2012, München, Germany, 11 September 2012.
• Linear models and partial identification LMU Munich, München, Germany, 27 June 2012.
• Necessity-measures and their Möbius inverses in the framework of generalized coherent previsions
• LMU Munich, München, Germany, 12 January 2012.