Analogy-Based Preference Learning with Kernels Mohsen Ahmadi Fahandar - PowerPoint PPT Presentation

Analogy-Based Preference Learning with Kernels Mohsen Ahmadi Fahandar , Eyke Hüllermeier Intelligent Systems and Machine Learning Group Heinz Nixdorf Institute and Department of Computer Science Paderborn University KI 2019, Wednesday, September 25th

Our Contribution Generalized (fuzzy) Equivalence Relations Kernel-based Machine Learning Analogical Reasoning 2 Intelligent Systems and Machine Learning

Analogical Reasoning  Formalization of analogical reasoning based on the notion of analogical proportion (Miclet and Prade 2009; Prade and Richard 2017) : :: : (pictures from ImageNet) 3 Intelligent Systems and Machine Learning

Analogical Proportions   Domain-based instantiation  Mathematically, a predicate on four objects Formalizing the “as” part Satisfy the set of axioms   4 Intelligent Systems and Machine Learning

A nalogical Proport ions ( numerical case)  Generalization of Boolean case: the four objects are in analogy to some degree   Example o o o 5 Intelligent Systems and Machine Learning

Ext ension t o Feat ure Vect ors  Extension from individual attributes to feature vectors 6 Intelligent Systems and Machine Learning

Analogy and Kernels Key observation analogical proportion (by definition) defines a kind of similarity similarity measure Image from https://testinternetspeed.org/blog/internet-connection-speed/ 7 Intelligent Systems and Machine Learning

Bridging Concept   Hence capture the notion of similarity  o Reflexive o Symmetric o T-transitive 8 Intelligent Systems and Machine Learning

Connection Motivation: certain types of fuzzy equivalence relations satisfy the properties of a kernel function (Moser 2006) Kernel-based Machine Learning 9 Intelligent Systems and Machine Learning

Kernels   Symmetric  Positive semi-definite  kernel trick linearization 10 Intelligent Systems and Machine Learning

Analogical Proportions as Kernels: analogy-kernel   11 Intelligent Systems and Machine Learning

Kernel-preserving Operations  Extending the analogy-kernel from individual variables to feature vectors  To allow for incorporating a certain degree of non-linearity 12 Intelligent Systems and Machine Learning

An Application: Preference Learning Query Predicted Ranking Ground Truth Ranking (normalized) ranking loss: 13 Intelligent Systems and Machine Learning

Inference Pattern (Ahmadi Fahandar and Hüllermeier AAAI-2018)  Analogy assumption : :: : (pictures from ImageNet) + Known knowledge (presumably) 14 Intelligent Systems and Machine Learning

Analogy-Kernel-Based Object Ranking (AnKer-rank) 1. Pairwise preference: 2. Rank aggregation : This preference relation is turned into an overall consensus ranking 15 Intelligent Systems and Machine Learning

AnKer-rank: 1. Prediction of Pairwise Preferences    Predictions in the unit interval using Platt-scaling (Plat 1999)  16 Intelligent Systems and Machine Learning

AnKer-rank: 2. Rank Aggregation  Bradley-Terry-Luce (BTL) model (Bradley and Terry 1952)   Predicted ranking: sort objects in descending order of their estimated parameter Ahmadi Fahandar et al., Statistical Inference for Incomplete Ranking Data: The Case of Rank-Dependent Coarsening (ICML 2017) 17 Intelligent Systems and Machine Learning

Baselines  Nearest Neighbor-based principle  able2rank (Ahmadi Fahandar and Hüllermeier AAAI-2018)  Linear Regression-based principle  Expected Rank Regression ( ERR ) (Kamishima et al., 2010; Kamishima and Akaho 2006)  SVM-based principle  RankingSVM (Joachims 2002)  Neural Network-based principle  RankNet (Burges et al., 2005) 18 Intelligent Systems and Machine Learning

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Experimental Setup  AnKer-rank and able2rank : Rescaling of feature vectors to take values in the unit interval  ERR, RankingSVM and RankNet : Standard normalization  Hyper-parameters: fixed using (internal) 2-fold CV (repeated 3 times) 20 Intelligent Systems and Machine Learning

 Quite competitive in terms of predictive accuracy  On a par with able2rank and Ranking SVM  ERR and RankNet show worse performance 21 Intelligent Systems and Machine Learning

Summary and Future Work  Connecting kernel-based machine learning and analogical reasoning in the context of preference learning  Building on the observation that analogical proportions define a kind of similarity  Utilizing generalized (fuzzy) equivalence relations as a bridging concept  Introducing analogy-kernel  Advocating a concrete kernel-based method for object ranking  First experimental results on real-world data from various domains are quite promising  To study kernel properties of other analogical proportions (e.g., geometric) My homepage  To study other types of applications, whether in preference learning or beyond  To study the use of kernel-base methods other than SVM https://github.com/mahmadif/able2rank THANKS 22 Intelligent Systems and Machine Learning