arXiv subjects

Eyke Hüllermeier

Publications and source records attributed to Eyke Hüllermeier.

At least 145 records · Page 8Linked to original sources

arXiv2020

Towards Meta-Algorithm Selection

Instance-specific algorithm selection (AS) deals with the automatic selection of an algorithm from a fixed set of candidates most suitable for a specific instance of an algorithmic problem class, where "suitability" often refers to an algorithm's runtime. Over the past years, a plethora of algorithm selectors have been proposed. As an algorithm selector is again an algorithm solving a specific problem, the idea of algorithm selection could also be applied to AS algorithms, leading to a meta-AS approach: Given an instance, the goal is to select an algorithm selector, which is then used to select the actual algorithm for solving the problem instance. We elaborate on consequences of applying AS on a meta-level and identify possible problems. Empirically, we show that meta-algorithm-selection can indeed prove beneficial in some cases. In general, however, successful AS approaches have problems with solving the meta-level problem.

cs.LG↗

arXiv2020

A Flexible Class of Dependence-aware Multi-Label Loss Functions

Multi-label classification is the task of assigning a subset of labels to a given query instance. For evaluating such predictions, the set of predicted labels needs to be compared to the ground-truth label set associated with that instance, and various loss functions have been proposed for this purpose. In addition to assessing predictive accuracy, a key concern in this regard is to foster and to analyze a learner's ability to capture label dependencies. In this paper, we introduce a new class of loss functions for multi-label classification, which overcome disadvantages of commonly used losses such as Hamming and subset 0/1. To this end, we leverage the mathematical framework of non-additive measures and integrals. Roughly speaking, a non-additive measure allows for modeling the importance of correct predictions of label subsets (instead of single labels), and thereby their impact on the overall evaluation, in a flexible way - by giving full importance to single labels and the entire label set, respectively, Hamming and subset 0/1 are rather extreme in this regard. We present concrete instantiations of this class, which comprise Hamming and subset 0/1 as special cases, and which appear to be especially appealing from a modeling perspective. The assessment of multi-label classifiers in terms of these losses is illustrated in an empirical study.

cs.LG↗

arXiv2020

Extreme Algorithm Selection With Dyadic Feature Representation

Algorithm selection (AS) deals with selecting an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem, e.g., choosing solvers for SAT problems. Benchmark suites for AS usually comprise candidate sets consisting of at most tens of algorithms, whereas in combined algorithm selection and hyperparameter optimization problems the number of candidates becomes intractable, impeding to learn effective meta-models and thus requiring costly online performance evaluations. Therefore, here we propose the setting of extreme algorithm selection (XAS) where we consider fixed sets of thousands of candidate algorithms, facilitating meta learning. We assess the applicability of state-of-the-art AS techniques to the XAS setting and propose approaches leveraging a dyadic feature representation in which both problem instances and algorithms are described. We find the latter to improve significantly over the current state of the art in various metrics.

cs.LG↗

arXiv2020

A Novel Higher-order Weisfeiler-Lehman Graph Convolution

Current GNN architectures use a vertex neighborhood aggregation scheme, which limits their discriminative power to that of the 1-dimensional Weisfeiler-Lehman (WL) graph isomorphism test. Here, we propose a novel graph convolution operator that is based on the 2-dimensional WL test. We formally show that the resulting 2-WL-GNN architecture is more discriminative than existing GNN approaches. This theoretical result is complemented by experimental studies using synthetic and real data. On multiple common graph classification benchmarks, we demonstrate that the proposed model is competitive with state-of-the-art graph kernels and GNNs.

cs.LG↗

arXiv2020

Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods

The notion of uncertainty is of major importance in machine learning and constitutes a key element of machine learning methodology. In line with the statistical tradition, uncertainty has long been perceived as almost synonymous with standard probability and probabilistic predictions. Yet, due to the steadily increasing relevance of machine learning for practical applications and related issues such as safety requirements, new problems and challenges have recently been identified by machine learning scholars, and these problems may call for new methodological developments. In particular, this includes the importance of distinguishing between (at least) two different types of uncertainty, often referred to as aleatoric and epistemic. In this paper, we provide an introduction to the topic of uncertainty in machine learning as well as an overview of attempts so far at handling uncertainty in general and formalizing this distinction in particular.

cs.LG↗

arXiv2020

Conformal Rule-Based Multi-label Classification

We advocate the use of conformal prediction (CP) to enhance rule-based multi-label classification (MLC). In particular, we highlight the mutual benefit of CP and rule learning: Rules have the ability to provide natural (non-)conformity scores, which are required by CP, while CP suggests a way to calibrate the assessment of candidate rules, thereby supporting better predictions and more elaborate decision making. We illustrate the potential usefulness of calibrated conformity scores in a case study on lazy multi-label rule learning.

cs.LG↗

arXiv2020

Learning Choice Functions via Pareto-Embeddings

We consider the problem of learning to choose from a given set of objects, where each object is represented by a feature vector. Traditional approaches in choice modelling are mainly based on learning a latent, real-valued utility function, thereby inducing a linear order on choice alternatives. While this approach is suitable for discrete (top-1) choices, it is not straightforward how to use it for subset choices. Instead of mapping choice alternatives to the real number line, we propose to embed them into a higher-dimensional utility space, in which we identify choice sets with Pareto-optimal points. To this end, we propose a learning algorithm that minimizes a differentiable loss function suitable for this task. We demonstrate the feasibility of learning a Pareto-embedding on a suite of benchmark datasets.

cs.LG↗

arXiv2020

Run2Survive: A Decision-theoretic Approach to Algorithm Selection based on Survival Analysis

Algorithm selection (AS) deals with the automatic selection of an algorithm from a fixed set of candidate algorithms most suitable for a specific instance of an algorithmic problem class, where "suitability" often refers to an algorithm's runtime. Due to possibly extremely long runtimes of candidate algorithms, training data for algorithm selection models is usually generated under time constraints in the sense that not all algorithms are run to completion on all instances. Thus, training data usually comprises censored information, as the true runtime of algorithms timed out remains unknown. However, many standard AS approaches are not able to handle such information in a proper way. On the other side, survival analysis (SA) naturally supports censored data and offers appropriate ways to use such data for learning distributional models of algorithm runtime, as we demonstrate in this work. We leverage such models as a basis of a sophisticated decision-theoretic approach to algorithm selection, which we dub Run2Survive. Moreover, taking advantage of a framework of this kind, we advocate a risk-averse approach to algorithm selection, in which the avoidance of a timeout is given high priority. In an extensive experimental study with the standard benchmark ASlib, our approach is shown to be highly competitive and in many cases even superior to state-of-the-art AS approaches.

cs.LG↗

arXiv2020

Machine Learning with the Sugeno Integral: The Case of Binary Classification

In this paper, we elaborate on the use of the Sugeno integral in the context of machine learning. More specifically, we propose a method for binary classification, in which the Sugeno integral is used as an aggregation function that combines several local evaluations of an instance, pertaining to different features or measurements, into a single global evaluation. Due to the specific nature of the Sugeno integral, this approach is especially suitable for learning from ordinal data, that is, when measurements are taken from ordinal scales. This is a topic that has not received much attention in machine learning so far. The core of the learning problem itself consists of identifying the capacity underlying the Sugeno integral. To tackle this problem, we develop an algorithm based on linear programming. The algorithm also includes a suitable technique for transforming the original feature values into local evaluations (local utility scores), as well as a method for tuning a threshold on the global evaluation. To control the flexibility of the classifier and mitigate the problem of overfitting the training data, we generalize our approach toward $k$-maxitive capacities, where $k$ plays the role of a hyper-parameter of the learner. We present experimental studies, in which we compare our method with competing approaches on several benchmark data sets.

cs.LG↗

arXiv2020

Learning Gradient Boosted Multi-label Classification Rules

In multi-label classification, where the evaluation of predictions is less straightforward than in single-label classification, various meaningful, though different, loss functions have been proposed. Ideally, the learning algorithm should be customizable towards a specific choice of the performance measure. Modern implementations of boosting, most prominently gradient boosted decision trees, appear to be appealing from this point of view. However, they are mostly limited to single-label classification, and hence not amenable to multi-label losses unless these are label-wise decomposable. In this work, we develop a generalization of the gradient boosting framework to multi-output problems and propose an algorithm for learning multi-label classification rules that is able to minimize decomposable as well as non-decomposable loss functions. Using the well-known Hamming loss and subset 0/1 loss as representatives, we analyze the abilities and limitations of our approach on synthetic data and evaluate its predictive performance on multi-label benchmarks.

cs.LG↗

arXiv2020

On Aggregation in Ensembles of Multilabel Classifiers

While a variety of ensemble methods for multilabel classification have been proposed in the literature, the question of how to aggregate the predictions of the individual members of the ensemble has received little attention so far. In this paper, we introduce a formal framework of ensemble multilabel classification, in which we distinguish two principal approaches: "predict then combine" (PTC), where the ensemble members first make loss minimizing predictions which are subsequently combined, and "combine then predict" (CTP), which first aggregates information such as marginal label probabilities from the individual ensemble members, and then derives a prediction from this aggregation. While both approaches generalize voting techniques commonly used for multilabel ensembles, they allow to explicitly take the target performance measure into account. Therefore, concrete instantiations of CTP and PTC can be tailored to concrete loss functions. Experimentally, we show that standard voting techniques are indeed outperformed by suitable instantiations of CTP and PTC, and provide some evidence that CTP performs well for decomposable loss functions, whereas PTC is the better choice for non-decomposable losses.

cs.LG↗

arXiv2020

Efficient Set-Valued Prediction in Multi-Class Classification

In cases of uncertainty, a multi-class classifier preferably returns a set of candidate classes instead of predicting a single class label with little guarantee. More precisely, the classifier should strive for an optimal balance between the correctness (the true class is among the candidates) and the precision (the candidates are not too many) of its prediction. We formalize this problem within a general decision-theoretic framework that unifies most of the existing work in this area. In this framework, uncertainty is quantified in terms of conditional class probabilities, and the quality of a predicted set is measured in terms of a utility function. We then address the problem of finding the Bayes-optimal prediction, i.e., the subset of class labels with highest expected utility. For this problem, which is computationally challenging as there are exponentially (in the number of classes) many predictions to choose from, we propose efficient algorithms that can be applied to a broad family of utility functions. Our theoretical results are complemented by experimental studies, in which we analyze the proposed algorithms in terms of predictive accuracy and runtime efficiency.

cs.LG↗

arXiv2020

Learning Tversky Similarity

In this paper, we advocate Tversky's ratio model as an appropriate basis for computational approaches to semantic similarity, that is, the comparison of objects such as images in a semantically meaningful way. We consider the problem of learning Tversky similarity measures from suitable training data indicating whether two objects tend to be similar or dissimilar. Experimentally, we evaluate our approach to similarity learning on two image datasets, showing that is performs very well compared to existing methods.

cs.CV↗

arXiv2020

Towards Analogy-Based Explanations in Machine Learning

Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is certainly useful for constructing new learning algorithms with high predictive accuracy, is is arguably not less interesting from an interpretability and explainability point of view. More specifically, we take the view that an analogy-based approach is a viable alternative to existing approaches in the realm of explainable AI and interpretable machine learning, and that analogy-based explanations of the predictions produced by a machine learning algorithm can complement similarity-based explanations in a meaningful way. To corroborate these claims, we outline the basic idea of an analogy-based explanation and illustrate its potential usefulness by means of some examples.

cs.LG↗

arXiv2020

Towards a Scalable and Flexible Simulation and Testing Environment Toolbox for Intelligent Microgrid Control

Micro- and smart grids (MSG) play an important role both for integrating renewable energy sources in conventional electricity grids and for providing power supply in remote areas. Modern MSGs are largely driven by power electronic converters due to their high efficiency and flexibility. Nevertheless, controlling MSGs is a challenging task due to highest requirements on energy availability, safety and voltage quality within a wide range of different MSG topologies. This results in a high demand for comprehensive testing of new control concepts during their development phase and comparisons with the state of the art in order to ensure their feasibility. This applies in particular to data-driven control approaches from the field of reinforcement learning (RL), whose stability and operating behavior can hardly be evaluated a priori. Therefore, the OpenModelica Microgrid Gym (OMG) package, an open-source software toolbox for the simulation and control optimization of MSGs, is proposed. It is capable of modeling and simulating arbitrary MSG topologies and offers a Python-based interface for plug \& play controller testing. In particular, the standardized OpenAI Gym interface allows for easy RL-based controller integration. Besides the presentation of the OMG toolbox, application examples are highlighted including safe Bayesian optimization for low-level controller tuning.

eess.SY↗

arXiv2020

Online Preselection with Context Information under the Plackett-Luce Model

We consider an extension of the contextual multi-armed bandit problem, in which, instead of selecting a single alternative (arm), a learner is supposed to make a preselection in the form of a subset of alternatives. More specifically, in each iteration, the learner is presented a set of arms and a context, both described in terms of feature vectors. The task of the learner is to preselect $k$ of these arms, among which a final choice is made in a second step. In our setup, we assume that each arm has a latent (context-dependent) utility, and that feedback on a preselection is produced according to a Plackett-Luce model. We propose the CPPL algorithm, which is inspired by the well-known UCB algorithm, and evaluate this algorithm on synthetic and real data. In particular, we consider an online algorithm selection scenario, which served as a main motivation of our problem setting. Here, an instance (which defines the context) from a certain problem class (such as SAT) can be solved by different algorithms (the arms), but only $k$ of these algorithms can actually be run.

cs.LG↗

arXiv2020

Reliable Multi-label Classification: Prediction with Partial Abstention

In contrast to conventional (single-label) classification, the setting of multilabel classification (MLC) allows an instance to belong to several classes simultaneously. Thus, instead of selecting a single class label, predictions take the form of a subset of all labels. In this paper, we study an extension of the setting of MLC, in which the learner is allowed to partially abstain from a prediction, that is, to deliver predictions on some but not necessarily all class labels. We propose a formalization of MLC with abstention in terms of a generalized loss minimization problem and present first results for the case of the Hamming loss, rank loss, and F-measure, both theoretical and experimental.

cs.LG↗

arXiv2020

Aleatoric and Epistemic Uncertainty with Random Forests

Due to the steadily increasing relevance of machine learning for practical applications, many of which are coming with safety requirements, the notion of uncertainty has received increasing attention in machine learning research in the last couple of years. In particular, the idea of distinguishing between two important types of uncertainty, often refereed to as aleatoric and epistemic, has recently been studied in the setting of supervised learning. In this paper, we propose to quantify these uncertainties with random forests. More specifically, we show how two general approaches for measuring the learner's aleatoric and epistemic uncertainty in a prediction can be instantiated with decision trees and random forests as learning algorithms in a classification setting. In this regard, we also compare random forests with deep neural networks, which have been used for a similar purpose.

cs.LG↗