Hendrik Blockeel

Kshitij Goyal, Sebastijan Dumancic, Hendrik Blockeel

As machine learning models, specifically neural networks, are becoming increasingly popular, there are concerns regarding their trustworthiness, specially in safety-critical applications, e.g. actions of an autonomous vehicle must be safe. There are approaches that can train neural networks where such domain requirements are enforced as constraints, but they either cannot guarantee that the constraint will be satisfied by all possible predictions (even on unseen data) or they are limited in the type of constraints that can be enforced. In this paper, we present an approach to train neural networks which can enforce a wide variety of constraints and guarantee that the constraint is satisfied by all possible predictions. The approach builds on earlier work where learning linear models is formulated as a constraint satisfaction problem (CSP). To make this idea applicable to neural networks, two crucial new elements are added: constraint propagation over the network layers, and weight updates based on a mix of gradient descent and CSP solving. Evaluation on various machine learning tasks demonstrates that our approach is flexible enough to enforce a wide variety of domain constraints and is able to guarantee them in neural networks.

Mariette Schönfeld, Laurens Devos, Wannes Meert et al.

Transfer learning makes it possible to use large vision networks on a variety of domains, by specializing their models' general filters to new tasks. However, these networks assume the input images to have 3 input channels, making them incompatible with multi- or hyperspectral images. Current approaches that mitigate this incompatibility sacrifice information in either the image, or the model. This work proposes a novel approach that preserves the image and spatial information present in the model by using partially trainable tensor decompositions. We create such decompositions of pretrained convolutional filters, separating the filters into spatial and spectral components. The spectral components are then replaced with trainable components of higher channel dimensionality. This creates hyperspectral filters that can specialize to new datasets, while retaining the spatial patterns of the original filter. Experiments on a variety of hyperspectral datasets show that our approach is more accurate and robust than other hyperspectral transfer learning methods.

Daan Van Wesenbeeck, Aras Yurtman, Wannes Meert et al.

Time Series Motif Discovery (TSMD) refers to the task of identifying patterns that occur multiple times (possibly with minor variations) in a time series. All existing methods for TSMD have one or more of the following limitations: they only look for the two most similar occurrences of a pattern; they only look for patterns of a pre-specified, fixed length; they cannot handle variability along the time axis; and they only handle univariate time series. In this paper, we present a new method, LoCoMotif, that has none of these limitations. The method is motivated by a concrete use case from physiotherapy. We demonstrate the value of the proposed method on this use case. We also introduce a new quantitative evaluation metric for motif discovery, and benchmark data for comparing TSMD methods. LoCoMotif substantially outperforms the existing methods, on top of being more broadly applicable.

Kshitij Goyal, Wannes Meert, Hendrik Blockeel et al.

Internet based businesses and products (e.g. e-commerce, music streaming) are becoming more and more sophisticated every day with a lot of focus on improving customer satisfaction. A core way they achieve this is by providing customers with an easy access to their products by structuring them in catalogues using navigation bars and providing recommendations. We refer to these catalogues as product concepts, e.g. product categories on e-commerce websites, public playlists on music streaming platforms. These product concepts typically contain products that are linked with each other through some common features (e.g. a playlist of songs by the same artist). How they are defined in the backend of the system can be different for different products. In this work, we represent product concepts using database queries and tackle two learning problems. First, given sets of products that all belong to the same unknown product concept, we learn a database query that is a representation of this product concept. Second, we learn product concepts and their corresponding queries when the given sets of products are associated with multiple product concepts. To achieve these goals, we propose two approaches that combine the concepts of PU learning with Decision Trees and Clustering. Our experiments demonstrate, via a simulated setup for a music streaming service, that our approach is effective in solving these problems.

Florian Busch, Moritz Kulessa, Eneldo Loza Mencía et al.

A common approach to aggregate classification estimates in an ensemble of decision trees is to either use voting or to average the probabilities for each class. The latter takes uncertainty into account, but not the reliability of the uncertainty estimates (so to say, the "uncertainty about the uncertainty"). More generally, much remains unknown about how to best combine probabilistic estimates from multiple sources. In this paper, we investigate a number of alternative prediction methods. Our methods are inspired by the theories of probability, belief functions and reliable classification, as well as a principle that we call evidence accumulation. Our experiments on a variety of data sets are based on random decision trees which guarantees a high diversity in the predictions to be combined. Somewhat unexpectedly, we found that taking the average over the probabilities is actually hard to beat. However, evidence accumulation showed consistently better results on all but very small leafs.

Mariette Schönfeld, Wannes Meert, Hendrik Blockeel

Industrial Anomaly Detection (IAD) is a subproblem within Computer Vision Anomaly Detection that has been receiving increasing amounts of attention due to its applicability to real-life scenarios. Recent research has focused on how to extract the most informative features, contrasting older kNN-based methods that use only pretrained features. These recent methods are much more expensive to train however and could complicate real-life application. Careful study of related work with regards to transformation invariance leads to the idea that popular benchmarks require robustness to only minor translations. With this idea we then formulate LWinNN, a local window based approach that creates a middle ground between kNN based methods that have either complete or no translation invariance. Our experiments demonstrate that this small change increases accuracy considerably, while simultaneously decreasing both train and test time. This teaches us two things: first, the gap between kNN-based approaches and more complex state-of-the-art methodology can still be narrowed by effective usage of the limited data available. Second, our assumption of requiring only limited translation invariance highlights potential areas of interest for future work and the need for more spatially diverse benchmarks, for which our method can hopefully serve as a new baseline. Our code can be found at https://github.com/marietteschonfeld/LWinNN .

Daan Van Wesenbeeck, Aras Yurtman, Wannes Meert et al.

Time Series Motif Discovery (TSMD), which aims at finding recurring patterns in time series, is an important task in numerous application domains, and many methods for this task exist. These methods are usually evaluated qualitatively. A few metrics for quantitative evaluation, where discovered motifs are compared to some ground truth, have been proposed, but they typically make implicit assumptions that limit their applicability. This paper introduces PROM, a broadly applicable metric that overcomes those limitations, and TSMD-Bench, a benchmark for quantitative evaluation of time series motif discovery. Experiments with PROM and TSMD-Bench show that PROM provides a more comprehensive evaluation than existing metrics, that TSMD-Bench is a more challenging benchmark than earlier ones, and that the combination can help understand the relative performance of TSMD methods. More generally, the proposed approach enables large-scale, systematic performance comparisons in this field.

Simiao Lin, Wannes Meert, Pieter Robberechts et al.

Comparing time series is essential in various tasks such as clustering and classification. While elastic distance measures that allow warping provide a robust quantitative comparison, a qualitative comparison on top of them is missing. Traditional visualizations focus on point-to-point alignment and do not convey the broader structural relationships at the level of subsequences. This limitation makes it difficult to understand how and where one time series shifts, speeds up or slows down with respect to another. To address this, we propose a novel technique that simplifies the warping path to highlight, quantify and visualize key transformations (shift, compression, difference in amplitude). By offering a clearer representation of how subsequences match between time series, our method enhances interpretability in time series comparison.

Aras Yurtman, Daan Van Wesenbeeck, Wannes Meert et al.

Time Series Motif Discovery (TSMD) identifies repeating patterns in time series data, but its unsupervised nature might result in motifs that are not interesting to the user. To address this, we propose a framework that allows the user to impose constraints on the motifs to be discovered, where constraints can easily be defined according to the properties of the desired motifs in the application domain. We also propose an efficient implementation of the framework, the LoCoMotif-DoK algorithm. We demonstrate that LoCoMotif-DoK can effectively leverage domain knowledge in real and synthetic data, outperforming other TSMD techniques which only support a limited form of domain knowledge.

Jonas Soenen, Elia Van Wolputte, Vincent Vercruyssen et al.

Most anomaly detection systems try to model normal behavior and assume anomalies deviate from it in diverse manners. However, there may be patterns in the anomalies as well. Ideally, an anomaly detection system can exploit patterns in both normal and anomalous behavior. In this paper, we present AD-MERCS, an unsupervised approach to anomaly detection that explicitly aims at doing both. AD-MERCS identifies multiple subspaces of the instance space within which patterns exist, and identifies conditions (possibly in other subspaces) that characterize instances that deviate from these patterns. Experiments show that this modeling of both normality and abnormality makes the anomaly detector performant on a wide range of types of anomalies. Moreover, by identifying patterns and conditions in (low-dimensional) subspaces, the anomaly detector can provide simple explanations of why something is considered an anomaly. These explanations can be both negative (deviation from some pattern) as positive (meeting some condition that is typical for anomalies).

Kshitij Goyal, Sebastijan Dumancic, Hendrik Blockeel

In many real world applications of machine learning, models have to meet certain domain-based requirements that can be expressed as constraints (e.g., safety-critical constraints in autonomous driving systems). Such constraints are often handled by including them in a regularization term, while learning a model. This approach, however, does not guarantee 100% satisfaction of the constraints: it only reduces violations of the constraints on the training set rather than ensuring that the predictions by the model will always adhere to them. In this paper, we present a framework for learning models that provably fulfil the constraints under all circumstances (i.e., also on unseen data). To achieve this, we cast learning as a maximum satisfiability problem, and solve it using a novel SaDe algorithm that combines constraint satisfaction with gradient descent. We compare our method against regularization based baselines on linear models and show that our method is capable of enforcing different types of domain constraints effectively on unseen data, without sacrificing predictive performance.

Kshitij Goyal, Sebastijan Dumancic, Hendrik Blockeel

In this paper, we investigate how feature interactions can be identified to be used as constraints in the gradient boosting tree models using XGBoost's implementation. Our results show that accurate identification of these constraints can help improve the performance of baseline XGBoost model significantly. Further, the improvement in the model structure can also lead to better interpretability.

Jonas Schouterden, Jesse Davis, Hendrik Blockeel

Propositionalization is the process of summarizing relational data into a tabular (attribute-value) format. The resulting table can next be used by any propositional learner. This approach makes it possible to apply a wide variety of learning methods to relational data. However, the transformation from relational to propositional format is generally not lossless: different relational structures may be mapped onto the same feature vector. At the same time, features may be introduced that are not needed for the learning task at hand. In general, it is hard to define a feature space that contains all and only those features that are needed for the learning task. This paper presents LazyBum, a system that can be considered a lazy version of the recently proposed OneBM method for propositionalization. LazyBum interleaves OneBM's feature construction method with a decision tree learner. This learner both uses and guides the propositionalization process. It indicates when and where to look for new features. This approach is similar to what has elsewhere been called dynamic propositionalization. In an experimental comparison with the original OneBM and with two other recently proposed propositionalization methods (nFOIL and MODL, which respectively perform dynamic and static propositionalization), LazyBum achieves a comparable accuracy with a lower execution time on most of the datasets.

Sebastijan Dumancic, Tias Guns, Wannes Meert et al.

Deep learning methods capable of handling relational data have proliferated over the last years. In contrast to traditional relational learning methods that leverage first-order logic for representing such data, these deep learning methods aim at re-representing symbolic relational data in Euclidean spaces. They offer better scalability, but can only numerically approximate relational structures and are less flexible in terms of reasoning tasks supported. This paper introduces a novel framework for relational representation learning that combines the best of both worlds. This framework, inspired by the auto-encoding principle, uses first-order logic as a data representation language, and the mapping between the original and latent representation is done by means of logic programs instead of neural networks. We show how learning can be cast as a constraint optimisation problem for which existing solvers can be used. The use of logic as a representation language makes the proposed framework more accurate (as the representation is exact, rather than approximate), more flexible, and more interpretable than deep learning methods. We experimentally show that these latent representations are indeed beneficial in relational learning tasks.

Toon Van Craenendonck, Wannes Meert, Sebastijan Dumancic et al.

Clustering is ubiquitous in data analysis, including analysis of time series. It is inherently subjective: different users may prefer different clusterings for a particular dataset. Semi-supervised clustering addresses this by allowing the user to provide examples of instances that should (not) be in the same cluster. This paper studies semi-supervised clustering in the context of time series. We show that COBRAS, a state-of-the-art semi-supervised clustering method, can be adapted to this setting. We refer to this approach as COBRAS-TS. An extensive experimental evaluation supports the following claims: (1) COBRAS-TS far outperforms the current state of the art in semi-supervised clustering for time series, and thus presents a new baseline for the field; (2) COBRAS-TS can identify clusters with separated components; (3) COBRAS-TS can identify clusters that are characterized by small local patterns; (4) a small amount of semi-supervision can greatly improve clustering quality for time series; (5) the choice of the clustering algorithm matters (contrary to earlier claims in the literature).

Toon Van Craenendonck, Sebastijan Dumančić, Elia Van Wolputte et al.

Constraint-based clustering algorithms exploit background knowledge to construct clusterings that are aligned with the interests of a particular user. This background knowledge is often obtained by allowing the clustering system to pose pairwise queries to the user: should these two elements be in the same cluster or not? Active clustering methods aim to minimize the number of queries needed to obtain a good clustering by querying the most informative pairs first. Ideally, a user should be able to answer a couple of these queries, inspect the resulting clustering, and repeat these two steps until a satisfactory result is obtained. We present COBRAS, an approach to active clustering with pairwise constraints that is suited for such an interactive clustering process. A core concept in COBRAS is that of a super-instance: a local region in the data in which all instances are assumed to belong to the same cluster. COBRAS constructs such super-instances in a top-down manner to produce high-quality results early on in the clustering process, and keeps refining these super-instances as more pairwise queries are given to get more detailed clusterings later on. We experimentally demonstrate that COBRAS produces good clusterings at fast run times, making it an excellent candidate for the iterative clustering scenario outlined above.

Toon Van Craenendonck, Sebastijan Dumancic, Hendrik Blockeel

Clustering is inherently ill-posed: there often exist multiple valid clusterings of a single dataset, and without any additional information a clustering system has no way of knowing which clustering it should produce. This motivates the use of constraints in clustering, as they allow users to communicate their interests to the clustering system. Active constraint-based clustering algorithms select the most useful constraints to query, aiming to produce a good clustering using as few constraints as possible. We propose COBRA, an active method that first over-clusters the data by running K-means with a $K$ that is intended to be too large, and subsequently merges the resulting small clusters into larger ones based on pairwise constraints. In its merging step, COBRA is able to keep the number of pairwise queries low by maximally exploiting constraint transitivity and entailment. We experimentally show that COBRA outperforms the state of the art in terms of clustering quality and runtime, without requiring the number of clusters in advance.

Sebastijan Dumančić, Hendrik Blockeel

Latent features learned by deep learning approaches have proven to be a powerful tool for machine learning. They serve as a data abstraction that makes learning easier by capturing regularities in data explicitly. Their benefits motivated their adaptation to relational learning context. In our previous work, we introduce an approach that learns relational latent features by means of clustering instances and their relations. The major drawback of latent representations is that they are often black-box and difficult to interpret. This work addresses these issues and shows that (1) latent features created by clustering are interpretable and capture interesting properties of data; (2) they identify local regions of instances that match well with the label, which partially explains their benefit; and (3) although the number of latent features generated by this approach is large, often many of them are highly redundant and can be removed without hurting performance much.

Toon Van Craenendonck, Hendrik Blockeel

Semi-supervised clustering methods incorporate a limited amount of supervision into the clustering process. Typically, this supervision is provided by the user in the form of pairwise constraints. Existing methods use such constraints in one of the following ways: they adapt their clustering procedure, their similarity metric, or both. All of these approaches operate within the scope of individual clustering algorithms. In contrast, we propose to use constraints to choose between clusterings generated by very different unsupervised clustering algorithms, run with different parameter settings. We empirically show that this simple approach often outperforms existing semi-supervised clustering methods.

Sebastijan Dumancic, Wannes Meert, Hendrik Blockeel

With this positional paper we present a representation learning view on predicate invention. The intention of this proposal is to bridge the relational and deep learning communities on the problem of predicate invention. We propose a theory reconstruction approach, a formalism that extends autoencoder approach to representation learning to the relational settings. Our intention is to start a discussion to define a unifying framework for predicate invention and theory revision.

Sebastijan Dumancic, Hendrik Blockeel

The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational data, which additionally describe relationships among instances. In this work we introduce an approach for relational unsupervised representation learning. Viewing a relational dataset as a hypergraph, new features are obtained by clustering vertices and hyperedges. To find a representation suited for many relational learning tasks, a wide range of similarities between relational objects is considered, e.g. feature and structural similarities. We experimentally evaluate the proposed approach and show that models learned on such latent representations perform better, have lower complexity, and outperform the existing approaches on classification tasks.

Sebastijan Dumancic, Hendrik Blockeel

Clustering is an underspecified task: there are no universal criteria for what makes a good clustering. This is especially true for relational data, where similarity can be based on the features of individuals, the relationships between them, or a mix of both. Existing methods for relational clustering have strong and often implicit biases in this respect. In this paper, we introduce a novel similarity measure for relational data. It is the first measure to incorporate a wide variety of types of similarity, including similarity of attributes, similarity of relational context, and proximity in a hypergraph. We experimentally evaluate how using this similarity affects the quality of clustering on very different types of datasets. The experiments demonstrate that (a) using this similarity in standard clustering methods consistently gives good results, whereas other measures work well only on datasets that match their bias; and (b) on most datasets, the novel similarity outperforms even the best among the existing ones.

Nima Taghipour, Daan Fierens, Jesse Davis et al.

Lifted probabilistic inference algorithms exploit regularities in the structure of graphical models to perform inference more efficiently. More specifically, they identify groups of interchangeable variables and perform inference once per group, as opposed to once per variable. The groups are defined by means of constraints, so the flexibility of the grouping is determined by the expressivity of the constraint language. Existing approaches for exact lifted inference use specific languages for (in)equality constraints, which often have limited expressivity. In this article, we decouple lifted inference from the constraint language. We define operators for lifted inference in terms of relational algebra operators, so that they operate on the semantic level (the constraints extension) rather than on the syntactic level, making them language-independent. As a result, lifted inference can be performed using more powerful constraint languages, which provide more opportunities for lifting. We empirically demonstrate that this can improve inference efficiency by orders of magnitude, allowing exact inference where until now only approximate inference was feasible.

Maurice Bruynooghe, Hendrik Blockeel, Bart Bogaerts et al.

This paper provides a gentle introduction to problem solving with the IDP3 system. The core of IDP3 is a finite model generator that supports first order logic enriched with types, inductive definitions, aggregates and partial functions. It offers its users a modeling language that is a slight extension of predicate logic and allows them to solve a wide range of search problems. Apart from a small introductory example, applications are selected from problems that arose within machine learning and data mining research. These research areas have recently shown a strong interest in declarative modeling and constraint solving as opposed to algorithmic approaches. The paper illustrates that the IDP3 system can be a valuable tool for researchers with such an interest. The first problem is in the domain of stemmatology, a domain of philology concerned with the relationship between surviving variant versions of text. The second problem is about a somewhat related problem within biology where phylogenetic trees are used to represent the evolution of species. The third and final problem concerns the classical problem of learning a minimal automaton consistent with a given set of strings. For this last problem, we show that the performance of our solution comes very close to that of a state-of-the art solution. For each of these applications, we analyze the problem, illustrate the development of a logic-based model and explore how alternatives can affect the performance.

Nima Taghipour, Jesse Davis, Hendrik Blockeel

Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the propositional case, there exist formal structures, such as decomposition trees (dtrees), that represent such a decomposition and allow us to determine the complexity of inference a priori. However, there is currently no equivalent structure nor analogous complexity results for lifted inference. In this paper, we introduce FO-dtrees, which upgrade propositional dtrees to the first-order level. We show how these trees can characterize a lifted inference solution for a probabilistic logical model (in terms of a sequence of lifted operations), and make a theoretical analysis of the complexity of lifted inference in terms of the novel notion of lifted width for the tree.

Nima Taghipour, Daan Fierens, Guy Van den Broeck et al.

Various methods for lifted probabilistic inference have been proposed, but our understanding of these methods and the relationships between them is still limited, compared to their propositional counterparts. The only existing theoretical characterization of lifting is for weighted first-order model counting (WFOMC), which was shown to be complete domain-lifted for the class of 2-logvar models. This paper makes two contributions to lifted variable elimination (LVE). First, we introduce a novel inference operator called group inversion. Second, we prove that LVE augmented with this operator is complete in the same sense as WFOMC.