arXiv subjects

Tijl De Bie

Publications and source records attributed to Tijl De Bie.

At least 73 records · Page 4Linked to original sources

arXiv2020

Explainable Subgraphs with Surprising Densities: A Subgroup Discovery Approach

The connectivity structure of graphs is typically related to the attributes of the nodes. In social networks for example, the probability of a friendship between two people depends on their attributes, such as their age, address, and hobbies. The connectivity of a graph can thus possibly be understood in terms of patterns of the form 'the subgroup of individuals with properties X are often (or rarely) friends with individuals in another subgroup with properties Y'. Such rules present potentially actionable and generalizable insights into the graph. We present a method that finds pairs of node subgroups between which the edge density is interestingly high or low, using an information-theoretic definition of interestingness. This interestingness is quantified subjectively, to contrast with prior information an analyst may have about the graph. This view immediately enables iterative mining of such patterns. Our work generalizes prior work on dense subgraph mining (i.e. subgraphs induced by a single subgroup). Moreover, not only is the proposed method more general, we also demonstrate considerable practical advantages for the single subgroup special case.

cs.SI↗

arXiv2019

Discovering Interesting Cycles in Directed Graphs

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and cycles in financial transaction networks can be an indication of money laundering. Identifying such interesting cycles, which can also be constrained to contain a given set of query nodes, although not extensively studied, is thus a problem of considerable importance. In this paper, we introduce the problem of discovering interesting cycles in graphs. We first address the problem of quantifying the extent to which a given cycle is interesting for a particular analyst. We then show that finding cycles according to this interestingness measure is related to the longest cycle and maximum mean-weight cycle problems (in the unconstrained setting) and to the maximum Steiner cycle and maximum mean Steiner cycle problems (in the constrained setting). A complexity analysis shows that finding interesting cycles is NP-hard, and is NP-hard to approximate within a constant factor in the unconstrained setting, and within a factor polynomial in the input size for the constrained setting. The latter inapproximability result implies a similar result for the maximum Steiner cycle and maximum mean Steiner cycle problems. Motivated by these hardness results, we propose a number of efficient heuristic algorithms. We verify the effectiveness of the proposed methods and demonstrate their practical utility on two real-world use cases: a food web and an international trade-network dataset.

cs.DS↗

arXiv2019

Conditional t-SNE: Complementary t-SNE embeddings through factoring out prior information

Dimensionality reduction and manifold learning methods such as t-Distributed Stochastic Neighbor Embedding (t-SNE) are routinely used to map high-dimensional data into a 2-dimensional space to visualize and explore the data. However, two dimensions are typically insufficient to capture all structure in the data, the salient structure is often already known, and it is not obvious how to extract the remaining information in a similarly effective manner. To fill this gap, we introduce \emph{conditional t-SNE} (ct-SNE), a generalization of t-SNE that discounts prior information from the embedding in the form of labels. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining a single, integrated, and elegant method. ct-SNE has one extra parameter over t-SNE; we investigate its effects and show how to efficiently optimize the objective. Factoring out prior knowledge allows complementary structure to be captured in the embedding, providing new insights. Qualitative and quantitative empirical results on synthetic and (large) real data show ct-SNE is effective and achieves its goal.

cs.LG↗

arXiv2019

ExplaiNE: An Approach for Explaining Network Embedding-based Link Predictions

Networks are powerful data structures, but are challenging to work with for conventional machine learning methods. Network Embedding (NE) methods attempt to resolve this by learning vector representations for the nodes, for subsequent use in downstream machine learning tasks. Link Prediction (LP) is one such downstream machine learning task that is an important use case and popular benchmark for NE methods. Unfortunately, while NE methods perform exceedingly well at this task, they are lacking in transparency as compared to simpler LP approaches. We introduce ExplaiNE, an approach to offer counterfactual explanations for NE-based LP methods, by identifying existing links in the network that explain the predicted links. ExplaiNE is applicable to a broad class of NE algorithms. An extensive empirical evaluation for the NE method `Conditional Network Embedding' in particular demonstrates its accuracy and scalability.

cs.LG↗

arXiv2019

Mining Subjectively Interesting Attributed Subgraphs

Community detection in graphs, data clustering, and local pattern mining are three mature fields of data mining and machine learning. In recent years, attributed subgraph mining is emerging as a new powerful data mining task in the intersection of these areas. Given a graph and a set of attributes for each vertex, attributed subgraph mining aims to find cohesive subgraphs for which (a subset of) the attribute values has exceptional values in some sense. While research on this task can borrow from the three abovementioned fields, the principled integration of graph and attribute data poses two challenges: the definition of a pattern language that is intuitive and lends itself to efficient search strategies, and the formalization of the interestingness of such patterns. We propose an integrated solution to both of these challenges. The proposed pattern language improves upon prior work in being both highly flexible and intuitive. We show how an effective and principled algorithm can enumerate patterns of this language. The proposed approach for quantifying interestingness of patterns of this language is rooted in information theory, and is able to account for prior knowledge on the data. Prior work typically quantifies interestingness based on the cohesion of the subgraph and for the exceptionality of its attributes separately, combining these in a parametrized trade-off. Instead, in our proposal this trade-off is implicitly handled in a principled, parameter-free manner. Extensive empirical results confirm the proposed pattern syntax is intuitive, and the interestingness measure aligns well with actual subjective interestingness.

cs.SI↗

arXiv2019

Opinion Dynamics with Backfire Effect and Biased Assimilation

The democratization of AI tools for content generation, combined with unrestricted access to mass media for all (e.g. through microblogging and social media), makes it increasingly hard for people to distinguish fact from fiction. This raises the question of how individual opinions evolve in such a networked environment without grounding in a known reality. The dominant approach to studying this problem uses simple models from the social sciences on how individuals change their opinions when exposed to their social neighborhood, and applies them on large social networks. We propose a novel model that incorporates two known social phenomena: (i) \emph{Biased Assimilation}: the tendency of individuals to adopt other opinions if they are similar to their own; (ii) \emph{Backfire Effect}: the fact that an opposite opinion may further entrench someone in their stance, making their opinion more extreme instead of moderating it. To the best of our knowledge this is the first model that captures the Backfire Effect. A thorough theoretical and empirical analysis of the proposed model reveals intuitive conditions for polarization and consensus to exist, as well as the properties of the resulting opinions.

cs.SI↗

arXiv2019

EvalNE: A Framework for Evaluating Network Embeddings on Link Prediction

In this paper we present EvalNE, a Python toolbox for evaluating network embedding methods on link prediction tasks. Link prediction is one of the most popular choices for evaluating the quality of network embeddings. However, the complexity of this task requires a carefully designed evaluation pipeline in order to provide consistent, reproducible and comparable results. EvalNE simplifies this process by providing automation and abstraction of tasks such as hyper-parameter tuning and model validation, edge sampling and negative edge sampling, computation of edge embeddings from node embeddings, and evaluation metrics. The toolbox allows for the evaluation of any off-the-shelf embedding method without the need to write extra code. Moreover, it can also be used for evaluating any other link prediction method, and integrates several link prediction heuristics as baselines.

cs.SI↗

arXiv2018

Conditional Network Embeddings

Network Embeddings (NEs) map the nodes of a given network into $d$-dimensional Euclidean space $\mathbb{R}^d$. Ideally, this mapping is such that `similar' nodes are mapped onto nearby points, such that the NE can be used for purposes such as link prediction (if `similar' means being `more likely to be connected') or classification (if `similar' means `being more likely to have the same label'). In recent years various methods for NE have been introduced, all following a similar strategy: defining a notion of similarity between nodes (typically some distance measure within the network), a distance measure in the embedding space, and a loss function that penalizes large distances for similar nodes and small distances for dissimilar nodes. A difficulty faced by existing methods is that certain networks are fundamentally hard to embed due to their structural properties: (approximate) multipartiteness, certain degree distributions, assortativity, etc. To overcome this, we introduce a conceptual innovation to the NE literature and propose to create \emph{Conditional Network Embeddings} (CNEs); embeddings that maximally add information with respect to given structural properties (e.g. node degrees, block densities, etc.). We use a simple Bayesian approach to achieve this, and propose a block stochastic gradient descent algorithm for fitting it efficiently. We demonstrate that CNEs are superior for link prediction and multi-label classification when compared to state-of-the-art methods, and this without adding significant mathematical or computational complexity. Finally, we illustrate the potential of CNE for network visualization.

stat.ML↗

arXiv2018

From acquaintance to best friend forever: robust and fine-grained inference of social tie strengths

Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer the strength of social ties, access to such information may be restricted or impractical. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging the Strong Triadic Closure (STC) property. The STC property states that if person A has strong social ties with persons B and C, B and C must be connected to each other as well (whether with a weak or strong tie). Sintos and Tsaparas exploited this to formulate the inference of the strength of social ties as NP-hard optimization problem, and proposed two approximation algorithms. We refine and improve upon this landmark paper, by developing a sequence of linear relaxations of this problem that can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. One of the relaxations simultaneously infers the presence of a limited number of STC violations. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, and sheds new light on the validity of the STC property in practice.

cs.SI↗

arXiv2017

Interactive Visual Data Exploration with Subjective Feedback: An Information-Theoretic Approach

Visual exploration of high-dimensional real-valued datasets is a fundamental task in exploratory data analysis (EDA). Existing methods use predefined criteria to choose the representation of data. There is a lack of methods that (i) elicit from the user what she has learned from the data and (ii) show patterns that she does not know yet. We construct a theoretical model where identified patterns can be input as knowledge to the system. The knowledge syntax here is intuitive, such as "this set of points forms a cluster", and requires no knowledge of maths. This background knowledge is used to find a Maximum Entropy distribution of the data, after which the system provides the user data projections in which the data and the Maximum Entropy distribution differ the most, hence showing the user aspects of the data that are maximally informative given the user's current knowledge. We provide an open source EDA system with tailored interactive visualizations to demonstrate these concepts. We study the performance of the system and present use cases on both synthetic and real data. We find that the model and the prototype system allow the user to learn information efficiently from various data sources and the system works sufficiently fast in practice. We conclude that the information theoretic approach to exploratory data analysis where patterns observed by a user are formalized as constraints provides a principled, intuitive, and efficient basis for constructing an EDA system.

stat.ML↗

arXiv2017

Subjectively Interesting Subgroup Discovery on Real-valued Targets

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the fact that there are exponentially many variable combinations to potentially consider, and there are infinitely many if we consider weighted combinations, even for linear combinations. Hence, an obvious question is whether we can automate the search for interesting patterns and visualizations. In this paper, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. For example, to understand the distribution of crime rates in different geographic areas in terms of other (numerical, ordinal and/or categorical) variables that describe the areas. We introduce a method to find subgroups in the data that are maximally informative (in the formal Information Theoretic sense) with respect to a single or set of real-valued target attributes. The subgroup descriptions are in terms of a succinct set of arbitrarily-typed other attributes. The approach is based on the Subjective Interestingness framework FORSIED to enable the use of prior knowledge when finding most informative non-redundant patterns, and hence the method also supports iterative data mining.

stat.ML↗

arXiv2015

Informative Data Projections: A Framework and Two Examples

Methods for Projection Pursuit aim to facilitate the visual exploration of high-dimensional data by identifying interesting low-dimensional projections. A major challenge is the design of a suitable quality metric of projections, commonly referred to as the projection index, to be maximized by the Projection Pursuit algorithm. In this paper, we introduce a new information-theoretic strategy for tackling this problem, based on quantifying the amount of information the projection conveys to a user given their prior beliefs about the data. The resulting projection index is a subjective quantity, explicitly dependent on the intended user. As a useful illustration, we developed this idea for two particular kinds of prior beliefs. The first kind leads to PCA (Principal Component Analysis), shining new light on when PCA is (not) appropriate. The second kind leads to a novel projection index, the maximization of which can be regarded as a robust variant of PCA. We show how this projection index, though non-convex, can be effectively maximized using a modified power method as well as using a semidefinite programming relaxation. The usefulness of this new projection index is demonstrated in comparative empirical experiments against PCA and a popular Projection Pursuit method.

cs.LG↗

arXiv2011

Interesting Multi-Relational Patterns

Mining patterns from multi-relational data is a problem attracting increasing interest within the data mining community. Traditional data mining approaches are typically developed for highly simplified types of data, such as an attribute-value table or a binary database, such that those methods are not directly applicable to multi-relational data. Nevertheless, multi-relational data is a more truthful and therefore often also a more powerful representation of reality. Mining patterns of a suitably expressive syntax directly from this representation, is thus a research problem of great importance. In this paper we introduce a novel approach to mining patterns in multi-relational data. We propose a new syntax for multi-relational patterns as complete connected subgraphs in a representation of the database as a K-partite graph. We show how this pattern syntax is generally applicable to multirelational data, while it reduces to well-known tiles [7] when the data is a simple binary or attribute-value table. We propose RMiner, an efficient algorithm to mine such patterns, and we introduce a method for quantifying their interestingness when contrasted with prior information of the data miner. Finally, we illustrate the usefulness of our approach by discussing results on real-world and synthetic databases.

cs.DB↗

arXiv2011

Meta-song evaluation for chord recognition

We present a new approach to evaluate chord recognition systems on songs which do not have full annotations. The principle is to use online chord databases to generate high accurate "pseudo annotations" for these songs and compute "pseudo accuracies" of test systems. Statistical models that model the relationship between "pseudo accuracy" and real performance are then applied to estimate test systems' performance. The approach goes beyond the existing evaluation metrics, allowing us to carry out extensive analysis on chord recognition systems, such as their generalizations to different genres. In the experiments we applied this method to evaluate three state-of-the-art chord recognition systems, of which the results verified its reliability.

cs.IR↗

arXiv2011

An end-to-end machine learning system for harmonic analysis of music

We present a new system for simultaneous estimation of keys, chords, and bass notes from music audio. It makes use of a novel chromagram representation of audio that takes perception of loudness into account. Furthermore, it is fully based on machine learning (instead of expert knowledge), such that it is potentially applicable to a wider range of genres as long as training data is available. As compared to other models, the proposed system is fast and memory efficient, while achieving state-of-the-art performance.

cs.SD↗

arXiv2010

Maximum entropy models and subjective interestingness: an application to tiles in binary databases

Recent research has highlighted the practical benefits of subjective interestingness measures, which quantify the novelty or unexpectedness of a pattern when contrasted with any prior information of the data miner (Silberschatz and Tuzhilin, 1995; Geng and Hamilton, 2006). A key challenge here is the formalization of this prior information in a way that lends itself to the definition of an interestingness subjective measure that is both meaningful and practical. In this paper, we outline a general strategy of how this could be achieved, before working out the details for a use case that is important in its own right. Our general strategy is based on considering prior information as constraints on a probabilistic model representing the uncertainty about the data. More specifically, we represent the prior information by the maximum entropy (MaxEnt) distribution subject to these constraints. We briefly outline various measures that could subsequently be used to contrast patterns with this MaxEnt model, thus quantifying their subjective interestingness.

cs.AI↗

arXiv2010

Reconstruction of Causal Networks by Set Covering

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show that global consistency with the data can be achieved through purely local considerations, inferring the neighbourhood of each node in turn. The optimisation problem solved for each individual node can be reduced to a Set Covering Problem, which is known to be NP-hard but can be approximated well in practice. We then extend our approach to account for noisy data, based on the Minimum Description Length principle. We demonstrate our algorithms on synthetic data, generated by an SIR-like epidemiological model.

cs.DS↗

arXiv2009

Explicit probabilistic models for databases and networks

Recent work in data mining and related areas has highlighted the importance of the statistical assessment of data mining results. Crucial to this endeavour is the choice of a non-trivial null model for the data, to which the found patterns can be contrasted. The most influential null models proposed so far are defined in terms of invariants of the null distribution. Such null models can be used by computation intensive randomization approaches in estimating the statistical significance of data mining results. Here, we introduce a methodology to construct non-trivial probabilistic models based on the maximum entropy (MaxEnt) principle. We show how MaxEnt models allow for the natural incorporation of prior information. Furthermore, they satisfy a number of desirable properties of previously introduced randomization approaches. Lastly, they also have the benefit that they can be represented explicitly. We argue that our approach can be used for a variety of data types. However, for concreteness, we have chosen to demonstrate it in particular for databases and networks.

cs.AI↗