Abstract Text classification with hierarchical labels is a prevalent and challenging task in natural language processing. Examples include assigning ICD codes to patient records, tagging patents with IPC classes, assigning EUROVOC descriptors to European legal texts, and more. Despite the prevalence of hierarchical text classification problems, a comprehensive understanding of state-of-the-art methods across different application domains has been lacking. In this paper, we propose a unified methodology to break down the boundaries between these different domains, thus enabling cross-domain transfer of innovative ideas. We first construct a Unified Framework that translates distinct domain-specific methods into a common architectural language. Applying this framework, we conduct a comprehensive Cross-Domain Benchmark that exposes architectural gaps often overlooked in single-domain studies. We then demonstrate the framework’s practical utility through a validation case study, where we synthesize a new state-of-the-art hierarchical text classification method by combining submodules that were developed for the medical and legal domains. Our extensive empirical analysis yields key insights and guidelines, confirming the necessity of cross-domain learning for designing effective methods. Our code and datasets are publicly available at https://github.com/aida-ugent/cross-domain-HTC .

Understanding labor market dynamics is essential for policymakers, employers, and job seekers. However, comprehensive datasets that capture real-world career trajectories are scarce. In this paper, we introduce JobHop, a large-scale public dataset derived from anonymized resumes provided by VDAB, the public employment service in Flanders, Belgium. Utilizing Large Language Models (LLMs), we process unstructured resume data to extract structured career information, which is then normalized to standardized ESCO occupation codes using a multi-label classification model. This results in a rich dataset of over 1.67 million work experiences, extracted from and grouped into more than 361,000 user resumes and mapped to standardized ESCO occupation codes, offering valuable insights into real-world occupational transitions. This dataset enables diverse applications, such as analyzing labor market mobility, job stability, and the effects of career breaks on occupational transitions. It also supports career path prediction and other data-driven decision-making processes. To illustrate its potential, we explore key dataset characteristics, including job distributions, career breaks, and job transitions, demonstrating its value for advancing labor market research.

Personalized recommendation systems often drive users towards more extreme content, exacerbating opinion polarization. While content-aware moderation has been proposed to mitigate these effects, such approaches risk curtailing the freedom of speech and information. To address this concern, we propose and explore the feasibility of content-agnostic moderation as an alternative approach for reducing polarization. Content-agnostic moderation does not rely on the actual content being moderated, arguably making it less prone to forms of censorship. We establish theoretically that content-agnostic moderation cannot be guaranteed to work in a fully generic setting. However, we show that it can often be effectively achieved in practice with plausible assumptions. We introduce two novel content-agnostic moderation methods that modify recommendations from the content recommender to disperse user-item co-clusters without relying on content features.

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and the statistical stability of the extracted features. Despite this tradeoff, reminiscent of time–frequency tradeoffs in signal processing, most methods rely on a \emph{fixed temporal resolution}. Choosing an appropriate resolution parameter is typically difficult, and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales. We address this challenge by proposing ANIE ($\textbf{A}$daptive $\textbf{N}$etwork $\textbf{I}$ntensity $\textbf{E}$stimation), a multi-resolution framework designed to automatically identify the time scales at which network structure evolves, enabling the joint detection of both rapid and gradual changes. Modeling interactions as Poisson processes, our method proceeds in two steps: (1) estimating a low-dimensional subspace of node behavior, and (2) deriving a set of novel *empirical affinity coefficients* that measure change in interaction intensity between latent factors and support statistical testing for structural change across time scales. We provide theoretical guarantees for subspace estimation and the asymptotic behavior of the affinity coefficients, enabling model-based change detection. Experiments on synthetic networks show that ANIE adapts to the appropriate time resolution, and is able to capture sharp structural changes while remaining robust to noise. Furthermore, applications to real-world data showcase the practical benefits of ANIE’s multiresolution approach to detecting structural change over fixed resolution methods. An open-source implementation of the method is available at [https://github.com/aida-ugent/anie].

Abstract Temporal networks allow representing connections between objects while incorporating the temporal dimension. While static network models can capture unchanging topological regularities, they often fail to model the effects associated with the causal generative process of the network that occurs in time. Hence, exploiting the temporal aspect of networks has been the focus of many recent studies. In this context, we propose a new framework for generative models of continuous-time temporal networks. We assume that the activation of the edges in a temporal network is driven by a specified temporal point process. This approach allows to directly model the waiting time between events while incorporating time-varying history-based features as covariates in the predictions. Coupled with a thinning algorithm designed for the simulation of point processes, SimHawNet enables simulation of the evolution of temporal networks in continuous time. Finally, we introduce a comprehensive evaluation framework to assess the performance of such an approach, in which we demonstrate that SimHawNet successfully simulates the evolution of networks with very different generative processes and achieves performance comparable to the state of the art, while being significantly faster.

The so-called ‘Impossibility Theorem’ for fairness definitions is one of the more striking research results with both theoretical and practical consequences, as it states that satisfying certain combinations of fairness definitions is impossible. To date, this negative result has not yet been complemented with a positive one: a characterization of which combinations of fairness notions are possible. This work aims to fill this gap by identifying maximal sets of commonly used fairness definitions for binary classification that can be simultaneously satisfied. The fairness definitions used are demographic parity, equal opportunity, predictive equality, predictive parity, false omission rate parity, overall accuracy equality and treatment equality. We conclude that in total 12 maximal sets of these fairness definitions are possible, among which are seven combinations of two definitions, and five combinations of three definitions. Our findings also shed light on the practical relevance and utility of each of these 12 maximal fairness definitions in various scenarios, regarding the accuracy of the classifier and ratios of false positives and false negatives, considering the base rates.

Automated occupation extraction and standardization from free-text job postings and resumes are crucial for applications like job recommendation and labor market policy formation. This paper introduces LLM4Jobs, a novel unsupervised methodology that taps into the capabilities of large language models (LLMs) for occupation coding. LLM4Jobs uniquely harnesses both the natural language understanding and generation capacities of LLMs. Evaluated on rigorous experimentation on synthetic and real-world datasets, we demonstrate that LLM4Jobs consistently surpasses unsupervised state-of-the-art benchmarks, demonstrating its versatility across diverse datasets and granularities. As a side result of our work, we present both synthetic and real-world datasets, which may be instrumental for subsequent research in this domain. Overall, this investigation highlights the promise of contemporary LLMs for the intricate task of occupation extraction and standardization, laying the foundation for a robust and adaptable framework relevant to both research and industrial contexts.

Current tools for machine learning fairness only admit a limited range of fairness definitions and have seen little integration with automatic differentiation libraries, despite the central role these libraries play in modern machine learning pipelines. We introduce a framework of fairness regularization terms (fairret) which quantify bias as modular objectives that are easily integrated in automatic differentiation pipelines. By employing a general definition of fairness in terms of linear-fractional statistics, a wide class of fairrets can be computed efficiently. Experiments show the behavior of their gradients and their utility in enforcing fairness with minimal loss of predictive power compared to baselines. Our contribution includes a PyTorch implementation of the fairret framework.

Numerous methods have been implemented that pursue fairness with respect to sensitive features by mitigating biases in machine learning. Yet, the problem settings that each method tackles vary significantly, including the stage of intervention, the composition of sensitive features, the fairness notion, and the distribution of the output. Even in binary classification, the greatest common denominator of problem settings is small, significantly complicating benchmarking.Hence, we introduce ABCFair, a benchmark approach which allows adapting to the desiderata of the real-world problem setting, enabling proper comparability between methods for any use case. We apply this benchmark to a range of pre-, in-, and postprocessing methods on both large-scale, traditional datasets and on a dual label (biased and unbiased) dataset to sidestep the fairness-accuracy trade-off.

Abstract Feature attribution maps are a popular approach to highlight the most important pixels in an image for a given prediction of a model. Despite a recent growth in popularity and available methods, the objective evaluation of such attribution maps remains an open problem. Building on previous work in this domain, we investigate existing quality metrics and propose new variants of metrics for the evaluation of attribution maps. We confirm a recent finding that different quality metrics seem to measure different underlying properties of attribution maps, and extend this finding to a larger selection of attribution methods, quality metrics, and datasets. We also find that metric results on one dataset do not necessarily generalize to other datasets, and methods with desirable theoretical properties do not necessarily outperform computationally cheaper alternatives in practice. Based on these findings, we propose a general benchmarking approach to help guide the selection of attribution methods for a given use case. Implementations of attribution metrics and our experiments are available online ( https://github.com/arnegevaert/benchmark-general-imaging ). Graphical abstract

Recommendation in settings such as e-recruitment and online dating involves distributing limited opportunities, which differs from recommending practically unlimited goods such as in e-commerce or music recommendation. This setting calls for novel approaches to quantify and enforce fairness. Indeed, typical recommender systems recommend each user their top relevant items, such that desirable items may be recommended simultaneously to more and to less qualified individuals. This is arguably unfair to the latter. Indeed, when they pursue such a desirable recommendation (e.g., by applying for a job), they are unlikely to be successful. To quantify fairness in such settings, we introduce inferiority : a novel (un)fairness measure that quantifies the competitive disadvantage of a user for their recommended items. Inferiority is complementary to envy : a previously-proposed fairness notion that quantifies the extent to which a user prefers other users’ recommendations over their own. We propose to use both inferiority and envy in combination with an accuracy-related measure called utility : the aggregated relevancy scores of the recommended items. Unfortunately, none of these three measures are differentiable, making it hard to optimize them, and restricting their immediate use to evaluation only. To remedy this, we reformulate them in the context of a probabilistic interpretation of recommender systems, resulting in differentiable versions. We show how these loss functions can be combined in a multi-objective optimization problem that we call FEIR (Fairness through Envy and Inferiority Reduction), used as a post-processing of the scores from any standard recommender system. Experiments on synthetic and real-world data show that the proposed approach effectively improves the trade-offs between inferiority, envy and utility, compared to the naive recommendation and the state-of-the-art method for the related problem of congestion alleviation in job recommendation. We discuss and enhance the practical impact of our findings on a wide range of real-world recommendation scenarios, and we offer implementations of visualization tools to render the envy and inferiority metrics more accessible.

Real-world data can often be represented as a heterogeneous network relating nodes of different types. E.g., a job market can be represented as a job seeker-skill-vacancy network. It can be relevant to consider theimbalancebetween nodes of different types, in terms of whether they are similarly connected in the network. For example, it is desirable that job seekers and vacancies are mixed well. If they are not, then there is imbalance. We propose to quantify the imbalancebetween two sets of nodesin a network as the Earth Mover's Distance between the sets. Given this quantification, we introduceGREASE(Graph imbalance REduction by Adding Sets of Edges), a method that selects a fixed number of unconnected node-pairs, which—if links were added between them—aims to maximally reduce the imbalance. In the job market network,GREASEcan be used to select skills that job seekers do not yet have, but could strive to acquire, to reduce the imbalance between job seekers and vacancies.GREASEmay also be used in other applications, such as reducing controversy between opposing sides on a polarizing topic. We evaluatedGREASEon several datasets and find thatGREASEoutperforms baselines in reducing network imbalance.

Recommender systems may suffer from congestion, meaning that there is an unequal distribution of the items in how often they are recommended. Some items may be recommended much more than others. Recommenders are increasingly used in domains where items have limited availability, such as the job market, where congestion is especially problematic: Recommending a vacancy—for which typically only one person will be hired—to a large number of job seekers may lead to frustration for job seekers, as they may be applying for jobs where they are not hired. This may also leave vacancies unfilled and result in job market inefficiency.

Distances between data points are widely used in machine learning applications. Yet, when corrupted by noise, these distances—and thus the models based upon them—may lose their usefulness in high dimensions. Indeed, the small marginal effects of the noise may then accumulate quickly, shifting empirical closest and furthest neighbors away from the ground truth. In this paper, we exactly characterize such effects in noisy high-dimensional data using an asymptotic probabilistic expression. Previously, it has been argued that neighborhood queries become meaningless and unstable when distance concentration occurs, which means that there is a poor relative discrimination between the furthest and closest neighbors in the data. However, we conclude that this is not necessarily the case when we decompose the data in a ground truth—which we aim to recover—and noise component. More specifically, we derive that under particular conditions, empirical neighborhood relations affected by noise are still likely to be truthful even when distance concentration occurs. We also include thorough empirical verification of our results, as well as interesting experiments in which our derived ‘phase shift’ where neighbors become random or not turns out to be identical to the phase shift where common dimensionality reduction methods perform poorly or well for recovering low-dimensional reconstructions of high-dimensional data with dense noise.

Quantifying the similarity between a group of companies has proven to be useful for several purposes, including company benchmarking, fraud detection, and searching for investment opportunities. This exercise can be done using a variety of data sources, such as company activity data and financial data. However, ledger account data is widely available and is standardized to a large extent. Such ledger accounts within a financial statement can be represented by means of a tree, i.e. a special type of graph, representing both the values of the ledger accounts and the relationships between them. Given their broad availability and rich information content, financial statements form a prime data source based on which company similarities or distances could be computed.In this paper, we present a graph distance metric that enables one to compute the similarity between the financial statements of two companies. We conduct a comprehensive experimental study using real-world financial data to demonstrate the usefulness of our proposed distance metric. The experimental results show promising results on a number of use cases. This method may be useful for investors looking for investment opportunities, government officials attempting to identify fraudulent companies, and accountants looking to benchmark a group of companies based on their financial statements.

In recent years, music storage and consumption has shifted massively to digital platforms, where large-scale libraries of songs are stored along with their metadata.As a byproduct of this transformation, music is increasingly being organized and accessed in the form of playlists.User-curated playlists have become massively available online, and the challenge of automatically generating playlists has gained popularity in the music information retrieval community.In this paper, we build on link prediction for graphs to propose a flexible music playlist generation method.We transform a playlist dataset into a weighted graph of songs and posit a Poisson model on the count of transitions between songs, where the rate is modulated by the euclidean distance between song embeddings.Our method yields prediction results superior to common deterministic baselines, suggesting that the learned embeddings can be used to derive a meaningful notion of song similarity.

In past work on fairness in machine learning, the focus has been on forcing the prediction of classifiers to have similar statistical properties for people of different demographics. To reduce the violation of these properties, fairness methods usually simply rescale the classifier scores, ignoring similarities and dissimilarities between members of different groups. Yet, we hypothesize that such information is relevant in quantifying the unfairness of a given classifier. To validate this hypothesis, we introduce Optimal Transport to Fairness (OTF), a method that quantifies the violation of fairness constraints as the smallest Optimal Transport cost between a probabilistic classifier and any score function that satisfies these constraints. For a flexible class of linear fairness constraints, we construct a practical way to compute OTF as a differentiable fairness regularizer that can be added to any standard classification setting. Experiments show that OTF can be used to achieve an improved trade-off between predictive power and fairness.

Dimensionality reduction and manifold learning methods such as t-distributed Stochastic Neighbor Embedding (t-SNE) are frequently used to map high-dimensional data into a two-dimensional space to visualize and explore that data. Going beyond the specifics of t-SNE, there are two substantial limitations of any such approach: (1) not all information can be captured in a single two-dimensional embedding, and (2) to well-informed users, the salient structure of such an embedding is often already known, preventing that any real new insights can be obtained. Currently, it is not known how to extract the remaining information in a similarly effective manner. We introduce conditional t-SNE (ct-SNE), a generalization of t-SNE that discounts prior information in the form of labels. This enables obtaining more informative and more relevant embeddings. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining an elegant method with a single integrated objective. We show how to efficiently optimize the objective and study the effects of the extra parameter that ct-SNE has over t-SNE. Qualitative and quantitative empirical results on synthetic and real data show ct-SNE is scalable, effective, and achieves its goal: it allows complementary structure to be captured in the embedding and provides new insights into data.

Abstract The connectivity structure of graphs is typically related to the attributes of the vertices. In social networks for example, the probability of a friendship between any pair of people depends on a range of attributes, such as their age, residence location, workplace, and hobbies. The high-level structure of a graph can thus possibly be described well by means of patterns of the form ‘the subgroup of all individuals with certain properties X are often (or rarely) friends with individuals in another subgroup defined by properties Y’, ideally relative to their expected connectivity. Such rules present potentially actionable and generalizable insight into the graph. Prior work has already considered the search for dense subgraphs (‘communities’) with homogeneous attributes. The first contribution in this paper is to generalize this type of pattern to densities between apair of subgroups, as well as betweenall pairs from a set of subgroups that partition the vertices. Second, we develop a novel information-theoretic approach for quantifying the subjective interestingness of such patterns, by contrasting them with prior information an analyst may have about the graph’s connectivity. We demonstrate empirically that in the special case of dense subgraphs, this approach yields results that are superior to the state-of-the-art. Finally, we propose algorithms for efficiently finding interesting patterns of these different types.

Abstract Dimensionality reduction and manifold learning methods such as t-distributed stochastic neighbor embedding (t-SNE) are frequently used to map high-dimensional data into a two-dimensional space to visualize and explore that data. Going beyond the specifics of t-SNE, there are two substantial limitations of any such approach: (1) not all information can be captured in a single two-dimensional embedding, and (2) to well-informed users, the salient structure of such an embedding is often already known, preventing that any real new insights can be obtained. Currently, it is not known how to extract the remaining information in a similarly effective manner. We introduce conditional t-SNE (ct-SNE), a generalization of t-SNE that discounts prior information in the form of labels. This enables obtaining more informative and more relevant embeddings. To achieve this, we propose a conditioned version of the t-SNE objective, obtaining an elegant method with a single integrated objective. We show how to efficiently optimize the objective and study the effects of the extra parameter that ct-SNE has over t-SNE. Qualitative and quantitative empirical results on synthetic and real data show ct-SNE is scalable, effective, and achieves its goal: it allows complementary structure to be captured in the embedding and provided new insights into real data.

The rising field of Topological Data Analysis (TDA) provides a new approach to learning from data through persistence diagrams, which are topological signatures that quantify topological properties of data in a comparable manner. For point clouds, these diagrams are often derived from the Vietoris-Rips filtration—based on the metric equipped on the data—which allows one to deduce topological patterns such as components and cycles of the underlying space. In metric trees these diagrams often fail to capture other crucial topological properties, such as the present leaves and multifurcations. Prior methods and results for persistent homology attempting to overcome this issue mainly target Rips graphs, which are often unfavorable in case of non-uniform density across our point cloud. We therefore introduce a new theoretical foundation for learning a wider variety of topological patterns through any given graph. Given particular powerful functions defining persistence diagrams to summarize topological patterns, including the normalized centrality or eccentricity, we prove a new stability result, explicitly bounding the bottleneck distance between the true and empirical diagrams for metric trees. This bound is tight if the metric distortion obtained through the graph and its maximal edge-weight are small. Through a case study of gene expression data, we demonstrate that our newly introduced diagrams provide novel quality measures and insights into cell trajectory inference.

Work in Counterfactual Explanations tends to focus on the principle of "the closest possible world" that identifies small changes leading to the desired outcome. In this paper we argue that while this approach might initially seem intuitively appealing it exhibits shortcomings not addressed in the current literature. First, a counterfactual example generated by the state-of-the-art systems is not necessarily representative of the underlying data distribution, and may therefore prescribe unachievable goals (e.g., an unsuccessful life insurance applicant with severe disability may be advised to do more sports). Secondly, the counterfactuals may not be based on a "feasible path" between the current state of the subject and the suggested one, making actionable recourse infeasible (e.g., low-skilled unsuccessful mortgage applicants may be told to double their salary, which may be hard without first increasing their skill level). These two shortcomings may render counterfactual explanations impractical and sometimes outright offensive. To address these two major flaws, first of all, we propose a new line of Counterfactual Explanations research aimed at providing actionable and feasible paths to transform a selected instance into one that meets a certain goal. Secondly, we propose FACE: an algorithmically sound way of uncovering these "feasible paths" based on the shortest path distances defined via density-weighted metrics. Our approach generates counterfactuals that are coherent with the underlying data distribution and supported by the "feasible paths" of change, which are achievable and can be tailored to the problem at hand.

Signed networks are mathematical structures that encode positive and negative relations between entities such as friend/foe or trust/distrust. Recently, several papers studied the construction of useful low-dimensional representations (embeddings) of these networks for the prediction of missing relations or signs. Existing network embedding methods for sign prediction, however, generally enforce different notions of status or balance theories in their optimization function. These theories, are often inaccurate or incomplete which negatively impacts method performance.

An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. By utilizing fast matrix block-approximation techniques, we propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions, while being able to meaningfully model local information of the graph (e.g., degrees) as well as global information (e.g., clustering coefficient, assortativity, etc.) if desired. This allows one to efficiently generate random networks with similar properties as an observed network, and the models can be used for several downstream tasks such as link prediction. Our methods are scalable to sparse graphs consisting of millions of nodes. Empirical evaluation demonstrates competitiveness in terms of both speed and accuracy with state-of-the-art methods-which are typically based on embedding the graph into some low-dimensional space- for link prediction, showcasing the potential of a more direct and interpretable probablistic model for this task.

Network embedding methods map a network's nodes to vectors in an embedding space, in such a way that these representations are useful for estimating some notion of similarity or proximity between pairs of nodes in the network. The quality of these node representations is then showcased through results of downstream prediction tasks. Commonly used benchmark tasks such as link prediction, however, present complex evaluation pipelines and an abundance of design choices. This, together with a lack of standardized evaluation setups can obscure the real progress in the field. In this paper, we aim to shed light on the state-of-the-art of network embedding methods for link prediction and show, using a consistent evaluation pipeline, that only thin progress has been made over the last years. The newly conducted benchmark that we present here, including 17 embedding methods, also shows that many approaches are outperformed even by simple heuristics. Finally, we argue that standardized evaluation tools can repair this situation and boost future progress in this field.

Real-world data often presents itself in the form of a network. Examples include social networks, citation networks, biological networks, and knowledge graphs. In their simplest form, networks represent real-life entities (e.g. people, papers, proteins, concepts) as nodes, and describe them in terms of their relations with other entities by means of edges between these nodes. This can be valuable for a range of purposes from the study of information diffusion to bibliographic analysis, bioinformatics research, and question-answering. The quality of networks is often problematic though, affecting downstream tasks. This paper focuses on the common problem where a node in the network in fact corresponds to multiple real-life entities. In particular, we introduce FONDUE, an algorithm based on network embedding for node disambiguation. Given a network, FONDUE identifies nodes that correspond to multiple entities, for subsequent splitting. Extensive experiments on fourteen benchmark datasets demonstrate that FONDUE is substantially and uniformly more accurate for ambiguous node identification compared to the existing state-of-the-art with a lower computational cost, while less optimal for determining the best way to split ambiguous nodes.

As machine learning algorithms are increasingly deployed for high-impact automated decision making, ethical and increasingly also legal standards demand that they treat all individuals fairly, without discrimination based on their age, gender, race or other sensitive traits. In recent years much progress has been made on ensuring fairness and reducing bias in standard machine learning settings. Yet, for network embedding, with applications in vulnerable domains ranging from social network analysis to recommender systems, current options remain limited both in number and performance. We thus propose DeBayes: a conceptually elegant Bayesian method that is capable of learning debiased embeddings by using a biased prior. Our experiments show that these representations can then be used to perform link prediction that is significantly more fair in terms of popular metrics such as demographic parity and equalized opportunity.

In machine learning, high-dimensional point clouds are often assumed to be sampled from a topological space of which the intrinsic dimension is significantly lower than the representation dimension. Proximity graphs, such as the Rips graph or kNN graph, are often used as an intermediate representation to learn or visualize topological and geometrical properties of this space. The key idea behind this approach is that distances on the graph preserve the geodesic distances on the unknown space well, and as such, can be used to infer local and global geometric patterns of this space. Prior results provide us with conditions under which these distances are well-preserved for geodesically convex, smooth, compact manifolds. Yet, proximity graphs are ideal representations for a much broader class of spaces, such as metric graphs, i.e., graphs embedded in the Euclidean space. It turns out-as proven in this paper-that these existing conditions cannot be straightforwardly adapted to these spaces. In this work, we provide novel, flexible, and insightful characteristics and results for topological pattern recognition of metric graphs to bridge this gap.

The local pattern mining literature has long struggled with the so-called pattern explosion problem: the size of the set of patterns found exceeds the size of the original data. This causes computational problems (enumerating a large set of patterns will inevitably take a substantial amount of time) as well as problems for interpretation and usability (trawling through a large set of patterns is often impractical). Two complementary research lines aim to address this problem. The first aims to develop better measures of interestingness, in order to reduce the number of uninteresting patterns that are returned [ 6 , 10 ]. The second aims to avoid an exhaustive enumeration of all ‘interesting’ patterns (where interestingness is quantified in a more traditional way, e.g. frequency), by directly sampling from this set in a way that more ‘interesting’ patterns are sampled with higher probability [ 2 ]. Unfortunately, the first research line does not reduce computational cost, while the second may miss out on the most interesting patterns. In this paper, we combine the best of both worlds for mining interesting tiles [ 8 ] from binary databases. Specifically, we propose a new pattern sampling approach based on Gibbs sampling, where the probability of sampling a pattern is proportional to their subjective interestingness [ 6 ]—an interestingness measure reported to better represent true interestingness. The experimental evaluation confirms the theory, but also reveals an important weakness of the proposed approach which we speculate is shared with any other pattern sampling approach. We thus conclude with a broader discussion of this issue, and a forward look.

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.

Abstract 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 thestrengthof social ties, access to such information may be restricted or impractical to obtain. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging theStrong Triadic Closure(STC) property. The STC property states that if personAhas strong social ties with personsBandC,BandCmust be connected to each other as well (whether with a weak or strong tie). They exploited this property to formulate the inference of the strength of social ties as a NP-hard maximization problem, and proposed two approximation algorithms. We refine and improve this line of work, by developing a sequence of linear relaxations of the problem, which 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 one to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. Moreover, these relaxations allow us to easily change the objective function to more sensible alternatives, instead of simply maximizing the number of strong edges. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, while at the same time questioning the validity of leveraging the STC property for edge strength inference in practice.

Abstract Data clustering, local pattern mining, and community detection in graphs are three mature areas of data mining and machine learning. In recent years, attributed subgraph mining has emerged 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 (some of) the attribute values have exceptional values. The principled integration of graph and attribute data poses two challenges: (1) the definition of a pattern syntax (the abstract form of patterns) that is intuitive and lends itself to efficient search, and (2) the formalization of the interestingness of such patterns. We propose an integrated solution to both of these challenges. The proposed pattern syntax improves upon prior work in being both highly flexible and intuitive. Plus, we define an effective and principled algorithm to enumerate patterns of this syntax. The proposed approach for quantifying interestingness of these patterns is rooted in information theory, and is able to account for background knowledge on the data. While prior work quantified the interestingness for the cohesion of the subgraph and for the exceptionality of its attributes separately, then combining these in a parameterized trade-off, we instead handle this trade-off implicitly in a principled, parameter-free manner. Empirical results confirm we can efficiently find highly interesting subgraphs.

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.

We consider the problem of inferring simplified topological substructures—which we term backbones—in metric and non-metric graphs. Intuitively, these are subgraphs with ‘few’ nodes, multifurcations, and cycles, that model the topology of the original graph well. We present a multistep procedure for inferring these backbones. First, we encode local (geometric) information of each vertex in the original graph by means of the boundary coefficient (BC) to identify ‘core’ nodes in the graph. Next, we construct a forest representation of the graph, termed an f-pine, that connects every node of the graph to a local ‘core’ node. The final backbone is then inferred from the f-pine through CLOF (Constrained Leaves Optimal subForest), a novel graph optimization problem we introduce in this paper. On a theoretical level, we show that CLOF is NP-hard for general graphs. However, we prove that CLOF can be efficiently solved for forest graphs, a surprising fact given that CLOF induces a nontrivial monotone submodular set function maximization problem on tree graphs. This result is the basis of our method for mining backbones in graphs through forest representation. We qualitatively and quantitatively confirm the applicability, effectiveness, and scalability of our method for discovering backbones in a variety of graph-structured data, such as social networks, earthquake locations scattered across the Earth, and high-dimensional cell trajectory data.

Data visualization and iterative/interactive data mining are growing rapidly in attention, both in research as well as in industry. However, while there are a plethora of advanced data mining methods and lots of works in the field of visualization, integrated methods that combine advanced visualization and/or interaction with data mining techniques in a principled way are rare. We present a framework based on constrained randomization which lets users explore high-dimensional data via `subjectively informative' two-dimensional data visualizations. The user is presented with `interesting' projections, allowing users to express their observations using visual interactions that update a background model representing the user's belief state. This background model is then considered by a projection-finding algorithm employing data randomization to compute a new `interesting' projection. By providing users with information that contrasts with the background model, we maximize the chance that the user encounters striking new information present in the data. This process can be iterated until the user runs out of time or until the difference between the randomized and the real data is insignificant. We present two case studies, one controlled study on synthetic data and another on census data, using the proof-of-concept tool SIDE that demonstrates the presented framework.

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.

Concepts are often described in terms of positive integer-valued attributes that are organized in a hierarchy. For example, cities can be described in terms of how many places there are of various types (e.g. nightlife spots, residences, food venues), and these places are organized in a hierarchy (e.g. a Portuguese restaurant is a type of food venue). This hierarchy imposes particular constraints on the values of related attributes---e.g. there cannot be more Portuguese restaurants than food venues. Moreover, knowing that a city has many food venues makes it less surprising that it also has many Portuguese restaurants, and vice versa. In the present paper, we attempt to characterize such concepts in terms of so-called contrastive antichains: particular kinds of subsets of their attributes and their values. We address the question of when a contrastive antichain is interesting, in the sense that it concisely describes the unique aspects of the concept, and this while duly taking into account the known attribute dependencies implied by the hierarchy. Our approach is capable of accounting for previously identified contrastive antichains, making iterative mining possible. Besides the interestingness measure, we also present an algorithm that scales well in practice, and demonstrate the usefulness of the method in an extensive empirical results section.

Consider a large graph or network, and a user-provided set of query vertices between which the user wishes to explore relations. For example, a researcher may want to connect research papers in a citation network, an analyst may wish to connect organized crime suspects in a communication network, or an internet user may want to organize their bookmarks given their location in the world wide web. A natural way to do this is to connect the vertices in the form of a tree structure that is present in the graph. However, in sufficiently dense graphs, most such trees will be large or somehow trivial (e.g. involving high degree vertices) and thus not insightful. Extending previous research, we define and investigate the new problem of mining subjectively interesting trees connecting a set of query vertices in a graph, i.e., trees that are highly surprising to the specific user at hand. Using information theoretic principles, we formalize the notion of interestingness of such trees mathematically, taking in account certain prior beliefs the user has specified about the graph. A remaining problem is efficiently fitting a prior belief model. We show how this can be done for a large class of prior beliefs. Given a specified prior belief model, we then propose heuristic algorithms to find the best trees efficiently. An empirical validation of our methods on a large real graphs evaluates the different heuristics and validates the interestingness of the given trees.

Deriving insights from high-dimensional data is one of the core problems in data mining. The difficulty mainly stems from the large number of variable combinations to potentially consider. Hence, an obvious question is whether we can automate the search for interesting patterns. Here, we consider the setting where a user wants to learn as efficiently as possible about real-valued attributes. We introduce a method to find subgroups in the data that are maximally informative (in the Information Theoretic sense) with respect to one or more real-valued target attributes. The succinct subgroup descriptions are in terms of arbitrarily-typed description attributes. The approach is based on the Subjective Interestingness framework FORSIED to use prior knowledge when mining most informative patterns.

Controversy, disagreement, conflict, polarization and opinion divergence in social networks have been the subject of much recent research. In particular, researchers have addressed the question of how such concepts can be quantified given people's prior opinions, and how they can be optimized by influencing the opinion of a small number of people or by editing the network's connectivity.

The information in high-dimensional datasets is often too complex for human users to perceive directly. Hence, it may be helpful to use dimensionality reduction methods to construct lower dimensional representations that can be visualized. The natural question that arises is how do we construct a most informative low dimensional representation? We study this question from an information-theoretic perspective and introduce a new method for linear dimensionality reduction. The obtained model that quantifies the informativeness also allows us to flexibly account for prior knowledge a user may have about the data. This enables us to provide representations that are subjectively interesting . We title the method Subjectively Interesting Component Analysis (SICA) and expect it is mainly useful for iterative data mining. SICA is based on a model of a user’s belief state about the data. This belief state is used to search for surprising views. The initial state is chosen by the user (it may be empty up to the data format) and is updated automatically as the analysis progresses. We study several types of prior beliefs: if a user only knows the scale of the data, SICA yields the same cost function as Principal Component Analysis (PCA), while if a user expects the data to have outliers, we obtain a variant that we term t -PCA. Finally, scientifically more interesting variants are obtained when a user has more complicated beliefs, such as knowledge about similarities between data points. The experiments suggest that SICA enables users to find subjectively more interesting representations.

Separating the singing from a polyphonic mixed audio signal is a challenging but important task, with a wide range of applications across the music industry and music informatics research. Various methods have been devised over the years, ranging from Deep Learning approaches to dedicated ad hoc solutions. In this paper, we present a novel machine learning method for the task, using a Conditional Random Field (CRF) approach for structured output prediction. We exploit the diversity of previously proposed approaches by using their predictions as input features to our method - thus effectively developing an ensemble method. Our empirical results demonstrate the potential of integrating predictions from different previously-proposed methods into one ensemble method, and additionally show that CRF models with larger complexities generally lead to superior performance.

Data is typically complex and relational. Therefore, the development of relational data mining methods is an increasingly active topic of research. Recent work has resulted in new formalisations of patterns in relational data and in a way to quantify their interestingness in a subjective manner, taking into account the data analyst's prior beliefs about the data. Yet, a scalable algorithm to find such most interesting patterns is lacking. We introduce a new algorithm based on two notions: (1) the use of Constraint Programming, which results in a notably shorter development time, faster runtimes, and more flexibility for extensions such as branch-and-bound search, and (2), the direct search for the most interesting patterns only, instead of exhaustive enumeration of patterns before ranking them. Through empirical evaluation, we find that our novel bounds yield speedups up to several orders of magnitude, especially on dense data with a simple schema. This makes it possible to mine the most subjectively-interesting relational patterns present in databases where this was previously impractical or impossible.

Methods that find insightful low-dimensional projections are essential to effectively explore high-dimensional data. Principal Component Analysis is used pervasively to find low-dimensional projections, not only because it is straightforward to use, but it is also often effective, because the variance in data is often dominated by relevant structure. However, even if the projections highlight real structure in the data, not all structure is interesting to every user. If a user is already aware of, or not interested in the dominant structure, Principal Component Analysis is less effective for finding interesting components. We introduce a new method called Subjectively Interesting Component Analysis (SICA), designed to find data projections that are subjectively interesting, i.e, projections that truly surprise the end-user. It is rooted in information theory and employs an explicit model of a user's prior expectations about the data. The corresponding optimization problem is a simple eigenvalue problem, and the result is a trade-off between explained variance and novelty. We present five case studies on synthetic data, images, time-series, and spatial data, to illustrate how SICA enables users to find (subjectively) interesting projections.

The utility of a dense subgraph in gaining a better understanding of a graph has been formalised in numerous ways, each striking a different balance between approximating actual interestingness and computational efficiency. A difficulty in making this trade-off is that, while computational cost of an algorithm is relatively well-defined, a pattern’s interestingness is fundamentally subjective. This means that this latter aspect is often treated only informally or neglected, and instead some form of density is used as a proxy. We resolve this difficulty by formalising what makes a dense subgraph pattern interesting to a given user. Unsurprisingly, the resulting measure is dependent on the prior beliefs of the user about the graph. For concreteness, in this paper we consider two cases: one case where the user only has a belief about the overall density of the graph, and another case where the user has prior beliefs about the degrees of the vertices. Furthermore, we illustrate how the resulting interestingness measure is different from previous proposals. We also propose effective exact and approximate algorithms for mining the most interesting dense subgraph according to the proposed measure. Usefully, the proposed interestingness measure and approach lend themselves well to iterative dense subgraph discovery. Contrary to most existing approaches, our method naturally allows subsequently found patterns to be overlapping. The empirical evaluation highlights the properties of the new interestingness measure given different prior belief sets, and our approach’s ability to find interesting subgraphs that other methods are unable to find.

Defining and computing distances between tree structures is a classical area of study in theoretical computer science, with practical applications in the areas of computational biology, information retrieval, text analysis, and many others. In this paper, we focus on rooted, unordered, uniquely-labelled trees such as taxonomies and other hierarchies. For trees as these, we introduce the intuitive concept of a ‘local move’ operation as an atomic edit of a tree. We then introduce SuMoTED, a new edit distance measure between such trees, defined as the minimal number of local moves required to convert one tree into another. We show how SuMoTED can be computed using a scalable algorithm with quadratic time complexity. Finally, we demonstrate its use on a collection of music genre taxonomies.

Local pattern mining methods are fragmented along two dimensions: the pattern syntax, and the data types on which they are applicable. Pattern syntaxes considered in the literature include subgroups, n-sets, itemsets, and many more; common data types include binary, categorical, and real-valued. Recent research on pattern mining in relational databases has shown how the aforementioned pattern syntaxes can be unified in a single framework. However, a unified understanding of how to deal with various data types is lacking, certainly for more complexly structured types such as time of day (which is circular), geographical location, terms from a taxonomy, etc. In this paper, we introduce a generic approach for mining interesting local patterns in (relational) data involving such structured data types as attributes. Importantly, we show how this can be done in a generic manner, by modelling the structure within a set of attribute values as a partial order. We then derive a measure of subjective interestingness of such patterns using Information Theory, and propose an algorithm for effectively enumerating all patterns of this syntax. Through empirical evaluation, we found that (a) the new interestingness derivation is relevant and cannot be approximated using existing tools, (b) the new tool, P-N-RMiner, finds patterns that are substantially more informative, and (c) the new enumeration algorithm is considerably faster.

Three recent trends aim to make local pattern mining more directly suited for use on data as it presents itself in practice, namely in a multi-relational form and affected by noise. The first of these trends is the generalisation of local pattern syntaxes to approximate, noise-tolerant, variants (notably fault-tolerant itemset mining and community detection). The second of these trends is to develop pattern syntaxes that are directly applicable to multi-relational data. The third one is to better quantify the interestingness of and redundancy between such local patterns. In this paper we leverage recent results from these lines of research to introduce a noise-tolerant pattern syntax for multi-relational data. We show how enumerating all patterns of this syntax in a given database can be done remarkably efficiently. We contribute a way to quantify the interestingness of these patterns, thus overcoming the pattern explosion problem. And finally, we show the usefulness of the pattern syntax and the scalability of the algorithm by presenting experimental results on real world and synthetic data.

In this overview article, we review research on the task of Automatic Chord Estimation (ACE). The major contributions from the last 14 years of research are summarized, with detailed discussions of the following topics: feature extraction, modeling strategies, model training and datasets, and evaluation strategies. Results from the annual benchmarking evaluation Music Information Retrieval Evaluation eXchange (MIREX) are also discussed as well as developments in software implementations and the impact of ACE within MIR. We conclude with possible directions for future research.

To assess the performance of an automatic chord estimation system, reference annotations are indispensable. However, owing to the complexity of music and the sometimes ambiguous harmonic structure of polyphonic music, chord annotations are inherently subjective, and as a result any derived accuracy estimates will be subjective as well. In this paper, we investigate the extent of the confounding effect of subjectivity in reference annotations. Our results show that this effect is important, and they affect different types of automatic chord estimation systems in different ways. Our results have implications for research on automatic chord estimation, but also on other fields that evaluate performance by comparing against human provided annotations that are confounded by subjectivity.

We present a new system for the harmonic analysis of popular musical audio. It is focused on chord estimation, although the proposed system additionally estimates the key sequence and bass notes. It is distinct from competing approaches in two main ways. First, it makes use of a new improved chromagram representation of audio that takes the human perception of loudness into account. Furthermore, it is the first system for joint estimation of chords, keys, and bass notes that is fully based on machine learning, requiring no expert knowledge to tune the parameters. This means that it will benefit from future increases in available annotated audio files, broadening its applicability to a wider range of genres. In all of three evaluation scenarios, including a new one that allows evaluation on audio for which no complete ground truth annotation is available, the proposed system is shown to be faster, more memory efficient, and more accurate than the state-of-the-art.

We describe the design of an autonomous agent that can teach itself how to translate from a foreign language, by first assembling its own training set, then using it to improve its vocabulary and language model. The key idea is that a Statistical Mac

Statistical assessment of the results of data mining is increasingly recognised as a core task in the knowledge discovery process. It is of key importance in practice, as results that might seem interesting at first glance can often be explained by well-known basic properties of the data. In pattern mining, for instance, such trivial results can be so overwhelming in number that filtering them out is a necessity in order to identify the truly interesting patterns. In this paper, we propose an approach for assessing results on real-valued rectangular databases. More specifically, using our analytical model we are able to statistically assess whether or not a discovered structure may be the trivial result of the row and column marginal distributions in the database. Our main approach is to use the Maximum Entropy principle to fit a background model to the data while respecting its marginal distributions. To find these distributions, we employ an MDL based histogram estimator, and we fit these in our model using efficient convex optimization techniques. Subsequently, our model can be used to calculate probabilities directly, as well as to efficiently sample data with the purpose of assessing results by means of empirical hypothesis testing. Notably, our approach is efficient, parameter-free, and naturally deals with missing values. As such, it represents a well-founded alternative to swap randomisation.

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 sub graphs 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.

We formalize the data mining process as a process of information exchange, defined by the following key components. The data miner's state of mind is modeled as a probability distribution, called the background distribution, which represents the uncertainty and misconceptions the data miner has about the data. This model initially incorporates any prior (possibly incorrect) beliefs a data miner has about the data. During the data mining process, properties of the data (to which we refer as patterns) are revealed to the data miner, either in batch, one by one, or even interactively. This acquisition of information in the data mining process is formalized by updates to the background distribution to account for the presence of the found patterns.

Inferring causal networks behind observed data is an active area of research with wide applicability to areas such as epidemiology, microbiology and social science. In particular recent research has focused on identifying how information propagates through the Internet. This research has so far only used temporal features of observations, and while reasonable results have been achieved, there is often further information which can be used.

We present NOAM, an integrated platform for the monitoring and analysis of news media content. NOAM is the data management system behind various applications and scientific studies aiming at modelling the mediasphere. The system is also intended to address the need in the AI community for platforms where various AI technologies are integrated and deployed in the real world. It combines a relational database (DB) with state of the art AI technologies, including data mining, machine learning and natural language processing. These technologies are organised in a robust, distributed architecture of collaborating modules, that are used to populate and annotate the DB. NOAM manages tens of millions of news items in multiple languages, automatically annotating them in order to enable queries based on their semantic properties. The system also includes a unified user interface for interacting with its various modules.

The task of finding informative recurring patterns in data has been central to data mining research since the introduction of the task of frequent itemset mining in [1, 2, 14]. In these seminal papers, the informativeness of a recurring itemset in a binary database was formalized by its support in the database. However, it is now widely recognized that an itemset's support is not the best measure of its informativeness. Furthermore, recent work has highlighted that the support of an itemset is highly susceptible to noise, such that it may be more appropriate to search for itemsets that recur only approximately. In this paper, we present a new measure of informativeness for noisy itemsets in binary databases within the formalism of tiles [6]. We demonstrate the benefits of our new measure by means of experiments on artificial and real-life data, allowing for objective and subjective evaluation.

BACKGROUND: The detection of cis-regulatory modules (CRMs) that mediate transcriptional responses in eukaryotes remains a key challenge in the postgenomic era. A CRM is characterized by a set of co-occurring transcription factor binding sites (TFBS). In silico methods have been developed to search for CRMs by determining the combination of TFBS that are statistically overrepresented in a certain geneset. Most of these methods solve this combinatorial problem by relying on computational intensive optimization methods. As a result their usage is limited to finding CRMs in small datasets (containing a few genes only) and using binding sites for a restricted number of transcription factors (TFs) out of which the optimal module will be selected. RESULTS: We present an itemset mining based strategy for computationally detecting cis-regulatory modules (CRMs) in a set of genes. We tested our method by applying it on a large benchmark data set, derived from a ChIP-Chip analysis and compared its performance with other well known cis-regulatory module detection tools. CONCLUSION: We show that by exploiting the computational efficiency of an itemset mining approach and combining it with a well-designed statistical scoring scheme, we were able to prioritize the biologically valid CRMs in a large set of coregulated genes using binding sites for a large number of potential TFs as input.

SUMMARY: We present CAFE (Computational Analysis of gene Family Evolution), a tool for the statistical analysis of the evolution of the size of gene families. It uses a stochastic birth and death process to model the evolution of gene family sizes over a phylogeny. For a specified phylogenetic tree, and given the gene family sizes in the extant species, CAFE can estimate the global birth and death rate of gene families, infer the most likely gene family size at all internal nodes, identify gene families that have accelerated rates of gain and loss (quantified by a p-value) and identify which branches cause the p-value to be small for significant families. AVAILABILITY: Software is available from http://www.bio.indiana.edu/~hahnlab/Software.html

MOTIVATION: During the past decade, the new focus on genomics has highlighted a particular challenge: to integrate the different views of the genome that are provided by various types of experimental data. RESULTS: This paper describes a computational framework for integrating and drawing inferences from a collection of genome-wide measurements. Each dataset is represented via a kernel function, which defines generalized similarity relationships between pairs of entities, such as genes or proteins. The kernel representation is both flexible and efficient, and can be applied to many different types of data. Furthermore, kernel functions derived from different types of data can be combined in a straightforward fashion. Recent advances in the theory of kernel methods have provided efficient algorithms to perform such combinations in a way that minimizes a statistical loss function. These methods exploit semidefinite programming techniques to reduce the problem of finding optimizing kernel combinations to a convex optimization problem. Computational experiments performed using yeast genome-wide datasets, including amino acid sequences, hydropathy profiles, gene expression data and known protein-protein interactions, demonstrate the utility of this approach. A statistical learning algorithm trained from all of these data to recognize particular classes of proteins--membrane proteins and ribosomal proteins--performs significantly better than the same algorithm trained on any single type of data. AVAILABILITY: Supplementary data at http://noble.gs.washington.edu/proj/sdp-svm

The 2-class transduction problem, as formulated by Vapnik [1], involves finding a separating hyperplane for a labelled data set that is also maximally distant from a given set of unlabelled test points. In this form, the problem has exponential computational complexity in the size of the working set. So far it has been attacked by means of integer programming techniques [2] that do not scale to reasonable problem sizes, or by local search procedures [3]. In this paper we present a relaxation of this task based on semi- definite programming (SDP), resulting in a convex optimization problem that has polynomial complexity in the size of the data set. The results are very encouraging for mid sized data sets, however the cost is still too high for large scale problems, due to the high di- mensional search space. To this end, we restrict the feasible region by introducing an approximation based on solving an eigenproblem. With this approximation, the computational cost of the algorithm is such that problems with more than 1000 points can be treated.