Aristides Gionis

Erica Coppolillo, Giuseppe Manco, Aristides Gionis

Providing recommendations that are both relevant and diverse is a key consideration of modern recommender systems. Optimizing both of these measures presents a fundamental trade-off, as higher diversity typically comes at the cost of relevance, resulting in lower user engagement. Existing recommendation algorithms try to resolve this trade-off by combining the two measures, relevance and diversity, into one aim and then seeking recommendations that optimize the combined objective, for a given number of items to recommend. Traditional approaches, however, do not consider the user interaction with the recommended items. In this paper, we put the user at the central stage, and build on the interplay between relevance, diversity, and user behavior. In contrast to applications where the goal is solely to maximize engagement, we focus on scenarios aiming at maximizing the total amount of knowledge encountered by the user. We use diversity as a surrogate of the amount of knowledge obtained by the user while interacting with the system, and we seek to maximize diversity. We propose a probabilistic user-behavior model in which users keep interacting with the recommender system as long as they receive relevant recommendations, but they may stop if the relevance of the recommended items drops. Thus, for a recommender system to achieve a high-diversity measure, it will need to produce recommendations that are both relevant and diverse. Finally, we propose a novel recommendation strategy that combines relevance and diversity by a copula function. We conduct an extensive evaluation of the proposed methodology over multiple datasets, and we show that our strategy outperforms several state-of-the-art competitors. Our implementation is publicly available at https://github.com/EricaCoppolillo/EXPLORE.

Guangyi Zhang, Aristides Gionis

Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART, rely on impurity-reduction functions that promote the discriminative power of each split. Thus, although these traditional methods are accurate in practice, there has been no theoretical guarantee that they will produce small trees. In this paper, we justify the use of a general family of impurity functions, including the popular functions of entropy and Gini-index, in scenarios where small trees are desirable, by showing that a simple enhancement can equip them with complexity guarantees. We consider a general setting, where objects to be classified are drawn from an arbitrary probability distribution, classification can be binary or multi-class, and splitting tests are associated with non-uniform costs. As a measure of tree complexity, we adopt the expected cost to classify an object drawn from the input distribution, which, in the uniform-cost case, is the expected number of tests. We propose a tree-induction algorithm that gives a logarithmic approximation guarantee on the tree complexity. This approximation factor is tight up to a constant factor under mild assumptions. The algorithm recursively selects a test that maximizes a greedy criterion defined as a weighted sum of three components. The first two components encourage the selection of tests that improve the balance and the cost-efficiency of the tree, respectively, while the third impurity-reduction component encourages the selection of more discriminative tests. As shown in our empirical evaluation, compared to the original heuristics, the enhanced algorithms strike an excellent balance between predictive accuracy and tree complexity.

Federico Cinus, Aristides Gionis, Francesco Bonchi

Social media have great potential for enabling public discourse on important societal issues. However, adverse effects, such as polarization and echo chambers, greatly impact the benefits of social media and call for algorithms that mitigate these effects. In this paper, we propose a novel problem formulation aimed at slightly nudging users' social feeds in order to strike a balance between relevance and diversity, thus mitigating the emergence of polarization, without lowering the quality of the feed. Our approach is based on re-weighting the relative importance of the accounts that a user follows, so as to calibrate the frequency with which the content produced by various accounts is shown to the user. We analyze the convexity properties of the problem, demonstrating the non-matrix convexity of the objective function and the convexity of the feasible set. To efficiently address the problem, we develop a scalable algorithm based on projected gradient descent. We also prove that our problem statement is a proper generalization of the undirected-case problem so that our method can also be adopted for undirected social networks. As a baseline for comparison in the undirected case, we develop a semidefinite programming approach, which provides the optimal solution. Through extensive experiments on synthetic and real-world datasets, we validate the effectiveness of our approach, which outperforms non-trivial baselines, underscoring its ability to foster healthier and more cohesive online communities.

Sijing Tu, Stefan Neumann, Aristides Gionis

In recent years, online social networks have been the target of adversaries who seek to introduce discord into societies, to undermine democracies and to destabilize communities. Often the goal is not to favor a certain side of a conflict but to increase disagreement and polarization. To get a mathematical understanding of such attacks, researchers use opinion-formation models from sociology, such as the Friedkin--Johnsen model, and formally study how much discord the adversary can produce when altering the opinions for only a small set of users. In this line of work, it is commonly assumed that the adversary has full knowledge about the network topology and the opinions of all users. However, the latter assumption is often unrealistic in practice, where user opinions are not available or simply difficult to estimate accurately. To address this concern, we raise the following question: Can an attacker sow discord in a social network, even when only the network topology is known? We answer this question affirmatively. We present approximation algorithms for detecting a small set of users who are highly influential for the disagreement and polarization in the network. We show that when the adversary radicalizes these users and if the initial disagreement/polarization in the network is not very high, then our method gives a constant-factor approximation on the setting when the user opinions are known. To find the set of influential users, we provide a novel approximation algorithm for a variant of MaxCut in graphs with positive and negative edge weights. We experimentally evaluate our methods, which have access only to the network topology, and we find that they have similar performance as methods that have access to the network topology and all user opinions. We further present an NP-hardness proof, which was an open question by Chen and Racz [IEEE Trans. Netw. Sci. Eng., 2021].

Bruno Ordozgoiti, Antonis Matakos, Aristides Gionis

In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are helpful in revealing column subsets to approximately factorize a matrix with quality guarantees. As such, they provide a solid foundation for a variety of machine-learning methods. In this paper we extend the definition of leverage scores to relate the columns of a matrix to arbitrary subsets of singular vectors. We establish a precise connection between column and singular-vector subsets, by relating the concepts of leverage scores and principal angles between subspaces. We employ this result to design approximation algorithms with provable guarantees for two well-known problems: generalized column subset selection and sparse canonical correlation analysis. We run numerical experiments to provide further insight on the proposed methods. The novel bounds we derive improve our understanding of fundamental concepts in matrix approximations. In addition, our insights may serve as building blocks for further contributions.

Guangyi Zhang, Nikolaj Tatti, Aristides Gionis

Submodular maximization has been the backbone of many important machine-learning problems, and has applications to viral marketing, diversification, sensor placement, and more. However, the study of maximizing submodular functions has mainly been restricted in the context of selecting a set of items. On the other hand, many real-world applications require a solution that is a ranking over a set of items. The problem of ranking in the context of submodular function maximization has been considered before, but to a much lesser extent than item-selection formulations. In this paper, we explore a novel formulation for ranking items with submodular valuations and budget constraints. We refer to this problem as max-submodular ranking (MSR). In more detail, given a set of items and a set of non-decreasing submodular functions, where each function is associated with a budget, we aim to find a ranking of the set of items that maximizes the sum of values achieved by all functions under the budget constraints. For the MSR problem with cardinality- and knapsack-type budget constraints we propose practical algorithms with approximation guarantees. In addition, we perform an empirical evaluation, which demonstrates the superior performance of the proposed algorithms against strong baselines.

Yifei Jin, Marios Daoutis, Sarunas Girdzijauskas et al.

Cellular coverage quality estimation has been a critical task for self-organized networks. In real-world scenarios, deep-learning-powered coverage quality estimation methods cannot scale up to large areas due to little ground truth can be provided during network design & optimization. In addition they fall short in produce expressive embeddings to adequately capture the variations of the cells' configurations. To deal with this challenge, we formulate the task in a graph representation and so that we can apply state-of-the-art graph neural networks, that show exemplary performance. We propose a novel training framework that can both produce quality cell configuration embeddings for estimating multiple KPIs, while we show it is capable of generalising to large (area-wide) scenarios given very few labeled cells. We show that our framework yields comparable accuracy with models that have been trained using massively labeled samples.

Martino Ciaperoni, Han Xiao, Aristides Gionis

Multi-label classification is becoming increasingly ubiquitous, but not much attention has been paid to interpretability. In this paper, we develop a multi-label classifier that can be represented as a concise set of simple "if-then" rules, and thus, it offers better interpretability compared to black-box models. Notably, our method is able to find a small set of relevant patterns that lead to accurate multi-label classification, while existing rule-based classifiers are myopic and wasteful in searching rules,requiring a large number of rules to achieve high accuracy. In particular, we formulate the problem of choosing multi-label rules to maximize a target function, which considers not only discrimination ability with respect to labels, but also diversity. Accounting for diversity helps to avoid redundancy, and thus, to control the number of rules in the solution set. To tackle the said maximization problem we propose a 2-approximation algorithm, which relies on a novel technique to sample high-quality rules. In addition to our theoretical analysis, we provide a thorough experimental evaluation, which indicates that our approach offers a trade-off between predictive performance and interpretability that is unmatched in previous work.

Yifei Jin, Marios Daoutis, Sarunas Girdzijauskas et al.

Accurate routing network status estimation is a key component in Software Defined Networking. However, existing deep-learning-based methods for modeling network routing are not able to extrapolate towards unseen feature distributions. Nor are they able to handle scaled and drifted network attributes in test sets that include open-world inputs. To deal with these challenges, we propose a novel approach for modeling network routing, using Graph Neural Networks. Our method can also be used for network-latency estimation. Supported by a domain-knowledge-assisted graph formulation, our model shares a stable performance across different network sizes and configurations of routing networks, while at the same time being able to extrapolate towards unseen sizes, configurations, and user behavior. We show that our model outperforms most conventional deep-learning-based models, in terms of prediction accuracy, computational resources, inference speed, as well as ability to generalize towards open-world input.

Honglian Wang, Haoyun Chen, Aristides Gionis

Link-analysis algorithms, such as PageRank, are instrumental in understanding the structural dynamics of networks by evaluating the importance of individual vertices based on their connectivity. Recently, with the rising importance of responsible AI, the question of fairness in link-analysis algorithms has gained traction. In this paper, we present a new approach for incorporating group fairness into the PageRank algorithm by reweighting the transition probabilities in the underlying transition matrix. We formulate the problem of achieving fair PageRank by seeking to minimize the fairness loss, which is the difference between the original group-wise PageRank distribution and a target PageRank distribution. We further define a group-adapted fairness notion, which accounts for group homophily by considering random walks with group-biased restart for each group. Since the fairness loss is non-convex, we propose an efficient projected gradient-descent method for computing locally-optimal edge weights. Unlike earlier approaches, we do not recommend adding new edges to the network, nor do we adjust the restart vector. Instead, we keep the topology of the underlying network unchanged and only modify the relative importance of existing edges. We empirically compare our approach with state-of-the-art baselines and demonstrate the efficacy of our method, where very small changes in the transition matrix lead to significant improvement in the fairness of the PageRank algorithm.

Guangyi Zhang, Lutz Oettershagen, Lixu Wang et al.

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled frameworks for fair data valuation; however, they suffer from exponential computational complexity. We address this challenge by developing efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers. We first establish the theoretical hardness of the problem by proving that it is \#P-hard. Despite this intractability, we exploit the locality properties of $k$NN classifiers to develop practical exact algorithms. Our main contribution is a dynamic programming framework that achieves significant computational improvements: we present a pseudo-polynomial algorithm with $O(Wkn^2)$ time complexity for weighted $k$NN classifiers, where $W$ is the maximum sum of top-$k$ weights, and a specialized algorithm for unweighted $k$NN that achieves $O(nk^2)$ time complexity, that is, linear in the number of data points. We also offer efficient Monte Carlo estimation methods. Extensive experiments on real-world datasets demonstrate the practical efficiency of our approach and its effectiveness in data valuation applications.

Ameet Gadekar, Aristides Gionis, Thibault Marette

Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information. In addition to seeking a high-quality solution for the task at hand, it is also crucial to ensure consistency by minimizing drastic changes from previous solutions. Applying this approach across many iterations, ensures that the solution evolves gradually and smoothly. In this paper, we study the above problem in the context of clustering, specifically focusing on the $k$-center problem. More precisely, we study the following problem: Given a set of points $X$, parameters $k$ and $b$, and a prior clustering solution $H$ for $X$, our goal is to compute a new solution $C$ for $X$, consisting of $k$ centers, which minimizes the clustering cost while introducing at most $b$ changes from $H$. We refer to this problem as label-consistent $k$-center, and we propose two constant-factor approximation algorithms for it. We complement our theoretical findings with an experimental evaluation demonstrating the effectiveness of our methods on real-world datasets.

Ameet Gadekar, Aristides Gionis, Suhas Thejaswi

Data summarization tasks are often modeled as $k$-clustering problems, where the goal is to choose $k$ data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to minimize the maximum distance between any data point and its nearest center, which is formalized as the $k$-center problem. While in some applications all data points can be chosen as centers, in the general setting, centers must be chosen from a predefined subset of points, referred as facilities or suppliers; this is known as the $k$-supplier problem. In this work, we focus on fair data summarization modeled as the fair $k$-supplier problem, where data consists of several groups, and a minimum number of centers must be selected from each group while minimizing the $k$-supplier objective. The groups can be disjoint or overlapping, leading to two distinct problem variants each with different computational complexity. We present $3$-approximation algorithms for both variants, improving the previously known factor of $5$. For disjoint groups, our algorithm runs in polynomial time, while for overlapping groups, we present a fixed-parameter tractable algorithm, where the exponential runtime depends only on the number of groups and centers. We show that these approximation factors match the theoretical lower bounds, assuming standard complexity theory conjectures. Finally, using an open-source implementation, we demonstrate the scalability of our algorithms on large synthetic datasets and assess the price of fairness on real-world data, comparing solution quality with and without fairness constraints.

Suhas Thejaswi, Ameet Gadekar, Bruno Ordozgoiti et al.

In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from each group should be within the range defined by a lower and upper bound threshold for each group, while simultaneously minimizing the clustering objective, which can be either $k$-median, $k$-means or $k$-supplier. We study the computational complexity of the proposed problems, offering insights into their NP-hardness, polynomial-time inapproximability, and fixed-parameter intractability. We present parameterized approximation algorithms with approximation ratios $1+ \frac{2}{e} + ε\approx 1.736$, $1+\frac{8}{e} + ε\approx 3.943$, and $5$ for diversity-aware $k$-median, diversity-aware $k$-means and diversity-aware $k$-supplier, respectively. Assuming Gap-ETH, the approximation ratios are tight for the diversity-aware $k$-median and diversity-aware $k$-means problems. Our results imply the same approximation factors for their respective fair variants with disjoint groups -- fair $k$-median, fair $k$-means, and fair $k$-supplier -- with lower bound requirements.

Martino Ciaperoni, Han Xiao, Aristides Gionis

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation of a learning task. An emerging paradigm in interpretable machine learning aims at exploring the Rashomon set of all models exhibiting near-optimal performance. Existing work on Rashomon-set exploration focuses on exhaustive search of the Rashomon set for particular classes of models, which can be a computationally challenging task. On the other hand, exhaustive enumeration leads to redundancy that often is not necessary, and a representative sample or an estimate of the size of the Rashomon set is sufficient for many applications. In this work, we propose, for the first time, efficient methods to explore the Rashomon set of rule set models with or without exhaustive search. Extensive experiments demonstrate the effectiveness of the proposed methods in a variety of scenarios.

Ruo-Chun Tzeng, Po-An Wang, Florian Adriaens et al.

Computing the top eigenvectors of a matrix is a problem of fundamental interest to various fields. While the majority of the literature has focused on analyzing the reconstruction error of low-rank matrices associated with the retrieved eigenvectors, in many applications one is interested in finding one vector with high Rayleigh quotient. In this paper we study the problem of approximating the top-eigenvector. Given a symmetric matrix $\mathbf{A}$ with largest eigenvalue $λ_1$, our goal is to find a vector \hu that approximates the leading eigenvector $\mathbf{u}_1$ with high accuracy, as measured by the ratio $R(\hat{\mathbf{u}})=λ_1^{-1}{\hat{\mathbf{u}}^T\mathbf{A}\hat{\mathbf{u}}}/{\hat{\mathbf{u}}^T\hat{\mathbf{u}}}$. We present a novel analysis of the randomized SVD algorithm of \citet{halko2011finding} and derive tight bounds in many cases of interest. Notably, this is the first work that provides non-trivial bounds of $R(\hat{\mathbf{u}})$ for randomized SVD with any number of iterations. Our theoretical analysis is complemented with a thorough experimental study that confirms the efficiency and accuracy of the method.

Guangyi Zhang, Aristides Gionis

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability of models has been recognized as an equally important quality as their predictive power. In particular, rule-based systems are experiencing a renaissance owing to their intuitive if-then representation. However, simply being rule-based does not ensure interpretability. For example, overlapped rules spawn ambiguity and hinder interpretation. Here we propose a novel approach of inferring diverse rule sets, by optimizing small overlap among decision rules with a 2-approximation guarantee under the framework of Max-Sum diversification. We formulate the problem as maximizing a weighted sum of discriminative quality and diversity of a rule set. In order to overcome an exponential-size search space of association rules, we investigate several natural options for a small candidate set of high-quality rules, including frequent and accurate rules, and examine their hardness. Leveraging the special structure in our formulation, we then devise an efficient randomized algorithm, which samples rules that are highly discriminative and have small overlap. The proposed sampling algorithm analytically targets a distribution of rules that is tailored to our objective. We demonstrate the superior predictive power and interpretability of our model with a comprehensive empirical study against strong baselines.

Han Xiao, Bruno Ordozgoiti, Aristides Gionis

Signed graphs have been used to model interactions in social net-works, which can be either positive (friendly) or negative (antagonistic). The model has been used to study polarization and other related phenomena in social networks, which can be harmful to the process of democratic deliberation in our society. An interesting and challenging task in this application domain is to detect polarized communities in signed graphs. A number of different methods have been proposed for this task. However, existing approaches aim at finding globally optimal solutions. Instead, in this paper we are interested in finding polarized communities that are related to a small set of seed nodes provided as input. Seed nodes may consist of two sets, which constitute the two sides of a polarized structure. In this paper we formulate the problem of finding local polarized communities in signed graphs as a locally-biased eigen-problem. By viewing the eigenvector associated with the smallest eigenvalue of the Laplacian matrix as the solution of a constrained optimization problem, we are able to incorporate the local information as an additional constraint. In addition, we show that the locally-biased vector can be used to find communities with approximation guarantee with respect to a local analogue of the Cheeger constant on signed graphs. By exploiting the sparsity in the input graph, an indicator vector for the polarized communities can be found in time linear to the graph size. Our experiments on real-world networks validate the proposed algorithm and demonstrate its usefulness in finding local structures in this semi-supervised manner.

Suhas Thejaswi, Aristides Gionis, Juho Lauri

We study a family of pattern-detection problems in vertex-colored temporal graphs. In particular, given a vertex-colored temporal graph and a multiset of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query. These types of problems have several applications, for example in recommending tours for tourists or detecting abnormal behavior in a network of financial transactions. For the family of pattern-detection problems we consider, we establish complexity results and design an algebraic-algorithmic framework based on constrained multilinear sieving. We demonstrate that our solution scales to massive graphs with up to a billion edges for a multiset query with five colors and up to hundred million edges for a multiset query with ten colors, despite the problems being NP-hard. Our implementation, which is publicly available, exhibits practical edge-linear scalability and is highly optimized. For instance, in a real-world graph dataset with more than six million edges and a multiset query with ten colors, we can extract an optimum solution in less than eight minutes on a Haswell desktop with four cores.

Nikolaj Tatti, Taneli Mielikainen, Aristides Gionis et al.

Many 0/1 datasets have a very large number of variables; on the other hand, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust measure of dimension for 0/1 datasets, and show that the basic idea of fractal dimension can be adapted for binary data. However, as such the fractal dimension is difficult to interpret. Hence we introduce the concept of normalized fractal dimension. For a dataset $D$, its normalized fractal dimension is the number of columns in a dataset $D'$ with independent columns and having the same (unnormalized) fractal dimension as $D$. The normalized fractal dimension measures the degree of dependency structure of the data. We study the properties of the normalized fractal dimension and discuss its computation. We give empirical results on the normalized fractal dimension, comparing it against baseline measures such as PCA. We also study the relationship of the dimension of the whole dataset and the dimensions of subgroups formed by clustering. The results indicate interesting differences between and within datasets.

Isak Karlsson, Jonathan Rebane, Panagiotis Papapetrou et al.

Time series classification has received great attention over the past decade with a wide range of methods focusing on predictive performance by exploiting various types of temporal features. Nonetheless, little emphasis has been placed on interpretability and explainability. In this paper, we formulate the novel problem of explainable time series tweaking, where, given a time series and an opaque classifier that provides a particular classification decision for the time series, we want to find the minimum number of changes to be performed to the given time series so that the classifier changes its decision to another class. We show that the problem is NP-hard, and focus on two instantiations of the problem, which we refer to as reversible and irreversible time series tweaking. The classifier under investigation is the random shapelet forest classifier. Moreover, we propose two algorithmic solutions for the two problems along with simple optimizations, as well as a baseline solution using the nearest neighbor classifier. An extensive experimental evaluation on a variety of real datasets demonstrates the usefulness and effectiveness of our problem formulation and solutions.

Ehsan Amid, Aristides Gionis, Antti Ukkonen

We consider the problem of metric learning subject to a set of constraints on relative-distance comparisons between the data items. Such constraints are meant to reflect side-information that is not expressed directly in the feature vectors of the data items. The relative-distance constraints used in this work are particularly effective in expressing structures at finer level of detail than must-link (ML) and cannot-link (CL) constraints, which are most commonly used for semi-supervised clustering. Relative-distance constraints are thus useful in settings where providing an ML or a CL constraint is difficult because the granularity of the true clustering is unknown. Our main contribution is an efficient algorithm for learning a kernel matrix using the log determinant divergence --- a variant of the Bregman divergence --- subject to a set of relative-distance constraints. The learned kernel matrix can then be employed by many different kernel methods in a wide range of applications. In our experimental evaluations, we consider a semi-supervised clustering setting and show empirically that kernels found by our algorithm yield clusterings of higher quality than existing approaches that either use ML/CL constraints or a different means to implement the supervision using relative comparisons.

Eric Malmi, Pyry Takala, Hannu Toivonen et al.

Writing rap lyrics requires both creativity to construct a meaningful, interesting story and lyrical skills to produce complex rhyme patterns, which form the cornerstone of good flow. We present a rap lyrics generation method that captures both of these aspects. First, we develop a prediction model to identify the next line of existing lyrics from a set of candidate next lines. This model is based on two machine-learning techniques: the RankSVM algorithm and a deep neural network model with a novel structure. Results show that the prediction model can identify the true next line among 299 randomly selected lines with an accuracy of 17%, i.e., over 50 times more likely than by random. Second, we employ the prediction model to combine lines from existing songs, producing lyrics with rhyme and a meaning. An evaluation of the produced lyrics shows that in terms of quantitative rhyme density, the method outperforms the best human rappers by 21%. The rap lyrics generator has been deployed as an online tool called DeepBeat, and the performance of the tool has been assessed by analyzing its usage logs. This analysis shows that machine-learned rankings correlate with user preferences.