arXiv subjects

Leonardo Pellegrina

Publications and source records attributed to Leonardo Pellegrina.

11 recordsLinked to original sources

arXiv2026

Few-Shot Resampling for Scalable Statistically-Sound Data Mining

A key step in knowledge discovery is the evaluation of data mining results. In several applications, including pattern mining, graph analysis, and others, this step includes the evaluation of the statistical significance of the results, to avoid spurious discoveries due only to noise or random fluctuations in the data. While specialized procedures have been developed for some specific applications, resampling-based approaches are widely used, in particular for complex analyses where analytical results cannot be derived. However, current resampling-based approaches require the generation and analysis of thousands of resampled datasets, and are therefore impractical for large datasets or computationally intensive analyses. In this paper, we introduce FewRS, a simple and effective resampling-based approach to assess the statistical significance of data mining results with rigorous guarantees on the probability of false discoveries. Our approach can be used in every situation where resampling-based approaches are applied. FewRS builds on our derivation of a novel bound to the supremum deviation of test statistics representing the quality of data mining results. We prove that FewRS needs to generate and analyze an extremely small number of resampled datasets, leading to a highly scalable approach with wide applicability. We test our approach on common tasks such as pattern mining and network analysis. In all cases, our approach results in a reduction of up to two orders of magnitude in running time compared to the state of the art, while preserving high statistical power, enabling the statistical validation of data mining results on large-scale real-world datasets.

cs.LG↗

arXiv2026

Sampling Random Graphs from the Colored Configuration Model

A fundamental step in knowledge discovery is statistically assessing data mining results. In network analysis, such evaluation compares the outcome of a given procedure with the outcomes obtained from randomized versions of the observed network. Despite its importance, available graph null models only preserve simple characteristics of the observed graph, such as its degree sequence. In this paper we introduce the Colored Configuration Model (CCM), a new null model for vertex-colored multigraphs. Our main motivation is the study of online social networks, where the color of a user represents their side in a debate. The key novelty of CCM is preserving the Colored Degree Matrix (CDM), which encodes, for each vertex, the number of neighbors of any given color. Preserving the CDM allows fixing the color assortativity of all nodes, e.g., the propensity of each user to interact with other like-minded users. This allows testing whether a given phenomenon is explained by the observed CDM, or whether other characteristics of the network might play a key role. Available graph null models do not preserve the CDM, so they cannot assess its impact on real-world tasks, such as testing the significance of network polarization measures. To sample from the CCM, we develop Sirius-B, a simple baseline adapting the Metropolis-Hastings approach, and Sirius, a refined algorithm tailored to preserve the CDM, thus achieving provably faster mixing. In our experimental evaluation, we test Sirius on real-world networks, comparing it with related network null models. We observed that the evaluation of the statistical significance of polarization measures with Sirius may lead to different insights compared to available null models. Thus, Sirius is an effective tool for the statistically-sound analysis of social networks.

cs.SI↗

arXiv2025

Fast Percolation Centrality Approximation with Importance Sampling

In this work we present PercIS, an algorithm based on Importance Sampling to approximate the percolation centrality of all the nodes of a graph. Percolation centrality is a generalization of betweenness centrality to attributed graphs, and is a useful measure to quantify the importance of the vertices in a contagious process or to diffuse information. However, it is impractical to compute it exactly on modern-sized networks. First, we highlight key limitations of state-of-the-art sampling-based approximation methods for the percolation centrality, showing that in most cases they cannot achieve accurate solutions efficiently. Then, we propose and analyze a novel sampling algorithm based on Importance Sampling, proving tight sample size bounds to achieve high-quality approximations. Our extensive experimental evaluation shows that PercIS computes high-quality estimates and scales to large real-world networks, while significantly outperforming, in terms of sample sizes, accuracy and running times, the state-of-the-art.

cs.SI↗

arXiv2024

Scalable Rule Lists Learning with Sampling

Learning interpretable models has become a major focus of machine learning research, given the increasing prominence of machine learning in socially important decision-making. Among interpretable models, rule lists are among the best-known and easily interpretable ones. However, finding optimal rule lists is computationally challenging, and current approaches are impractical for large datasets. We present a novel and scalable approach to learn nearly optimal rule lists from large datasets. Our algorithm uses sampling to efficiently obtain an approximation of the optimal rule list with rigorous guarantees on the quality of the approximation. In particular, our algorithm guarantees to find a rule list with accuracy very close to the optimal rule list when a rule list with high accuracy exists. Our algorithm builds on the VC-dimension of rule lists, for which we prove novel upper and lower bounds. Our experimental evaluation on large datasets shows that our algorithm identifies nearly optimal rule lists with a speed-up up to two orders of magnitude over state-of-the-art exact approaches. Moreover, our algorithm is as fast as, and sometimes faster than, recent heuristic approaches, while reporting higher quality rule lists. In addition, the rules reported by our algorithm are more similar to the rules in the optimal rule list than the rules from heuristic approaches.

cs.LG↗

arXiv2024

Efficient Discovery of Significant Patterns with Few-Shot Resampling

Significant pattern mining is a fundamental task in mining transactional data, requiring to identify patterns significantly associated with the value of a given feature, the target. In several applications, such as biomedicine, basket market analysis, and social networks, the goal is to discover patterns whose association with the target is defined with respect to an underlying population, or process, of which the dataset represents only a collection of observations, or samples. A natural way to capture the association of a pattern with the target is to consider its statistical significance, assessing its deviation from the (null) hypothesis of independence between the pattern and the target. While several algorithms have been proposed to find statistically significant patterns, it remains a computationally demanding task, and for complex patterns such as subgroups, no efficient solution exists. We present FSR, an efficient algorithm to identify statistically significant patterns with rigorous guarantees on the probability of false discoveries. FSR builds on a novel general framework for mining significant patterns that captures some of the most commonly considered patterns, including itemsets, sequential patterns, and subgroups. FSR uses a small number of resampled datasets, obtained by assigning i.i.d. labels to each transaction, to rigorously bound the supremum deviation of a quality statistic measuring the significance of patterns. FSR builds on novel tight bounds on the supremum deviation that require to mine a small number of resampled datasets, while providing a high effectiveness in discovering significant patterns. As a test case, we consider significant subgroup mining, and our evaluation on several real datasets shows that FSR is effective in discovering significant subgroups, while requiring a small number of resampled datasets.

cs.LG↗

arXiv2023

Efficient Centrality Maximization with Rademacher Averages

The identification of the set of k most central nodes of a graph, or centrality maximization, is a key task in network analysis, with various applications ranging from finding communities in social and biological networks to understanding which seed nodes are important to diffuse information in a graph. As the exact computation of centrality measures does not scale to modern-sized networks, the most practical solution is to resort to rigorous, but efficiently computable, randomized approximations. In this work we present CentRA, the first algorithm based on progressive sampling to compute high-quality approximations of the set of k most central nodes. CentRA is based on a novel approach to efficiently estimate Monte Carlo Rademacher Averages, a powerful tool from statistical learning theory to compute sharp data-dependent approximation bounds. Then, we study the sample complexity of centrality maximization using the VC-dimension, a key concept from statistical learning theory. We show that the number of random samples required to compute high-quality approximations scales with finer characteristics of the graph, such as its vertex diameter, or of the centrality of interest, significantly improving looser bounds derived from standard techniques. We apply CentRA to analyze large real-world networks, showing that it significantly outperforms the state-of-the-art approximation algorithm in terms of number of samples, running times, and accuracy.

cs.SI↗

arXiv2022

SILVAN: Estimating Betweenness Centralities with Progressive Sampling and Non-uniform Rademacher Bounds

Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high probability, accurate estimates of the betweenness centrality of all nodes of a graph and a high-quality approximation of the top-k betweenness centralities. SILVAN follows a progressive sampling approach, and builds on novel bounds based on Monte-Carlo Empirical Rademacher Averages, a powerful and flexible tool from statistical learning theory. SILVAN relies on a novel estimation scheme providing non-uniform bounds on the deviation of the estimates of the betweenness centrality of all the nodes from their true values, and a refined characterisation of the number of samples required to obtain a high-quality approximation. Our extensive experimental evaluation shows that SILVAN extracts high-quality approximations while outperforming, in terms of number of samples and accuracy, the state-of-the-art approximation algorithm with comparable quality guarantees.

cs.DS↗

arXiv2021

SPRISS: Approximating Frequent $k$-mers by Sampling Reads, and Applications

The extraction of $k$-mers is a fundamental component in many complex analyses of large next-generation sequencing datasets, including reads classification in genomics and the characterization of RNA-seq datasets. The extraction of all $k$-mers and their frequencies is extremely demanding in terms of running time and memory, owing to the size of the data and to the exponential number of $k$-mers to be considered. However, in several applications, only frequent $k$-mers, which are $k$-mers appearing in a relatively high proportion of the data, are required by the analysis. In this work we present SPRISS, a new efficient algorithm to approximate frequent $k$-mers and their frequencies in next-generation sequencing data. SPRISS employs a simple yet powerful reads sampling scheme, which allows to extract a representative subset of the dataset that can be used, in combination with any $k$-mer counting algorithm, to perform downstream analyses in a fraction of the time required by the analysis of the whole data, while obtaining comparable answers. Our extensive experimental evaluation demonstrates the efficiency and accuracy of SPRISS in approximating frequent $k$-mers, and shows that it can be used in various scenarios, such as the comparison of metagenomic datasets and the identification of discriminative $k$-mers, to extract insights in a fraction of the time required by the analysis of the whole dataset.

q-bio.QM↗

arXiv2021

Sharper convergence bounds of Monte Carlo Rademacher Averages through Self-Bounding functions

We derive sharper probabilistic concentration bounds for the Monte Carlo Empirical Rademacher Averages (MCERA), which are proved through recent results on the concentration of self-bounding functions. Our novel bounds are characterized by convergence rates that depend on data-dependent characteristic quantities of the set of functions under consideration, such as the empirical wimpy variance, an essential improvement w.r.t. standard bounds based on the methods of bounded differences. For this reason, our new results are applicable to yield sharper bounds to (Local) Rademacher Averages. We also derive improved novel variance-dependent bounds for the special case where only one vector of Rademacher random variables is used to compute the MCERA, through the application of Bousquet's inequality and novel data-dependent bounds to the wimpy variance. Then, we leverage the framework of self-bounding functions to derive novel probabilistic bounds to the supremum deviations, that may be of independent interest.

cs.LG↗

arXiv2020

MCRapper: Monte-Carlo Rademacher Averages for Poset Families and Approximate Pattern Mining

We present MCRapper, an algorithm for efficient computation of Monte-Carlo Empirical Rademacher Averages (MCERA) for families of functions exhibiting poset (e.g., lattice) structure, such as those that arise in many pattern mining tasks. The MCERA allows us to compute upper bounds to the maximum deviation of sample means from their expectations, thus it can be used to find both statistically-significant functions (i.e., patterns) when the available data is seen as a sample from an unknown distribution, and approximations of collections of high-expectation functions (e.g., frequent patterns) when the available data is a small sample from a large dataset. This feature is a strong improvement over previously proposed solutions that could only achieve one of the two. MCRapper uses upper bounds to the discrepancy of the functions to efficiently explore and prune the search space, a technique borrowed from pattern mining itself. To show the practical use of MCRapper, we employ it to develop an algorithm TFP-R for the task of True Frequent Pattern (TFP) mining. TFP-R gives guarantees on the probability of including any false positives (precision) and exhibits higher statistical power (recall) than existing methods offering the same guarantees. We evaluate MCRapper and TFP-R and show that they outperform the state-of-the-art for their respective tasks.

cs.LG↗

arXiv2019

Fast Approximation of Frequent $k$-mers and Applications to Metagenomics

Estimating the abundances of all $k$-mers in a set of biological sequences is a fundamental and challenging problem with many applications in biological analysis. While several methods have been designed for the exact or approximate solution of this problem, they all require to process the entire dataset, that can be extremely expensive for high-throughput sequencing datasets. While in some applications it is crucial to estimate all $k$-mers and their abundances, in other situations reporting only frequent $k$-mers, that appear with relatively high frequency in a dataset, may suffice. This is the case, for example, in the computation of $k$-mers' abundance-based distances among datasets of reads, commonly used in metagenomic analyses. In this work, we develop, analyze, and test, a sampling-based approach, called SAKEIMA, to approximate the frequent $k$-mers and their frequencies in a high-throughput sequencing dataset while providing rigorous guarantees on the quality of the approximation. SAKEIMA employs an advanced sampling scheme and we show how the characterization of the VC dimension, a core concept from statistical learning theory, of a properly defined set of functions leads to practical bounds on the sample size required for a rigorous approximation. Our experimental evaluation shows that SAKEIMA allows to rigorously approximate frequent $k$-mers by processing only a fraction of a dataset and that the frequencies estimated by SAKEIMA lead to accurate estimates of $k$-mer based distances between high-throughput sequencing datasets. Overall, SAKEIMA is an efficient and rigorous tool to estimate $k$-mers abundances providing significant speed-ups in the analysis of large sequencing datasets.

q-bio.QM↗