arXiv subjects

Josée Desharnais

Publications and source records attributed to Josée Desharnais.

7 recordsLinked to original sources

arXiv2025

$ε$-Distance via Lévy-Prokhorov Lifting

The most studied and accepted pseudometric for probabilistic processes is one based on the Kantorovich distance between distributions. It comes with many theoretical and motivating results, in particular it is the fixpoint of a given functional and defines a functor on (complete) pseudometric spaces. Other notions of behavioural pseudometrics have also been proposed, one of them ($ε$-distance) based on $ε$-bisimulation. $ε$-Distance has the advantages that it is intuitively easy to understand, it relates systems that are conceptually close (for example, an imperfect implementation is close to its specification), and it comes equipped with a natural notion of $ε$-coupling. Finally, this distance is easy to compute. We show that $ε$-distance is also the greatest fixpoint of a functional and provides a functor. The latter is obtained by replacing the Kantorovich distance in the lifting functor with the Lévy-Prokhorov distance. In addition, we show that $ε$-couplings and $ε$-bisimulations have an appealing coalgebraic characterization.

cs.LO↗

arXiv2024

GRAND : Graph Reconstruction from potential partial Adjacency and Neighborhood Data

Cryptographic approaches, such as secure multiparty computation, can be used to compute in a secure manner the function of a distributed graph without centralizing the data of each participant. However, the output of the protocol itself can leak sensitive information about the structure of the original graph. In particular, in this work we propose an approach by which an adversary observing the result of a private protocol for the computation of the number of common neighbors between all pairs of vertices, can reconstruct the adjacency matrix of the graph. In fact, this can only be done up to co-squareness, a notion we introduce, as two different graphs can have the same matrix of common neighbors. We consider two models of adversary, one who observes the common neighbors matrix only, and a knowledgeable one, that has a partial knowledge of the original graph. Our results demonstrate that secure multiparty protocols are not enough for privacy protection, especially in the context of highly structured data such as graphs. The reconstruction that we propose is interesting in itself from the point of view of graph theory.

cs.CR↗

arXiv2023

Out-of-distribution detection for regression tasks: parameter versus predictor entropy

It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task consists of learning a diversity of predictors that all can explain the training data. This information can be used to estimate the epistemic uncertainty at a given newly observed instance in terms of a measure of the disagreement of the predictions. Evaluation and certification of the ability of a method to detect OOD require specifying instances which are likely to occur in deployment yet on which no prediction is available. Focusing on regression tasks, we choose a simple yet insightful model for this OOD distribution and conduct an empirical evaluation of the ability of various methods to discriminate OOD samples from the data. Moreover, we exhibit evidence that a diversity of parameters may fail to translate to a diversity of predictors. Based on the choice of an OOD distribution, we propose a new way of estimating the entropy of a distribution on predictors based on nearest neighbors in function space. This leads to a variational objective which, combined with the family of distributions given by a generative neural network, systematically produces a diversity of predictors that provides a robust way to detect OOD samples.

cs.LG↗

arXiv2022

Unsupervised User-Based Insider Threat Detection Using Bayesian Gaussian Mixture Models

Insider threats are a growing concern for organizations due to the amount of damage that their members can inflict by combining their privileged access and domain knowledge. Nonetheless, the detection of such threats is challenging, precisely because of the ability of the authorized personnel to easily conduct malicious actions and because of the immense size and diversity of audit data produced by organizations in which the few malicious footprints are hidden. In this paper, we propose an unsupervised insider threat detection system based on audit data using Bayesian Gaussian Mixture Models. The proposed approach leverages a user-based model to optimize specific behaviors modelization and an automatic feature extraction system based on Word2Vec for ease of use in a real-life scenario. The solution distinguishes itself by not requiring data balancing nor to be trained only on normal instances, and by its little domain knowledge required to implement. Still, results indicate that the proposed method competes with state-of-the-art approaches, presenting a good recall of 88\%, accuracy and true negative rate of 93%, and a false positive rate of 6.9%. For our experiments, we used the benchmark dataset CERT version 4.2.

cs.CR↗

arXiv2020

General Cops and Robbers Games with randomness

Cops and Robbers games have been studied for the last few decades in computer science and mathematics. As in general pursuit evasion games, pursuers (cops) seek to capture evaders (robbers); however, players move in turn and are constrained to move on a discrete structure, usually a graph, and know the exact location of their opponent. In 2017, Bonato and MacGillivray presented a general characterization of Cops and Robbers games in order for them to be globally studied. However, their model doesn't cover cases where stochastic events may occur, such as the robbers moving in a random fashion. In this paper we present a novel model with stochastic elements that we call a Generalized Probabilistic Cops and Robbers game (GPCR). A typical such game is one where the robber moves according to a probabilistic distribution, either because she is rather lost or drunk than evading, or because she is a robot. We present results to solve GPCR games, thus enabling one to study properties relating to the optimal strategies in large classes of Cops and Robbers games. Some classic Cops and Robbers games properties are also extended.

cs.DM↗

arXiv2011

Computing Distances between Probabilistic Automata

We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical characterisations of these notions by choosing suitable logics which differ from the elementary ones, L with negation and L without negation, by the modal operator. Using flow networks, we show how to compute the relations in PTIME. This allows the definition of an efficiently computable non-discounted distance between the states of a PA. A natural modification of this distance is introduced, to obtain a discounted distance, which weakens the influence of long term transitions. We compare our notions of distance to others previously defined and illustrate our approach on various examples. We also show that our distance is not expansive with respect to process algebra operators. Although L without negation is a suitable logic to characterise epsilon-(bi)simulation on deterministic PAs, it is not for general PAs; interestingly, we prove that it does characterise weaker notions, called a priori epsilon-(bi)simulation, which we prove to be NP-difficult to decide.

cs.FL↗

arXiv2011

Analysis of Non-Linear Probabilistic Hybrid Systems

This paper shows how to compute, for probabilistic hybrid systems, the clock approximation and linear phase-portrait approximation that have been proposed for non probabilistic processes by Henzinger et al. The techniques permit to define a rectangular probabilistic process from a non rectangular one, hence allowing the model-checking of any class of systems. Clock approximation, which applies under some restrictions, aims at replacing a non rectangular variable by a clock variable. Linear phase-approximation applies without restriction and yields an approximation that simulates the original process. The conditions that we need for probabilistic processes are the same as those for the classic case.

cs.LO↗