arXiv subjects

David Naccache

Publications and source records attributed to David Naccache.

At least 37 records · Page 2Linked to original sources

arXiv2021

Noise-Resilient Ensemble Learning using Evidence Accumulation Clustering

Ensemble Learning methods combine multiple algorithms performing the same task to build a group with superior quality. These systems are well adapted to the distributed setup, where each peer or machine of the network hosts one algorithm and communicate its results to its peers. Ensemble learning methods are naturally resilient to the absence of several peers thanks to the ensemble redundancy. However, the network can be corrupted, altering the prediction accuracy of a peer, which has a deleterious effect on the ensemble quality. In this paper, we propose a noise-resilient ensemble classification method, which helps to improve accuracy and correct random errors. The approach is inspired by Evidence Accumulation Clustering , adapted to classification ensembles. We compared it to the naive voter model over four multi-class datasets. Our model showed a greater resilience, allowing us to recover prediction under a very high noise level. In addition as the method is based on the evidence accumulation clustering, our method is highly flexible as it can combines classifiers with different label definitions.

cs.LG↗

arXiv2021

Tagged Documents Co-Clustering

Tags are short sequences of words allowing to describe textual and non-texual resources such as as music, image or book. Tags could be used by machine information retrieval systems to access quickly a document. These tags can be used to build recommender systems to suggest similar items to a user. However, the number of tags per document is limited, and often distributed according to a Zipf law. In this paper, we propose a methodology to cluster tags into conceptual groups. Data are preprocessed to remove power-law effects and enhance the context of low-frequency words. Then, a hierarchical agglomerative co-clustering algorithm is proposed to group together the most related tags into clusters. The capabilities were evaluated on a sparse synthetic dataset and a real-world tag collection associated with scientific papers. The task being unsupervised, we propose some stopping criterion for selectecting an optimal partitioning.

cs.IR↗

arXiv2021

The Multiplicative Persistence Conjecture Is True for Odd Targets

In 1973, Neil Sloane published a very short paper introducing an intriguing problem: Pick a decimal integer $n$ and multiply all its digits by each other. Repeat the process until a single digit $Δ(n)$ is obtained. $Δ(n)$ is called the \textsl{multiplicative digital root of $n$} or \textsl{the target of $n$}. The number of steps $Ξ(n)$ needed to reach $Δ(n)$, called the multiplicative persistence of $n$ or \textsl{the height of $n$} is conjectured to always be at most $11$. Like many other very simple to state number-theoretic conjectures, the multiplicative persistence mystery resisted numerous explanation attempts. This paper proves that the conjecture holds for all odd target values: Namely that if $Δ(n)\in\{1,3,7,9\}$, then $Ξ(n) \leq 1$ and that if $Δ(n)=5$, then $Ξ(n) \leq 5$. Naturally, we overview the difficulties currently preventing us from extending the approach to (nonzero) even targets.

math.NT↗

arXiv2021

Co-Embedding: Discovering Communities on Bipartite Graphs through Projection

Many datasets take the form of a bipartite graph where two types of nodes are connected by relationships, like the movies watched by a user or the tags associated with a file. The partitioning of the bipartite graph could be used to fasten recommender systems, or reduce the information retrieval system's index size, by identifying groups of items with similar properties. This type of graph is often processed by algorithms using the Vector Space Model representation, where a binary vector represents an item with 0 and 1. The main problem with this representation is the dimension relatedness, like words' synonymity, which is not considered. This article proposes a co-clustering algorithm using items projection, allowing the measurement of features similarity. We evaluated our algorithm on a cluster retrieval task. Over various datasets, our algorithm produced well balanced clusters with coherent items in, leading to high retrieval scores on this task..

cs.IR↗

arXiv2021

Index $t$-SNE: Tracking Dynamics of High-Dimensional Datasets with Coherent Embeddings

$t$-SNE is an embedding method that the data science community has widely Two interesting characteristics of t-SNE are the structure preservation property and the answer to the crowding problem, where all neighbors in high dimensional space cannot be represented correctly in low dimensional space. $t$-SNE preserves the local neighborhood, and similar items are nicely spaced by adjusting to the local density. These two characteristics produce a meaningful representation, where the cluster area is proportional to its size in number, and relationships between clusters are materialized by closeness on the embedding. This algorithm is non-parametric, therefore two initializations of the algorithm would lead to two different embedding. In a forensic approach, analysts would like to compare two or more datasets using their embedding. An approach would be to learn a parametric model over an embedding built with a subset of data. While this approach is highly scalable, points could be mapped at the same exact position, making them indistinguishable. This type of model would be unable to adapt to new outliers nor concept drift. This paper presents a methodology to reuse an embedding to create a new one, where cluster positions are preserved. The optimization process minimizes two costs, one relative to the embedding shape and the second relative to the support embedding' match. The proposed algorithm has the same complexity than the original $t$-SNE to embed new items, and a lower one when considering the embedding of a dataset sliced into sub-pieces. The method showed promising results on a real-world dataset, allowing to observe the birth, evolution and death of clusters. The proposed approach facilitates identifying significant trends and changes, which empowers the monitoring high dimensional datasets' dynamics.

cs.LG↗

arXiv2021

Generating Local Maps of Science using Deep Bibliographic Coupling

Bibliographic and co-citation coupling are two analytical methods widely used to measure the degree of similarity between scientific papers. These approaches are intuitive, easy to put into practice, and computationally cheap. Moreover, they have been used to generate a map of science, allowing visualizing research field interactions. Nonetheless, these methods do not work unless two papers share a standard reference, limiting the two papers usability with no direct connection. In this work, we propose to extend bibliographic coupling to the deep neighborhood, by using graph diffusion methods. This method allows defining similarity between any two papers, making it possible to generate a local map of science, highlighting field organization.

cs.DL↗

arXiv2021

Near-Optimal Pool Testing under Urgency Constraints

Detection of rare traits or diseases in a large population is challenging. Pool testing allows covering larger swathes of population at a reduced cost, while simplifying logistics. However, testing precision decreases as it becomes unclear which member of a pool made the global test positive. In this paper we discuss testing strategies that provably approach best-possible strategy - optimal in the sense that no other strategy can give exact results with fewer tests. Our algorithms guarantee that they provide a complete and exact result for every individual, without exceeding $1/0.99$ times the number of tests the optimal strategy would require. This threshold is arbitrary: algorithms closer to the optimal bound can be described, however their complexity increases, making them less practical. Moreover, the way the algorithms process input samples leads to some individuals' status to be known sooner, thus allowing to take urgency into account when assigning individuals to tests.

cs.IT↗

arXiv2021

Explaining the Entombed Algorithm

In \cite{entombed}, John Aycock and Tara Copplestone pose an open question, namely the explanation of the mysterious lookup table used in the Entombed Game's Algorithm for two dimensional maze generation. The question attracted media attention (BBC etc) and was open until today. This paper answers this question, explains the algorithm and even extends it to three dimensions.

cs.CG↗

arXiv2021

Return-Oriented Programming on RISC-V

This paper provides the first analysis on the feasibility of Return-Oriented Programming (ROP) on RISC-V, a new instruction set architecture targeting embedded systems. We show the existence of a new class of gadgets, using several Linear Code Sequences And Jumps (LCSAJ), undetected by current Galileo-based ROP gadget searching tools. We argue that this class of gadgets is rich enough on RISC-V to mount complex ROP attacks, bypassing traditional mitigation like DEP, ASLR, stack canaries, G-Free, as well as some compiler-based backward-edge CFI, by jumping over any guard inserted by a compiler to protect indirect jump instructions. We provide examples of such gadgets, as well as a proof-of-concept ROP chain, using C code injection to leverage a privilege escalation attack on two standard Linux operating systems. Additionally, we discuss some of the required mitigations to prevent such attacks and provide a new ROP gadget finder algorithm that handles this new class of gadgets.

cs.CR↗

arXiv2021

Convergence Voting: From Pairwise Comparisons to Consensus

An important aspect of AI design and ethics is to create systems that reflect aggregate preferences of the society. To this end, the techniques of social choice theory are often utilized. We propose a new social choice function motivated by the PageRank algorithm. The function ranks voting options based on the Condorcet graph of pairwise comparisons. To this end, we transform the Condorcet graph into a Markov chain whose stationary distribution provides the scores of the options. We show how the values in the stationary distribution can be interpreted as quantified aggregate support for the voting options, to which the community of voters converges through an imaginary sequence of negotiating steps. Because of that, we suggest the name "convergence voting" for the new voting scheme, and "negotiated community support" for the resulting stationary allocation of scores. Our social choice function can be viewed as a consensus voting method, sitting somewhere between Copeland and Borda. On the one hand, it does not necessarily choose the Condorcet winner, as strong support from a part of the society can outweigh mediocre uniform support. On the other hand, the influence of unpopular candidates on the outcome is smaller than in the primary technique of consensus voting, i.e., the Borda count. We achieve that without having to introduce an ad hoc weighting that some other methods do.

cs.MA↗

arXiv2020

Preservation of DNA Privacy During the Large Scale Detection of COVID-19

As humanity struggles to contain the global COVID-19 pandemic, privacy concerns are emerging regarding confinement, tracing and testing. The scientific debate concerning privacy of the COVID-19 tracing efforts has been intense, especially focusing on the choice between centralised and decentralised tracing apps. The privacy concerns regarding COVID-19 testing, however, have not received as much attention even though the privacy at stake is arguably even higher. COVID-19 tests require the collection of samples. Those samples possibly contain viral material but inevitably also human DNA. Patient DNA is not necessary for the test but it is technically impossible to avoid collecting it. The unlawful preservation, or misuse, of such samples at a massive scale may hence disclose patient DNA information with far-reaching privacy consequences. Inspired by the cryptographic concept of "Indistinguishability under Chosen Plaintext Attack", this paper poses the blueprint of novel types of tests allowing to detect viral presence without leaving persisting traces of the patient's DNA. Authors are listed in alphabetical order.

cs.CR↗

arXiv2020

A Fractional $3n+1$ Conjecture

In this paper we introduce and discuss the sequence of \emph{real numbers} defined as $u_0 \in \mathbb R$ and $u_{n+1} = Δ(u_n)$ where \begin{equation*} Δ(x) = \begin{cases} \frac{x}{2} &\text{if } \operatorname{frac}(x)<\frac{1}{2} \\[4px] \frac{3x+1}{2} & \text{if } \operatorname{frac}(x)\geq\frac{1}{2} \end{cases} \end{equation*} This sequence is reminiscent of the famous Collatz sequence, and seems to exhibit an interesting behaviour. Indeed, we conjecture that iterating $Δ$ will eventually either converge to zero, or loop over sequences of real numbers with integer parts $1,2,4,7,11,18,9,4,7,3,5,9,4,7,11,18,9,4,7,3,6,3,1,2,4,7,3,6,3$. We prove this conjecture for $u_0 \in [0, 100]$. Extending the proof to larger fixed values seems to be a matter of computing power. The authors pledge to offer a reward to the first person who proves or refutes the conjecture completely -- with a proof published in a serious refereed mathematical conference or journal.

math.DS↗

arXiv2020

The Look-and-Say The Biggest Sequence Eventually Cycles

In this paper we consider a variant of Conway's sequence (OEIS A005150, A006715) defined as follows: the next term in the sequence is obtained by considering contiguous runs of digits, and rewriting them as $ab$ where $b$ is the digit and $a$ is the maximum of $b$ and the run's length. We dub this the "look-and-say the biggest" (LSB) sequence. Conway's sequence is very similar ($b$ is just the run's length). For any starting value except 22, Conway's sequence grows exponentially: the ration of lengths converges to a known constant $λ$. We show that LSB does not: for every starting value, LSB eventually reaches a cycle. Furthermore, all cycles have a period of at most 9.

math.DS↗

arXiv2020

Stuttering Conway Sequences Are Still Conway Sequences

A look-and-say sequence is obtained iteratively by reading off the digits of the current value, grouping identical digits together: starting with 1, the sequence reads: 1, 11, 21, 1211, 111221, 312211, etc. (OEIS A005150). Starting with any digit $d \neq 1$ gives Conway's sequence: $d$, $1d$, $111d$, $311d$, $13211d$, etc. (OEIS A006715). Conway popularised these sequences and studied some of their properties. In this paper we consider a variant subbed "look-and-say again" where digits are repeated twice. We prove that the look-and-say again sequence contains only the digits $1, 2, 4, 6, d$, where $d$ represents the starting digit. Such sequences decompose and the ratio of successive lengths converges to Conway's constant. In fact, these properties result from a commuting diagram between look-and-say again sequences and "classical" look-and-say sequences. Similar results apply to the "look-and-say three times" sequence.

math.DS↗

arXiv2020

At Most 43 Moves, At Least 29: Optimal Strategies and Bounds for Ultimate Tic-Tac-Toe

Ultimate Tic-Tac-Toe is a variant of the well known tic-tac-toe (noughts and crosses) board game. Two players compete to win three aligned "fields", each of them being a tic-tac-toe game. Each move determines which field the next player must play in. We show that there exist a winning strategy for the first player, and therefore that there exist an optimal winning strategy taking at most 43 moves; that the second player can hold on at least 29 rounds; and identify any optimal strategy's first two moves.

cs.GT↗

arXiv2020

Keyed Non-Parametric Hypothesis Tests

The recent popularity of machine learning calls for a deeper understanding of AI security. Amongst the numerous AI threats published so far, poisoning attacks currently attract considerable attention. In a poisoning attack the opponent partially tampers the dataset used for learning to mislead the classifier during the testing phase. This paper proposes a new protection strategy against poisoning attacks. The technique relies on a new primitive called keyed non-parametric hypothesis tests allowing to evaluate under adversarial conditions the training input's conformance with a previously learned distribution $\mathfrak{D}$. To do so we use a secret key $κ$ unknown to the opponent. Keyed non-parametric hypothesis tests differs from classical tests in that the secrecy of $κ$ prevents the opponent from misleading the keyed test into concluding that a (significantly) tampered dataset belongs to $\mathfrak{D}$.

cs.CR↗

arXiv2020

Optimal Covid-19 Pool Testing with a priori Information

As humanity struggles to contain the global Covid-19 infection, prophylactic actions are grandly slowed down by the shortage of testing kits. Governments have taken several measures to work around this shortage: the FDA has become more liberal on the approval of Covid-19 tests in the US. In the UK emergency measures allowed to increase the daily number of locally produced test kits to 100,000. China has recently launched a massive test manufacturing program. However, all those efforts are very insufficient and many poor countries are still under threat. A popular method for reducing the number of tests consists in pooling samples, i.e. mixing patient samples and testing the mixed samples once. If all the samples are negative, pooling succeeds at a unitary cost. However, if a single sample is positive, failure does not indicate which patient is infected. This paper describes how to optimally detect infected patients in pools, i.e. using a minimal number of tests to precisely identify them, given the a priori probabilities that each of the patients is healthy. Those probabilities can be estimated using questionnaires, supervised machine learning or clinical examinations. The resulting algorithms, which can be interpreted as informed divide-and-conquer strategies, are non-intuitive and quite surprising. They are patent-free. Co-authors are listed in alphabetical order.

cs.AI↗

arXiv2020

Approaching Optimal Duplicate Detection in a Sliding Window

Duplicate detection is the problem of identifying whether a given item has previously appeared in a (possibly infinite) stream of data, when only a limited amount of memory is available. Unfortunately the infinite stream setting is ill-posed, and error rates of duplicate detection filters turn out to be heavily constrained: consequently they appear to provide no advantage, asymptotically, over a biased coin toss [8]. In this paper we formalize the sliding window setting introduced by [13,16], and show that a perfect (zero error) solution can be used up to a maximal window size $w_\text{max}$. Above this threshold we show that some existing duplicate detection filters (designed for the $\textit{non-windowed}$ setting) perform better that those targeting the windowed problem. Finally, we introduce a "queuing construction" that improves on the performance of some duplicate detection filters in the windowed setting. We also analyse the security of our filters in an adversarial setting.

cs.DS↗