arXiv subjects

Wasim Huleihel

Publications and source records attributed to Wasim Huleihel.

At least 37 records · Page 2Linked to original sources

arXiv2023

Testing Dependency of Unlabeled Databases

In this paper, we investigate the problem of deciding whether two random databases $\mathsf{X}\in\mathcal{X}^{n\times d}$ and $\mathsf{Y}\in\mathcal{Y}^{n\times d}$ are statistically dependent or not. This is formulated as a hypothesis testing problem, where under the null hypothesis, these two databases are statistically independent, while under the alternative, there exists an unknown row permutation $σ$, such that $\mathsf{X}$ and $\mathsf{Y}^σ$, a permuted version of $\mathsf{Y}$, are statistically dependent with some known joint distribution, but have the same marginal distributions as the null. We characterize the thresholds at which optimal testing is information-theoretically impossible and possible, as a function of $n$, $d$, and some spectral properties of the generative distributions of the datasets. For example, we prove that if a certain function of the eigenvalues of the likelihood function and $d$, is below a certain threshold, as $d\to\infty$, then weak detection (performing slightly better than random guessing) is statistically impossible, no matter what the value of $n$ is. This mimics the performance of an efficient test that thresholds a centered version of the log-likelihood function of the observed matrices. We also analyze the case where $d$ is fixed, for which we derive strong (vanishing error) and weak detection lower and upper bounds.

cs.LG↗

arXiv2023

Online Auditing of Information Flow

Modern social media platforms play an important role in facilitating rapid dissemination of information through their massive user networks. Fake news, misinformation, and unverifiable facts on social media platforms propagate disharmony and affect society. In this paper, we consider the problem of online auditing of information flow/propagation with the goal of classifying news items as fake or genuine. Specifically, driven by experiential studies on real-world social media platforms, we propose a probabilistic Markovian information spread model over networks modeled by graphs. We then formulate our inference task as a certain sequential detection problem with the goal of minimizing the combination of the error probability and the time it takes to achieve correct decision. For this model, we find the optimal detection algorithm minimizing the aforementioned risk and prove several statistical guarantees. We then test our algorithm over real-world datasets. To that end, we first construct an offline algorithm for learning the probabilistic information spreading model, and then apply our optimal detection algorithm. Experimental study show that our algorithm outperforms state-of-the-art misinformation detection algorithms in terms of accuracy and detection time.

cs.LG↗

arXiv2023

Detection and Recovery of Hidden Submatrices

In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the planted matrices are disjoint, and their row and column indices can be arbitrary. Inspired by scientific applications, the second model restricts the row and column indices to be consecutive. In the detection problem, under the null hypothesis, the observed matrix is a realization of independent and identically distributed standard normal entries. Under the alternative, there exists a set of hidden submatrices with elevated means inside the same standard normal matrix. Recovery refers to the task of locating the hidden submatrices. For both problems, and for both models, we characterize the statistical and computational barriers by deriving information-theoretic lower bounds, designing and analyzing algorithms matching those bounds, and proving computational lower bounds based on the low-degree polynomials conjecture. In particular, we show that the space of the model parameters (i.e., number of planted submatrices, their dimensions, and elevated mean) can be partitioned into three regions: the impossible regime, where all algorithms fail; the hard regime, where while detection or recovery are statistically possible, we give some evidence that polynomial-time algorithm do not exist; and finally the easy regime, where polynomial-time algorithms exist.

cs.IT↗

arXiv2023

Phase Transitions in the Detection of Correlated Databases

We study the problem of detecting the correlation between two Gaussian databases $\mathsf{X}\in\mathbb{R}^{n\times d}$ and $\mathsf{Y}^{n\times d}$, each composed of $n$ users with $d$ features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation $σ$ over the set of $n$ users (or, row permutation), such that $\mathsf{X}$ is $ρ$-correlated with $\mathsf{Y}^σ$, a permuted version of $\mathsf{Y}$. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of $n$ and $d$. Specifically, we prove that if $ρ^2d\to0$, as $d\to\infty$, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of $n$. This compliments the performance of a simple test that thresholds the sum all entries of $\mathsf{X}^T\mathsf{Y}$. Furthermore, when $d$ is fixed, we prove that strong detection (vanishing error probability) is impossible for any $ρ<ρ^\star$, where $ρ^\star$ is an explicit function of $d$, while weak detection is again impossible as long as $ρ^2d\to0$. These results close significant gaps in current recent related studies.

cs.LG↗

arXiv2022

Optimal Reference for DNA Synthesis

In the recent years, DNA has emerged as a potentially viable storage technology. DNA synthesis, which refers to the task of writing the data into DNA, is perhaps the most costly part of existing storage systems. Accordingly, this high cost and low throughput limits the practical use in available DNA synthesis technologies. It has been found that the homopolymer run (i.e., the repetition of the same nucleotide) is a major factor affecting the synthesis and sequencing errors. Quite recently, [26] studied the role of batch optimization in reducing the cost of large scale DNA synthesis, for a given pool $\mathcal{S}$ of random quaternary strings of fixed length. Among other things, it was shown that the asymptotic cost savings of batch optimization are significantly greater when the strings in $\mathcal{S}$ contain repeats of the same character (homopolymer run of length one), as compared to the case where strings are unconstrained. Following the lead of [26], in this paper, we take a step forward towards the theoretical understanding of DNA synthesis, and study the homopolymer run of length $k\geq1$. Specifically, we are given a set of DNA strands $\mathcal{S}$, randomly drawn from a natural Markovian distribution modeling a general homopolymer run length constraint, that we wish to synthesize. For this problem, we prove that for any $k\geq 1$, the optimal reference strand, minimizing the cost of DNA synthesis is, perhaps surprisingly, the periodic sequence $\overline{\mathsf{ACGT}}$. It turns out that tackling the homopolymer constraint of length $k\geq2$ is a challenging problem; our main technical contribution is the representation of the DNA synthesis process as a certain constrained system, for which string techniques can be applied.

cs.IT↗

arXiv2022

Inferring Hidden Structures in Random Graphs

We study the two inference problems of detecting and recovering an isolated community of \emph{general} structure planted in a random graph. The detection problem is formalized as a hypothesis testing problem, where under the null hypothesis, the graph is a realization of an Erdős-Rényi random graph $\mathcal{G}(n,q)$ with edge density $q\in(0,1)$; under the alternative, there is an unknown structure $Γ_k$ on $k$ nodes, planted in $\mathcal{G}(n,q)$, such that it appears as an \emph{induced subgraph}. In case of a successful detection, we are concerned with the task of recovering the corresponding structure. For these problems, we investigate the fundamental limits from both the statistical and computational perspectives. Specifically, we derive lower bounds for detecting/recovering the structure $Γ_k$ in terms of the parameters $(n,k,q)$, as well as certain properties of $Γ_k$, and exhibit computationally unbounded optimal algorithms that achieve these lower bounds. We also consider the problem of testing in polynomial-time. As is customary in many similar structured high-dimensional problems, our model undergoes an "easy-hard-impossible" phase transition and computational constraints can severely penalize the statistical performance. To provide an evidence for this phenomenon, we show that the class of low-degree polynomials algorithms match the statistical performance of the polynomial-time algorithms we develop.

cs.DS↗

arXiv2021

Fuzzy Clustering with Similarity Queries

The fuzzy or soft $k$-means objective is a popular generalization of the well-known $k$-means problem, extending the clustering capability of the $k$-means to datasets that are uncertain, vague, and otherwise hard to cluster. In this paper, we propose a semi-supervised active clustering framework, where the learner is allowed to interact with an oracle (domain expert), asking for the similarity between a certain set of chosen items. We study the query and computational complexities of clustering in this framework. We prove that having a few of such similarity queries enables one to get a polynomial-time approximation algorithm to an otherwise conjecturally NP-hard problem. In particular, we provide algorithms for fuzzy clustering in this setting that asks $O(\mathsf{poly}(k)\log n)$ similarity queries and run with polynomial-time-complexity, where $n$ is the number of items. The fuzzy $k$-means objective is nonconvex, with $k$-means as a special case, and is equivalent to some other generic nonconvex problem such as non-negative matrix factorization. The ubiquitous Lloyd-type algorithms (or alternating minimization algorithms) can get stuck at a local minimum. Our results show that by making a few similarity queries, the problem becomes easier to solve. Finally, we test our algorithms over real-world datasets, showing their effectiveness in real-world applications.

cs.LG↗

arXiv2021

Variability in mRNA Translation: A Random Matrix Theory Approach

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

q-bio.SC↗

arXiv2021

Learning User Preferences in Non-Stationary Environments

Recommendation systems often use online collaborative filtering (CF) algorithms to identify items a given user likes over time, based on ratings that this user and a large number of other users have provided in the past. This problem has been studied extensively when users' preferences do not change over time (static case); an assumption that is often violated in practical settings. In this paper, we introduce a novel model for online non-stationary recommendation systems which allows for temporal uncertainties in the users' preferences. For this model, we propose a user-based CF algorithm, and provide a theoretical analysis of its achievable reward. Compared to related non-stationary multi-armed bandit literature, the main fundamental difficulty in our model lies in the fact that variations in the preferences of a certain user may affect the recommendations for other users severely. We also test our algorithm over real-world datasets, showing its effectiveness in real-world applications. One of the main surprising observations in our experiments is the fact our algorithm outperforms other static algorithms even when preferences do not change over time. This hints toward the general conclusion that in practice, dynamic algorithms, such as the one we propose, might be beneficial even in stationary environments.

cs.LG↗

arXiv2020

Centralized vs Decentralized Targeted Brute-Force Attacks: Guessing with Side-Information

According to recent empirical studies, a majority of users have the same, or very similar, passwords across multiple password-secured online services. This practice can have disastrous consequences, as one password being compromised puts all the other accounts at much higher risk. Generally, an adversary may use any side-information he/she possesses about the user, be it demographic information, password reuse on a previously compromised account, or any other relevant information to devise a better brute-force strategy (so called targeted attack). In this work, we consider a distributed brute-force attack scenario in which $m$ adversaries, each observing some side information, attempt breaching a password secured system. We compare two strategies: an uncoordinated attack in which the adversaries query the system based on their own side-information until they find the correct password, and a fully coordinated attack in which the adversaries pool their side-information and query the system together. For passwords $\mathbf{X}$ of length $n$, generated independently and identically from a distribution $P_X$, we establish an asymptotic closed-form expression for the uncoordinated and coordinated strategies when the side-information $\mathbf{Y}_{(m)}$ are generated independently from passing $\mathbf{X}$ through a memoryless channel $P_{Y|X}$, as the length of the password $n$ goes to infinity. We illustrate our results for binary symmetric channels and binary erasure channels, two families of side-information channels which model password reuse. We demonstrate that two coordinated agents perform asymptotically better than any finite number of uncoordinated agents for these channels, meaning that sharing side-information is very valuable in distributed attacks.

cs.IT↗

arXiv2020

Sharp Thresholds of the Information Cascade Fragility Under a Mismatched Model

We analyze a sequential decision making model in which decision makers (or, players) take their decisions based on their own private information as well as the actions of previous decision makers. Such decision making processes often lead to what is known as the \emph{information cascade} or \emph{herding} phenomenon. Specifically, a cascade develops when it seems rational for some players to abandon their own private information and imitate the actions of earlier players. The risk, however, is that if the initial decisions were wrong, then the whole cascade will be wrong. Nonetheless, information cascade are known to be fragile: there exists a sequence of \emph{revealing} probabilities $\{p_{\ell}\}_{\ell\geq1}$, such that if with probability $p_{\ell}$ player $\ell$ ignores the decisions of previous players, and rely on his private information only, then wrong cascades can be avoided. Previous related papers which study the fragility of information cascades always assume that the revealing probabilities are known to all players perfectly, which might be unrealistic in practice. Accordingly, in this paper we study a mismatch model where players believe that the revealing probabilities are $\{q_\ell\}_{\ell\in\mathbb{N}}$ when they truly are $\{p_\ell\}_{\ell\in\mathbb{N}}$, and study the effect of this mismatch on information cascades. We consider both adversarial and probabilistic sequential decision making models, and derive closed-form expressions for the optimal learning rates at which the error probability associated with a certain decision maker goes to zero. We prove several novel phase transitions in the behaviour of the asymptotic learning rate.

cs.LG↗

arXiv2019

Reducibility and Computational Lower Bounds for Problems with Planted Sparse Structure

The prototypical high-dimensional statistics problem entails finding a structured signal in noise. Many of these problems exhibit an intriguing phenomenon: the amount of data needed by all known computationally efficient algorithms far exceeds what is needed for inefficient algorithms that search over all possible structures. A line of work initiated by Berthet and Rigollet in 2013 has aimed to explain these statistical-computational gaps by reducing from conjecturally hard average-case problems in computer science. However, the delicate nature of average-case reductions has limited the applicability of this approach. In this work we introduce several new techniques to give a web of average-case reductions showing strong computational lower bounds based on the planted clique conjecture using natural problems as intermediates. These include tight lower bounds for Planted Independent Set, Planted Dense Subgraph, Sparse Spiked Wigner, Sparse PCA, a subgraph variant of the Stochastic Block Model and a biased variant of Sparse PCA. We also give algorithms matching our lower bounds and identify the information-theoretic limits of the models we consider.

cs.CC↗

arXiv2019

Same-Cluster Querying for Overlapping Clusters

Overlapping clusters are common in models of many practical data-segmentation applications. Suppose we are given $n$ elements to be clustered into $k$ possibly overlapping clusters, and an oracle that can interactively answer queries of the form "do elements $u$ and $v$ belong to the same cluster?" The goal is to recover the clusters with minimum number of such queries. This problem has been of recent interest for the case of disjoint clusters. In this paper, we look at the more practical scenario of overlapping clusters, and provide upper bounds (with algorithms) on the sufficient number of queries. We provide algorithmic results under both arbitrary (worst-case) and statistical modeling assumptions. Our algorithms are parameter free, efficient, and work in the presence of random noise. We also derive information-theoretic lower bounds on the number of queries needed, proving that our algorithms are order optimal. Finally, we test our algorithms over both synthetic and real-world data, showing their practicality and effectiveness.

cs.LG↗

arXiv2019

Why Botnets Work: Distributed Brute-Force Attacks Need No Synchronization

In September 2017, McAffee Labs quarterly report estimated that brute force attacks represent 20\% of total network attacks, making them the most prevalent type of attack ex-aequo with browser based vulnerabilities. These attacks have sometimes catastrophic consequences, and understanding their fundamental limits may play an important role in the risk assessment of password-secured systems, and in the design of better security protocols. While some solutions exist to prevent online brute-force attacks that arise from one single IP address, attacks performed by botnets are more challenging. In this paper, we analyze these distributed attacks by using a simplified model. Our aim is to understand the impact of distribution and asynchronization on the overall computational effort necessary to breach a system. Our result is based on Guesswork, a measure of the number of queries (guesses) required of an adversary before a correct sequence, such as a password, is found in an optimal attack. Guesswork is a direct surrogate for time and computational effort of guessing a sequence from a set of sequences with associated likelihoods. We model the lack of synchronization by a worst-case optimization in which the queries made by multiple adversarial agents are received in the worst possible order for the adversary, resulting in a min-max formulation. We show that, even without synchronization, and for sequences of growing length, the asymptotic optimal performance is achievable by using randomized guesses drawn from an appropriate distribution. Therefore, randomization is key for distributed asynchronous attacks. In other words, asynchronous guessers can asymptotically perform brute-force attacks as efficiently as synchronized guessers.

cs.IT↗

arXiv2019

Universality of Computational Lower Bounds for Submatrix Detection

In the general submatrix detection problem, the task is to detect the presence of a small $k \times k$ submatrix with entries sampled from a distribution $\mathcal{P}$ in an $n \times n$ matrix of samples from $\mathcal{Q}$. This formulation includes a number of well-studied problems, such as biclustering when $\mathcal{P}$ and $\mathcal{Q}$ are Gaussians and the planted dense subgraph formulation of community detection when the submatrix is a principal minor and $\mathcal{P}$ and $\mathcal{Q}$ are Bernoulli random variables. These problems all seem to exhibit a universal phenomenon: there is a statistical-computational gap depending on $\mathcal{P}$ and $\mathcal{Q}$ between the minimum $k$ at which this task can be solved and the minimum $k$ at which it can be solved in polynomial time. Our main result is to tightly characterize this computational barrier as a tradeoff between $k$ and the KL divergences between $\mathcal{P}$ and $\mathcal{Q}$ through average-case reductions from the planted clique conjecture. These computational lower bounds hold given mild assumptions on $\mathcal{P}$ and $\mathcal{Q}$ arising naturally from classical binary hypothesis testing. Our results recover and generalize the planted clique lower bounds for Gaussian biclustering in Ma-Wu (2015) and Brennan et al. (2018) and for the sparse and general regimes of planted dense subgraph in Hajek et al. (2015) and Brennan et al. (2018). This yields the first universality principle for computational lower bounds obtained through average-case reductions.

math.ST↗

arXiv2018

Codewords With Memory Improve Achievable Rate Regions of the Memoryless Gaussian Interference Channel

The two-user Gaussian interference channel (GIC) has been extensively studied in the literature during the last four decades. The full characterization of the capacity region of the GIC is a long-standing open problem, except the case of strong or very strong interference. For general GIC's, many inner bounds have been provided over the years, among of them, the Han-Kobayashi (HK) region, is the most celebrated one. Unfortunately, the calculation of the HK region is prohibitively complex, due to the appearance of some auxiliary random variables, whose optimal choice is an open problem. As in other multi-user communication systems, these achievable regions are based on ensembles of i.i.d. (memoryless) codewords, in the sense that the symbols within each codeword are drawn independently. In this paper, we show that for the GIC, it is worthwhile to employ random coding ensembles of codewords with memory. Specifically, we take known achievable regions for the GIC, and generalize/improve them by allowing dependency between the code symbols. For example, we improve the state-of-the-art HK region by drawing the codewords (of each codeword and for each user) from a first-order autoregressive moving average (ARMA) Gaussian process. In this way, we suggest several new achievable rate regions, which are easily calculable, and which are strictly better than state-of-the-art known achievable regions.

cs.IT↗

arXiv2017

Erasure/List Random Coding Error Exponents Are Not Universally Achievable

We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical erasure/list decoder developed in earlier studies, which is based on the competitive minimax methodology, and guarantees universal achievability of a certain fraction of the optimum random coding error exponents. In this paper, we derive an exact single-letter expression for the maximum achievable fraction. Examples are given in which the maximal achievable fraction is strictly less than unity, which imply that, in general, there is no universal erasure/list decoder which achieves the same random coding error exponents as the optimal decoder for a known channel. This is in contrast to the situation in ordinary decoding (without the erasure/list option), where optimum exponents are universally achievable, as is well known. It is also demonstrated that previous lower bounds derived for the maximal achievable fraction are not tight in general. We then analyze a generalized random coding ensemble which incorporate a training sequence, in conjunction with a suboptimal practical decoder ("plug-in" decoder), which first estimates the channel using the known training sequence, and then decodes the remaining symbols of the codeword using the estimated channel. One of the implications of our results, is setting the stage for a reasonable criterion of optimal training. Finally, we compare the performance of the "plug-in" decoder and the universal decoder, in terms of the achievable error exponents, and show that the latter is noticeably better than the former.

cs.IT↗

arXiv2017

Random Coding Error Exponents for the Two-User Interference Channel

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, etc.). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. Also, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles, and find a lower bound on the error exponent associated with the celebrated Han-Kobayashi (HK) random coding ensemble, which is based on superposition coding.

cs.IT↗