arXiv subjects

Wasim Huleihel

Publications and source records attributed to Wasim Huleihel.

At least 19 recordsLinked to original sources

arXiv2026

Fundamental Limits of Query-Based Subgraph Detection

The planted subgraph detection problem asks whether a random graph contains a hidden structured subgraph. In the classical formulation, the entire adjacency matrix is observed and one distinguishes between an Erd\H{o}s--R\'enyi random graph and one obtained by planting a copy of a prescribed graph inside an Erd\H{o}s--R\'enyi random graph. The statistical and computational limits of this problem under full observation are now well understood, even for arbitrary planted subgraphs. In this paper, we investigate an information-limited version of the problem in which the planted structure is an arbitrary sequence of graphs $\Gamma=(\Gamma_n)_{n\geq1}$, where $\Gamma_n$ is embedded in an ambient graph on $n$ vertices, but the observer does not have access to the full adjacency matrix. Instead, information is acquired through a limited number of non-adaptive edge queries. We study the minimum query complexity required for reliable detection. We derive general information-theoretic lower bounds and complementary algorithmic upper bounds on the query complexity as functions of the query budget and structural properties of the planted graph. The proposed algorithms exploit three distinct structural mechanisms: dense local motifs, high-degree vertices, and global edge density. We establish matching bounds, up to polylogarithmic factors, for several broad families of planted graphs, including clique-like, bounded-cover, and hub-dominated graph classes. Our framework substantially generalizes existing query-complexity results for planted clique and planted dense subgraph models, providing a unified treatment of arbitrary planted subgraphs under restricted graph access.

math.ST↗

arXiv2026

Recovery of Planted Subgraphs

Understanding the fundamental limits of recovering planted subgraphs in random graphs is a central challenge in high-dimensional statistics and theoretical computer science. While existing work has largely focused on special subgraph families such as cliques, bicliques, or dense blocks, the exact recovery of a general planted subgraph in Erd\H{o}s--R\'enyi random graphs remains poorly understood. In this paper, we study the exact recovery of an arbitrary planted subgraph $\Gamma = \Gamma_n$ embedded in a dense Erd\H{o}s--R\'enyi random graph $\mathcal{G}(n,q_n)$, where edges within $\Gamma$ are present independently with probability $p_n > q_n$. Our main results identify sharp conditions under which exact recovery is possible with high probability, and we establish matching lower bounds showing the necessity of these conditions. The resulting statistical threshold is characterized by a new graph-theoretic quantity, which we term the \emph{minimal maximum subgraph density}. This quantity is defined as the maximum subgraph density of the smallest induced balanced subgraph of $\Gamma$. We then turn to the problem of recovery under polynomial-time constraints. We propose a computationally efficient recovery algorithm that applies to arbitrary planted subgraphs and analyze its performance in terms of certain spectral properties of the adjacency matrix. In addition, we derive computational lower bounds for recovery using the low-degree polynomial framework, establishing regimes where recovery is statistically possible but computationally hard. Finally, we consider several extensions of our setting, including recovery in semi-random models and weaker notions of recovery.

cs.IT↗

arXiv2026

Testing for a Hidden Geometry in Random Graphs

We study the problem of detecting a faint geometric signal hidden in an otherwise random graph. Formally, we consider a hypothesis testing problem in which, under the null, the observed graph is an Erd\H{o}s--R\'enyi random graph $\mathcal{G}(n,q)$, while under the alternative a random geometric graph $\mathcal{G}(k,q,d)$ is planted on $k\le n$ vertices. The planted subgraph is generated from independent random points on the unit sphere $\mathbb{S}^{d-1}$, with edges determined by latent geometric proximity and calibrated to have edge density $q$. Our goal is to characterize the statistical and computational limits of detecting this hidden geometry. We derive sharp information-theoretic lower bounds that identify regimes where detection is impossible and provide algorithms that achieve these limits whenever detection is feasible. We further investigate the computational complexity of the problem and determine when efficient polynomial-time tests exist. The model exhibits an \emph{easy--hard--impossible} phase transition: some regimes allow efficient detection, others permit detection only with computationally intractable procedures, and still others render detection impossible even with unlimited computational power. As evidence for the computational barrier, we prove that all low-degree polynomial algorithms fail throughout the conjecturally hard regime, demonstrating a sharp gap between statistical and computational feasibility.

cs.IT↗

arXiv2026

Inhomogeneous Submatrix Detection

In this paper, we study the problem of detecting multiple hidden submatrices in a large Gaussian random matrix when the planted signal is inhomogeneous across entries. Under the null hypothesis, the observed matrix has independent and identically distributed standard normal entries. Under the alternative, there exist several planted submatrices whose entries deviate from the background in one of two ways: in the mean-shift model, planted entries (templates) have nonzero and possibly varying means; in the variance-shift model, planted entries have inflated and possibly varying variances. We consider two placement regimes for the planted submatrices. In the first, the row and column index sets are arbitrary. Motivated by scientific applications, in the second regime the row and column indices are restricted to be consecutive. For both alternatives and both placement regimes, we analyze the statistical limits of detection by proving information-theoretic lower bounds and by designing algorithms that match these bounds up to logarithmic factors, for a wide family of templates.

math.ST↗

arXiv2025

Robust Detection of Planted Subgraphs in Semi-Random Models

Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds. However, most prior work assumes a purely random generative model, making the resulting algorithms potentially fragile in the face of real-world perturbations. In this work, we initiate the study of semi-random models for the planted subgraph detection problem, wherein an adversary is allowed to remove edges outside the planted subgraph before the graph is revealed to the statistician. Crucially, the statistician remains unaware of which edges have been removed, introducing fundamental challenges to the inference task. We establish fundamental statistical limits for detection under this semi-random model, revealing a sharp dichotomy. Specifically, for planted subgraphs with strongly sub-logarithmic maximum density detection becomes information-theoretically impossible in the presence of an adversary-despite being possible for some planted subgraphs in the classical random model. In stark contrast, for subgraphs with super-logarithmic density, the statistical limits remain essentially unchanged; we prove that the optimal (albeit computationally intractable) likelihood ratio test remains robust. Beyond these statistical boundaries, we design a new computationally efficient and robust detection algorithm, and provide rigorous statistical guarantees for its performance. Our results establish the first robust framework for planted subgraph detection and open new directions in the study of semi-random models, computational-statistical trade-offs, and robustness in graph inference problems.

cs.IT↗

arXiv2025

Expectation-maximization for low-SNR multi-reference alignment

We study the multi-reference alignment (MRA) problem of recovering a signal from noisy observations acted on by unknown random circular shifts. While the information-theoretic limits of MRA are well characterized in many settings, the algorithmic behavior at low signal-to-noise ratio (SNR), the regime of practical interest, remains poorly understood. In this paper, we analyze the expectation-maximization (EM) algorithm, a widely used method for MRA, and characterize its convergence dynamics and initialization dependence in the low-SNR limit. On the convergence side, we prove a two-phase phenomenon near the ground truth as $\mathrm{SNR}\to 0$: an initial contraction with error decaying as $\exp(-\, \mathrm{SNR} \cdot t)$ followed by a much slower phase scaling as $\exp(- \,\mathrm{SNR}^2 \cdot t)$, where $t$ is the iteration number. This yields an iteration-complexity lower bound $T \gtrsim \mathrm{SNR}^{-2}$ to reach a small fixed target accuracy, revealing a severe computational bottleneck at low SNR. We also identify a finite-sample instability, which we term \emph{Ghost of Newton}, in which EM initially approaches the ground truth but later diverges, degrading reconstruction quality. On the bias side, we analyze EM in the noise-only setting ($\mathrm{SNR}=0$), a regime referred to as Einstein from Noise, to highlight its pronounced sensitivity to initialization. We prove that the EM map preserves the Fourier phases of the initialization across all iterations, while the corresponding Fourier magnitudes contract toward zero at a slow rate of $(1+T)^{-1/2}$. Consequently, although the amplitudes vanish in the limit of $T \to \infty$ iterations, the reconstructed structure continues to reflect the geometry encoded by the template's Fourier phases. Together, these results expose fundamental computational and initialization-driven limitations of EM for MRA in the low-SNR regime.

eess.SP↗

arXiv2025

Detecting Arbitrary Planted Subgraphs in Random Graphs

The problems of detecting and recovering planted structures/subgraphs in Erd\H{o}s-R\'{e}nyi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an \emph{arbitrary} planted subgraph $\Gamma = \Gamma_n$ in an Erd\H{o}s-R\'{e}nyi random graph $\mathcal{G}(n, q_n)$, where the edge probability within $\Gamma$ is $p_n$. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities $p_n$ and $q_n$ are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting $\Gamma$, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on $\Gamma$ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of $p_n$ and $q_n$ as functions of $n$. Accordingly, we also analyze the sparse regime where $q_n = \Theta(n^{-\alpha})$ and $p_n-q_n =\Theta(q_n)$, with $\alpha\in[0,2]$, as well as the critical regime where $p_n=1-o(1)$ and $q_n = \Theta(n^{-\alpha})$, both of which have been widely studied, for specific choices of $\Gamma$. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus far\textemdash{}and many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of $q_n$.

math.ST↗

arXiv2024

AdaRankGrad: Adaptive Gradient-Rank and Moments for Memory-Efficient LLMs Training and Fine-Tuning

Training and fine-tuning large language models (LLMs) come with challenges related to memory and computational requirements due to the increasing size of the model weights and the optimizer states. Various techniques have been developed to tackle these challenges, such as low-rank adaptation (LoRA), which involves introducing a parallel trainable low-rank matrix to the fixed pre-trained weights at each layer. However, these methods often fall short compared to the full-rank weight training approach, as they restrict the parameter search to a low-rank subspace. This limitation can disrupt training dynamics and require a full-rank warm start to mitigate the impact. In this paper, we introduce a new method inspired by a phenomenon we formally prove: as training progresses, the rank of the estimated layer gradients gradually decreases, and asymptotically approaches rank one. Leveraging this, our approach involves adaptively reducing the rank of the gradients during Adam optimization steps, using an efficient online-updating low-rank projections rule. We further present a randomized SVD scheme for efficiently finding the projection matrix. Our technique enables full-parameter fine-tuning with adaptive low-rank gradient updates, significantly reducing overall memory requirements during training compared to state-of-the-art methods while improving model performance in both pretraining and fine-tuning. Finally, we provide a convergence analysis of our method and demonstrate its merits for training and fine-tuning language and biological foundation models.

cs.LG↗

arXiv2024

Testing Dependency of Weighted Random Graphs

In this paper, we study the task of detecting the edge dependency between two weighted random graphs. We formulate this task as a simple hypothesis testing problem, where under the null hypothesis, the two observed graphs are statistically independent, whereas under the alternative, the edges of one graph are dependent on the edges of a uniformly and randomly vertex-permuted version of the other graph. For general edge-weight distributions, we establish thresholds at which optimal testing becomes information-theoretically possible or impossible, as a function of the total number of nodes in the observed graphs and the generative distributions of the weights. Finally, we identify a statistical-computational gap, and present evidence suggesting that this gap is inherent using the framework of low-degree polynomials.

cs.LG↗

arXiv2024

Sequential Classification of Misinformation

In recent years there have been a growing interest in online auditing of information flow over social networks with the goal of monitoring undesirable effects, such as, misinformation and fake news. Most previous work on the subject, focus on the binary classification problem of classifying information as fake or genuine. Nonetheless, in many practical scenarios, the multi-class/label setting is of particular importance. For example, it could be the case that a social media platform may want to distinguish between ``true", ``partly-true", and ``false" information. Accordingly, in this paper, we consider the problem of online multiclass classification of information flow. To that end, driven by empirical studies on information flow over real-world social media networks, we propose a probabilistic information flow model over graphs. Then, the learning task is to detect the label of the information flow, with the goal of minimizing a combination of the classification error and the detection time. For this problem, we propose two detection algorithms; the first is based on the well-known multiple sequential probability ratio test, while the second is a novel graph neural network based sequential decision algorithm. For both algorithms, we prove several strong statistical guarantees. We also construct a data driven algorithm for learning the proposed probabilistic model. Finally, we test our algorithms over two real-world datasets, and show that they outperform other state-of-the-art misinformation detection algorithms, in terms of detection time and classification error.

cs.LG↗

arXiv2024

Confirmation Bias in Gaussian Mixture Models

Confirmation bias, the tendency to interpret information in a way that aligns with one's preconceptions, can profoundly impact scientific research, leading to conclusions that reflect the researcher's hypotheses even when the observational data do not support them. This issue is especially critical in scientific fields involving highly noisy observations, such as cryo-electron microscopy. This study investigates confirmation bias in Gaussian mixture models. We consider the following experiment: A team of scientists assumes they are analyzing data drawn from a Gaussian mixture model with known signals (hypotheses) as centroids. However, in reality, the observations consist entirely of noise without any informative structure. The researchers use a single iteration of the K-means or expectation-maximization algorithms, two popular algorithms to estimate the centroids. Despite the observations being pure noise, we show that these algorithms yield biased estimates that resemble the initial hypotheses, contradicting the unbiased expectation that averaging these noise observations would converge to zero. Namely, the algorithms generate estimates that mirror the postulated model, although the hypotheses (the presumed centroids of the Gaussian mixture) are not evident in the observations. Specifically, among other results, we prove a positive correlation between the estimates produced by the algorithms and the corresponding hypotheses. We also derive explicit closed-form expressions of the estimates for a finite and infinite number of hypotheses. This study underscores the risks of confirmation bias in low signal-to-noise environments, provides insights into potential pitfalls in scientific methodologies, and highlights the importance of prudent data interpretation.

stat.ML↗

arXiv2024

Learning k-Level Structured Sparse Neural Networks Using Group Envelope Regularization

The extensive need for computational resources poses a significant obstacle to deploying large-scale Deep Neural Networks (DNN) on devices with constrained resources. At the same time, studies have demonstrated that a significant number of these DNN parameters are redundant and extraneous. In this paper, we introduce a novel approach for learning structured sparse neural networks, aimed at bridging the DNN hardware deployment challenges. We develop a novel regularization technique, termed Weighted Group Sparse Envelope Function (WGSEF), generalizing the Sparse Envelop Function (SEF), to select (or nullify) neuron groups, thereby reducing redundancy and enhancing computational efficiency. The method speeds up inference time and aims to reduce memory demand and power consumption, thanks to its adaptability which lets any hardware specify group definitions, such as filters, channels, filter shapes, layer depths, a single parameter (unstructured), etc. The properties of the WGSEF enable the pre-definition of a desired sparsity level to be achieved at the training convergence. In the case of redundant parameters, this approach maintains negligible network accuracy degradation or can even lead to improvements in accuracy. Our method efficiently computes the WGSEF regularizer and its proximal operator, in a worst-case linear complexity relative to the number of group variables. Employing a proximal-gradient-based optimization technique, to train the model, it tackles the non-convex minimization problem incorporating the neural network loss and the WGSEF. Finally, we experiment and illustrate the efficiency of our proposed method in terms of the compression ratio, accuracy, and inference latency.

cs.LG↗

arXiv2024

Detection of Correlated Random Vectors

In this paper, we investigate the problem of deciding whether two standard normal random vectors $\mathsf{X}\in\mathbb{R}^{n}$ and $\mathsf{Y}\in\mathbb{R}^{n}$ are correlated or not. This is formulated as a hypothesis testing problem, where under the null hypothesis, these vectors are statistically independent, while under the alternative, $\mathsf{X}$ and a randomly and uniformly permuted version of $\mathsf{Y}$, are correlated with correlation $ρ$. We analyze the thresholds at which optimal testing is information-theoretically impossible and possible, as a function of $n$ and $ρ$. To derive our information-theoretic lower bounds, we develop a novel technique for evaluating the second moment of the likelihood ratio using an orthogonal polynomials expansion, which among other things, reveals a surprising connection to integer partition functions. We also study a multi-dimensional generalization of the above setting, where rather than two vectors we observe two databases/matrices, and furthermore allow for partial correlations between these two.

cs.IT↗

arXiv2024

Einstein from Noise: Statistical Analysis

``Einstein from noise" (EfN) is a prominent example of the model bias phenomenon: systematic errors in the statistical model that lead to spurious but consistent estimates. In the EfN experiment, one falsely believes that a set of observations contains noisy, shifted copies of a template signal (e.g., an Einstein image), whereas in reality, it contains only pure noise observations. To estimate the signal, the observations are first aligned with the template using cross-correlation, and then averaged. Although the observations contain nothing but noise, it was recognized early on that this process produces a signal that resembles the template signal! This pitfall was at the heart of a central scientific controversy about validation techniques in structural biology. This paper provides a comprehensive statistical analysis of the EfN phenomenon above. We show that the Fourier phases of the EfN estimator (namely, the average of the aligned noise observations) converge to the Fourier phases of the template signal, explaining the observed structural similarity. Additionally, we prove that the convergence rate is inversely proportional to the number of noise observations and, in the high-dimensional regime, to the Fourier magnitudes of the template signal. Moreover, in the high-dimensional regime, the Fourier magnitudes converge to a scaled version of the template signal's Fourier magnitudes. This work not only deepens the theoretical understanding of the EfN phenomenon but also highlights potential pitfalls in template matching techniques and emphasizes the need for careful interpretation of noisy observations across disciplines in engineering, statistics, physics, and biology.

eess.SP↗

arXiv2024

Random Subgraph Detection Using Queries

The planted densest subgraph detection problem refers to the task of testing whether in a given (random) graph there is a subgraph that is unusually dense. Specifically, we observe an undirected and unweighted graph on $n$ vertices. Under the null hypothesis, the graph is a realization of an Erdős-Rényi graph with edge probability (or, density) $q$. Under the alternative, there is a subgraph on $k$ vertices with edge probability $p>q$. The statistical as well as the computational barriers of this problem are well-understood for a wide range of the edge parameters $p$ and $q$. In this paper, we consider a natural variant of the above problem, where one can only observe a relatively small part of the graph using adaptive edge queries. For this model, we determine the number of queries necessary and sufficient (accompanied with a quasi-polynomial optimal algorithm) for detecting the presence of the planted subgraph. We also propose a polynomial-time algorithm which is able to detect the planted subgraph, albeit with more queries compared to the above lower bound. We conjecture that in the leftover regime, no polynomial-time algorithms exist. Our results resolve two open questions posed in the past literature.

cs.DS↗

arXiv2024

Planted Bipartite Graph Detection

We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erdős-Rényi random graph over $n$ vertices with edge density $q$. Under the alternative, there exists a planted $k_{\mathsf{R}} \times k_{\mathsf{L}}$ bipartite subgraph with edge density $p>q$. We characterize the statistical and computational barriers for this problem. Specifically, we derive information-theoretic lower bounds, and design and analyze optimal algorithms matching those bounds, in both the dense regime, where $p,q = Θ\left(1\right)$, and the sparse regime where $p,q = Θ\left(n^{-α}\right), α\in \left(0,2\right]$. We also consider the problem of testing in polynomial-time. As is customary in similar structured high-dimensional problems, our model undergoes an "easy-hard-impossible" phase transition and computational constraints penalize the statistical performance. To provide an evidence for this statistical computational gap, we prove computational lower bounds based on the low-degree conjecture, and show that the class of low-degree polynomials algorithms fail in the conjecturally hard region.

cs.DS↗

arXiv2024

Mathematical Framework for Online Social Media Auditing

Social media platforms (SMPs) leverage algorithmic filtering (AF) as a means of selecting the content that constitutes a user's feed with the aim of maximizing their rewards. Selectively choosing the contents to be shown on the user's feed may yield a certain extent of influence, either minor or major, on the user's decision-making, compared to what it would have been under a natural/fair content selection. As we have witnessed over the past decade, algorithmic filtering can cause detrimental side effects, ranging from biasing individual decisions to shaping those of society as a whole, for example, diverting users' attention from whether to get the COVID-19 vaccine or inducing the public to choose a presidential candidate. The government's constant attempts to regulate the adverse effects of AF are often complicated, due to bureaucracy, legal affairs, and financial considerations. On the other hand SMPs seek to monitor their own algorithmic activities to avoid being fined for exceeding the allowable threshold. In this paper, we mathematically formalize this framework and utilize it to construct a data-driven statistical auditing procedure to regulate AF from deflecting users' beliefs over time, along with sample complexity guarantees. This state-of-the-art algorithm can be used either by authorities acting as external regulators or by SMPs for self-auditing.

cs.LG↗

arXiv2023

Deep Learning-Aided Subspace-Based DOA Recovery for Sparse Arrays

Sparse arrays enable resolving more direction of arrivals (DoAs) than antenna elements using non-uniform arrays. This is typically achieved by reconstructing the covariance of a virtual large uniform linear array (ULA), which is then processed by subspace DoA estimators. However, these method assume that the signals are non-coherent and the array is calibrated; the latter often challenging to achieve in sparse arrays, where one cannot access the virtual array elements. In this work, we propose Sparse-SubspaceNet, which leverages deep learning to enable subspace-based DoA recovery from sparse miscallibrated arrays with coherent sources. Sparse- SubspaceNet utilizes a dedicated deep network to learn from data how to compute a surrogate virtual array covariance that is divisible into distinguishable subspaces. By doing so, we learn to cope with coherent sources and miscalibrated sparse arrays, while preserving the interpretability and the suitability of model-based subspace DoA estimators.

eess.SP↗