arXiv subjects

Malik Magdon-Ismail

Publications and source records attributed to Malik Magdon-Ismail.

At least 19 recordsLinked to original sources

arXiv2026

Tracking and Predicting Evolution of Social Communities

We develop an algorithmic framework for studying the evolution of communities in social networks. We begin with the theoretical foundation, from which we conclude that an evolution is at most as strong as its weakest link. This allows us to formulate an efficient algorithm to identify all evolutionary sequences in a dynamic social network. We use this algorithm to empirically study community evolution in several large social networks, to identify those features of the early stages of a community that indicate whether a community is going to be shortlived or not. Our results show that it is possible to correlate the lifespan of a community to structural parameters of its early evolution; these conclusions are robust across all the social networks we have investigated.

cs.SI↗

arXiv2026

Let's Ask Gauss: Improved One-Run Privacy Auditing

Privacy auditing provides an important safeguard by estimating the actual information leaked by a model, thus ensuring that theoretical privacy guarantees hold in practice. We study empirical privacy auditing for differentially private (DP) machine learning, focusing on efficient one-run methods for mechanisms such as DP-SGD. Prior one-run approaches threshold training examples or "canaries" into binary membership guesses, which discards useful information. We show that, in the white-box DP-SGD setting, canary-aligned signals naturally form a sequence of random variables whose normalized sum is asymptotically Gaussian. Leveraging this distributional perspective, we develop a DP-auditing framework that leads to tighter privacy lower bounds from a single training run.

cs.LG↗

arXiv2026

The Normal Distributions Indistinguishability Spectrum and its Application to Privacy-Preserving Machine Learning

We investigate the privacy of {\em any} algorithm whose outputs have Gaussian distribution. This work is motivated by the prevalence of such algorithms in several useful (ML) applications, and the comparatively little research that focuses on privacy-preserving learning outside of adding Gaussian noise to the data (such as DP-SGD). {\em What is the DP of any algorithm with multivariate Gaussian output?} We answer the above research question with a general lemma which we call {\em Normal Distributions Indistinguishability Spectrum} (NDIS), a closed-form analytic computation of the hockey-stick divergence $δ$ between an arbitrary pair of multivariate Gaussians, parameterized by privacy parameter $ε$. To show its practical implications, we prove several properties of our NDIS lemma. These properties form a {\em toolbox} of results which lead to potentially {\em easier} privacy proofs for any Gaussian-output algorithm. As an example application of our toolbox, we prove a tighter parametrisation of the privacy of {\em random projection (RP)}, and obtaining from it a more noise-frugal DP mechanism. Beyond random projection, NDIS can be used to lift {\em any} Gaussian-output algorithm with a `sensitivity' (which we define) to a Gaussian-output DP mechanism. The mechanism boosts the existing randomness in the algorithm, so that one can describe the mechanism's privacy as the IS between a single pair of Gaussians, which can then be analyzed via NDIS. Lastly, we leverage the connections between NDIS and the CDF of the generalized $χ^2$ distribution (which have efficient empirical estimators) to present a tool for white-box auditing of Gaussian-output algorithms.

cs.CR↗

arXiv2026

WIN-U: Woodbury-Informed Newton-Unlearning as a retain-free Machine Unlearning Framework

Privacy concerns in LLMs have led to the rapidly growing need to enforce a data's "right to be forgotten". Machine unlearning addresses precisely this task, namely the removal of the influence of some specific data, i.e., the forget set, from a trained model. The gold standard for unlearning is to produce the model that would have been learned on only the rest of the training data, i.e., the retain set. Most existing unlearning methods rely on direct access to the retained data, which may not be practical due to privacy or cost constraints. We propose WIN-U, a retained-data free unlearning framework that requires only second order information for the originally trained model on the full data. The unlearning is performed using a single Newton-style step. Using the Woodbury matrix identity and a generalized Gauss-Newton approximation for the forget set curvature, the WIN-U update recovers the closed-form linear solution and serves as a local second-order approximation to the gold-standard retraining optimum. Extensive experiments on various vision and language benchmarks demonstrate that WIN-U achieves SOTA performance in terms of unlearning efficacy and utility preservation, while being more robust against relearning attacks compared to existing methods. Importantly, WIN-U does not require access to the retained data.

cs.LG↗

arXiv2025

Tight Success Probabilities for Quantum Period Finding and Phase Estimation

Period finding and phase estimation are fundamental in quantum computing. Prior work has established lower bounds on their success probabilities. Such quantum algorithms measure a state $|\hat\ell\rangle$ in an $n$-qubit computational basis, $\hat\ell \in [0, 2^n - 1]$, and then post-process this measurement to produce the final output, in the case of period finding, a divisor of the period $r$. We consider a general post-processing algorithm which succeeds whenever the measured $\hat\ell$ is within some tolerance $M$ of a positive integer multiple of $2^n / r$. We give new (tight) lower and upper bounds on the success probability that converge to 1. The parameter $n$ captures the complexity of the quantum circuit. The parameter $M$ can be tuned by varying the post-processing algorithm (e.g., additional brute-force search, lattice methods). Our tight analysis allows for the careful exploitation of the tradeoffs between the complexity of the quantum circuit and the effort spent in classical processing when optimizing the probability of success. We note that the most recent prior work in most recent work does not give tight bounds for general $M$.

quant-ph↗

arXiv2025

Consistent Causal Inference of Group Effects in Non-Targeted Trials with Finitely Many Effect Levels

A treatment may be appropriate for some group (the ``sick" group) on whom it has a positive effect, but it can also have a detrimental effect on subjects from another group (the ``healthy" group). In a non-targeted trial both sick and healthy subjects may be treated, producing heterogeneous effects within the treated group. Inferring the correct treatment effect on the sick population is then difficult, because the effects on the different groups get tangled. We propose an efficient nonparametric approach to estimating the group effects, called {\bf PCM} (pre-cluster and merge). We prove its asymptotic consistency in a general setting and show, on synthetic data, more than a 10x improvement in accuracy over existing state-of-the-art. Our approach applies more generally to consistent estimation of functions with a finite range.

cs.LG↗

arXiv2025

Efficient parameter inference in networked dynamical systems via steady states: A surrogate objective function approach integrating mean-field and nonlinear least squares

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on time-series data, particularly systems that converge over extreme time ranges, only noisy steady-state data is available, requiring a new approach to infer dynamical parameters from noisy observations of steady states. However, the traditional optimization process is computationally demanding, requiring repeated simulation of coupled ordinary differential equations (ODEs). To overcome these limitations, we introduce a surrogate objective function that leverages decoupled equations to compute steady states, significantly reducing computational complexity. Furthermore, by optimizing the surrogate objective function, we obtain steady states that more accurately approximate the ground truth than noisy observations and predict future equilibria when topology changes. We empirically demonstrate the effectiveness of the proposed method across ecological, gene regulatory, and epidemic networks. Our approach provides an efficient and effective way to estimate parameters from steady-state data and has the potential to improve predictions in networked dynamical systems.

nlin.AO↗

arXiv2024

Predicting Time Series of Networked Dynamical Systems without Knowing Topology

Many real-world complex systems, such as epidemic spreading networks and ecosystems, can be modeled as networked dynamical systems that produce multivariate time series. Learning the intrinsic dynamics from observational data is pivotal for forecasting system behaviors and making informed decisions. However, existing methods for modeling networked time series often assume known topologies, whereas real-world networks are typically incomplete or inaccurate, with missing or spurious links that hinder precise predictions. Moreover, while networked time series often originate from diverse topologies, the ability of models to generalize across topologies has not been systematically evaluated. To address these gaps, we propose a novel framework for learning network dynamics directly from observed time-series data, when prior knowledge of graph topology or governing dynamical equations is absent. Our approach leverages continuous graph neural networks with an attention mechanism to construct a latent topology, enabling accurate reconstruction of future trajectories for network states. Extensive experiments on real and synthetic networks demonstrate that our model not only captures dynamics effectively without topology knowledge but also generalizes to unseen time series originating from diverse topologies.

cs.LG↗

arXiv2023

Reduced Label Complexity For Tight $\ell_2$ Regression

Given data ${\rm X}\in\mathbb{R}^{n\times d}$ and labels $\mathbf{y}\in\mathbb{R}^{n}$ the goal is find $\mathbf{w}\in\mathbb{R}^d$ to minimize $\Vert{\rm X}\mathbf{w}-\mathbf{y}\Vert^2$. We give a polynomial algorithm that, \emph{oblivious to $\mathbf{y}$}, throws out $n/(d+\sqrt{n})$ data points and is a $(1+d/n)$-approximation to optimal in expectation. The motivation is tight approximation with reduced label complexity (number of labels revealed). We reduce label complexity by $Ω(\sqrt{n})$. Open question: Can label complexity be reduced by $Ω(n)$ with tight $(1+d/n)$-approximation?

cs.LG↗

arXiv2021

Learning GraphQL Query Costs (Extended Version)

GraphQL is a query language for APIs and a runtime for executing those queries, fetching the requested data from existing microservices, REST APIs, databases, or other sources. Its expressiveness and its flexibility have made it an attractive candidate for API providers in many industries, especially through the web. A major drawback to blindly servicing a client's query in GraphQL is that the cost of a query can be unexpectedly large, creating computation and resource overload for the provider, and API rate-limit overages and infrastructure overload for the client. To mitigate these drawbacks, it is necessary to efficiently estimate the cost of a query before executing it. Estimating query cost is challenging, because GraphQL queries have a nested structure, GraphQL APIs follow different design conventions, and the underlying data sources are hidden. Estimates based on worst-case static query analysis have had limited success because they tend to grossly overestimate cost. We propose a machine-learning approach to efficiently and accurately estimate the query cost. We also demonstrate the power of this approach by testing it on query-response data from publicly available commercial APIs. Our framework is efficient and predicts query costs with high accuracy, consistently outperforming the static analysis by a large margin.

cs.SE↗

arXiv2021

NoisyCUR: An algorithm for two-cost budgeted matrix completion

Matrix completion is a ubiquitous tool in machine learning and data analysis. Most work in this area has focused on the number of observations necessary to obtain an accurate low-rank approximation. In practice, however, the cost of observations is an important limiting factor, and experimentalists may have on hand multiple modes of observation with differing noise-vs-cost trade-offs. This paper considers matrix completion subject to such constraints: a budget is imposed and the experimentalist's goal is to allocate this budget between two sampling modalities in order to recover an accurate low-rank approximation. Specifically, we consider that it is possible to obtain low noise, high cost observations of individual entries or high noise, low cost observations of entire columns. We introduce a regression-based completion algorithm for this setting and experimentally verify the performance of our approach on both synthetic and real data sets. When the budget is low, our algorithm outperforms standard completion algorithms. When the budget is high, our algorithm has comparable error to standard nuclear norm completion algorithms and requires much less computational effort.

cs.LG↗

arXiv2021

An Algorithm for Reconstructing the Orphan Stream Progenitor with MilkyWay@home Volunteer Computing

We have developed a method for estimating the properties of the progenitor dwarf galaxy from the tidal stream of stars that were ripped from it as it fell into the Milky Way. In particular, we show that the mass and radial profile of a progenitor dwarf galaxy evolved along the orbit of the Orphan Stream, including the stellar and dark matter components, can be reconstructed from the distribution of stars in the tidal stream it produced. We use MilkyWay@home, a PetaFLOPS-scale distributed supercomputer, to optimize our dwarf galaxy parameters until we arrive at best-fit parameters. The algorithm fits the dark matter mass, dark matter radius, stellar mass, radial profile of stars, and orbital time. The parameters are recovered even though the dark matter component extends well past the half light radius of the dwarf galaxy progenitor, proving that we are able to extract information about the dark matter halos of dwarf galaxies from the tidal debris. Our simulations assumed that the Milky Way potential, dwarf galaxy orbit, and the form of the density model for the dwarf galaxy were known exactly; more work is required to evaluate the sources of systematic error in fitting real data. This method can be used to estimate the dark matter content in dwarf galaxies without the assumption of virial equilibrium that is required to estimate the mass using line-of-sight velocities. This demonstration is a first step towards building an infrastructure that will fit the Milky Way potential using multiple tidal streams.

astro-ph.GA↗

arXiv2020

Training Deep Neural Networks with Constrained Learning Parameters

Today's deep learning models are primarily trained on CPUs and GPUs. Although these models tend to have low error, they consume high power and utilize large amount of memory owing to double precision floating point learning parameters. Beyond the Moore's law, a significant portion of deep learning tasks would run on edge computing systems, which will form an indispensable part of the entire computation fabric. Subsequently, training deep learning models for such systems will have to be tailored and adopted to generate models that have the following desirable characteristics: low error, low memory, and low power. We believe that deep neural networks (DNNs), where learning parameters are constrained to have a set of finite discrete values, running on neuromorphic computing systems would be instrumental for intelligent edge computing systems having these desirable characteristics. To this extent, we propose the Combinatorial Neural Network Training Algorithm (CoNNTrA), that leverages a coordinate gradient descent-based approach for training deep learning models with finite discrete learning parameters. Next, we elaborate on the theoretical underpinnings and evaluate the computational complexity of CoNNTrA. As a proof of concept, we use CoNNTrA to train deep learning models with ternary learning parameters on the MNIST, Iris and ImageNet data sets and compare their performance to the same models trained using Backpropagation. We use following performance metrics for the comparison: (i) Training error; (ii) Validation error; (iii) Memory usage; and (iv) Training time. Our results indicate that CoNNTrA models use 32x less memory and have errors at par with the Backpropagation models.

cs.LG↗

arXiv2020

A New Mathematical Model for Controlled Pandemics Like COVID-19 : AI Implemented Predictions

We present a new mathematical model to explicitly capture the effects that the three restriction measures: the lockdown date and duration, social distancing and masks, and, schools and border closing, have in controlling the spread of COVID-19 infections $i(r, t)$. Before restrictions were introduced, the random spread of infections as described by the SEIR model grew exponentially. The addition of control measures introduces a mixing of order and disorder in the system's evolution which fall under a different mathematical class of models that can eventually lead to critical phenomena. A generic analytical solution is hard to obtain. We use machine learning to solve the new equations for $i(r,t)$, the infections $i$ in any region $r$ at time $t$ and derive predictions for the spread of infections over time as a function of the strength of the specific measure taken and their duration. The machine is trained in all of the COVID-19 published data for each region, county, state, and country in the world. It utilizes optimization to learn the best-fit values of the model's parameters from past data in each region in the world, and it updates the predicted infections curves for any future restrictions that may be added or relaxed anywhere. We hope this interdisciplinary effort, a new mathematical model that predicts the impact of each measure in slowing down infection spread combined with the solving power of machine learning, is a useful tool in the fight against the current pandemic and potentially future ones.

q-bio.PE↗

arXiv2020

Inferring Degrees from Incomplete Networks and Nonlinear Dynamics

Inferring topological characteristics of complex networks from observed data is critical to understand the dynamical behavior of networked systems, ranging from the Internet and the World Wide Web to biological networks and social networks. Prior studies usually focus on the structure-based estimation to infer network sizes, degree distributions, average degrees, and more. Little effort attempted to estimate the specific degree of each vertex from a sampled induced graph, which prevents us from measuring the lethality of nodes in protein networks and influencers in social networks. The current approaches dramatically fail for a tiny sampled induced graph and require a specific sampling method and a large sample size. These approaches neglect information of the vertex state, representing the dynamical behavior of the networked system, such as the biomass of species or expression of a gene, which is useful for degree estimation. We fill this gap by developing a framework to infer individual vertex degrees using both information of the sampled topology and vertex state. We combine the mean-field theory with combinatorial optimization to learn vertex degrees. Experimental results on real networks with a variety of dynamics demonstrate that our framework can produce reliable degree estimates and dramatically improve existing link prediction methods by replacing the sampled degrees with our estimated degrees.

cs.MA↗

arXiv2020

Machine Learning the Phenomenology of COVID-19 From Early Infection Dynamics

We present a robust data-driven machine learning analysis of the COVID-19 pandemic from its early infection dynamics, specifically infection counts over time. The goal is to extract actionable public health insights. These insights include the infectious force, the rate of a mild infection becoming serious, estimates for asymtomatic infections and predictions of new infections over time. We focus on USA data starting from the first confirmed infection on January 20 2020. Our methods reveal significant asymptomatic (hidden) infection, a lag of about 10 days, and we quantitatively confirm that the infectious force is strong with about a 0.14% transition from mild to serious infection. Our methods are efficient, robust and general, being agnostic to the specific virus and applicable to different populations or cohorts.

q-bio.PE↗

arXiv2020

True Nonlinear Dynamics from Incomplete Networks

We study nonlinear dynamics on complex networks. Each vertex $i$ has a state $x_i$ which evolves according to a networked dynamics to a steady-state $x_i^*$. We develop fundamental tools to learn the true steady-state of a small part of the network, without knowing the full network. A naive approach and the current state-of-the-art is to follow the dynamics of the observed partial network to local equilibrium. This dramatically fails to extract the true steady state. We use a mean-field approach to map the dynamics of the unseen part of the network to a single node, which allows us to recover accurate estimates of steady-state on as few as 5 observed vertices in domains ranging from ecology to social networks to gene regulation. Incomplete networks are the norm in practice, and we offer new ways to think about nonlinear dynamics when only sparse information is available.

cs.SI↗

arXiv2019

Fast Fixed Dimension L2-Subspace Embeddings of Arbitrary Accuracy, With Application to L1 and L2 Tasks

We give a fast oblivious L2-embedding of $A\in \mathbb{R}^{n x d}$ to $B\in \mathbb{R}^{r x d}$ satisfying $(1-\varepsilon)\|A x\|_2^2 \le \|B x\|_2^2 <= (1+\varepsilon) \|Ax\|_2^2.$ Our embedding dimension $r$ equals $d$, a constant independent of the distortion $\varepsilon$. We use as a black-box any L2-embedding $Π^T A$ and inherit its runtime and accuracy, effectively decoupling the dimension $r$ from runtime and accuracy, allowing downstream machine learning applications to benefit from both a low dimension and high accuracy (in prior embeddings higher accuracy means higher dimension). We give applications of our L2-embedding to regression, PCA and statistical leverage scores. We also give applications to L1: 1.) An oblivious L1-embedding with dimension $d+O(d\ln^{1+η} d)$ and distortion $O((d\ln d)/\ln\ln d)$, with application to constructing well-conditioned bases; 2.) Fast approximation of L1-Lewis weights using our L2 embedding to quickly approximate L2-leverage scores.

cs.LG↗