arXiv subjects

Sara Ahmadian

Publications and source records attributed to Sara Ahmadian.

At least 19 recordsLinked to original sources

arXiv2026

Multi-Level Aggregation via Dual Fitting: An $O(D)$-Competitive Algorithm

We present a new online algorithm for the well-known Multi-Level Aggregation Problem (MLAP) with arbitrary delay functions, achieving a $2D$-competitive ratio, where $D$ is the depth of the underlying tree. This result improves the current best-known competitive ratio of $O(D^2)$ and asymptotically matches the $D$-competitive bound previously known only for the deadline variant, thereby closing the asymptotic gap between the two settings. Our key technical contribution is a novel dual fitting framework that provides a unified analysis for both settings; in particular, it also establishes a $D$-competitive ratio for MLAP with deadlines. Our analysis is built upon two new ideas: a hindsight dual construction, which resolves the infeasibility issues in traditional online primal-dual methods, and a time-dependent dual packing that maintains feasibility over dynamic request sets.

cs.DS↗

arXiv2026

Stochastic Matching via Local Sparsification

The classic online stochastic matching problem typically requires immediate and irrevocable matching decisions. However, in many modern decentralized systems such as real-time ride-hailing and distributed cloud computing, the primary bottleneck is often local communication bandwidth rather than the timing of the match itself. We formalize this challenge by introducing a two-stage local sparsification framework. In this setting, arriving requests must prune their realized compatibility sets to a strict budget of $k$ edges before a central coordinator optimizes the global matching. This creates a "middle ground" between local information constraints and global optimization utility. We propose a local selection strategy, parametrized by a fractional solution of the expected instance. Theoretically, we quantify the approximation ratio as a function of the solution's {\em spread}. We prove that under sufficient spread, our sparsifier globally preserves the expected size of the maximum matching. Empirically, we demonstrate the robustness of our approach using the New York City ride-hailing datasets and adversarial synthetic benchmarks. Our results show that near-optimal global matching is achievable even with highly constrained local budgets, significantly outperforming standard online baselines.

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arXiv2025

Generalized Top-k Mallows Model for Ranked Choices

The classic Mallows model is a foundational tool for modeling user preferences. However, it has limitations in capturing real-world scenarios, where users often focus only on a limited set of preferred items and are indifferent to the rest. To address this, extensions such as the top-k Mallows model have been proposed, aligning better with practical applications. In this paper, we address several challenges related to the generalized top-k Mallows model, with a focus on analyzing buyer choices. Our key contributions are: (1) a novel sampling scheme tailored to generalized top-k Mallows models, (2) an efficient algorithm for computing choice probabilities under this model, and (3) an active learning algorithm for estimating the model parameters from observed choice data. These contributions provide new tools for analysis and prediction in critical decision-making scenarios. We present a rigorous mathematical analysis for the performance of our algorithms. Furthermore, through extensive experiments on synthetic data and real-world data, we demonstrate the scalability and accuracy of our proposed methods, and we compare the predictive power of Mallows model for top-k lists compared to the simpler Multinomial Logit model.

cs.LG↗

arXiv2025

GIST: Greedy Independent Set Thresholding for Max-Min Diversification with Submodular Utility

This work studies a novel subset selection problem called max-min diversification with monotone submodular utility ($\textsf{MDMS}$), which has a wide range of applications in machine learning, e.g., data sampling and feature selection. Given a set of points in a metric space, the goal of $\textsf{MDMS}$ is to maximize $f(S) = g(S) + λ\cdot \texttt{div}(S)$ subject to a cardinality constraint $|S| \le k$, where $g(S)$ is a monotone submodular function and $\texttt{div}(S) = \min_{u,v \in S : u \ne v} \text{dist}(u,v)$ is the max-min diversity objective. We propose the $\texttt{GIST}$ algorithm, which gives a $\frac{1}{2}$-approximation guarantee for $\textsf{MDMS}$ by approximating a series of maximum independent set problems with a bicriteria greedy algorithm. We also prove that it is NP-hard to approximate within a factor of $0.5584$. Finally, we show in our empirical study that $\texttt{GIST}$ outperforms state-of-the-art benchmarks for a single-shot data sampling task on ImageNet.

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arXiv2025

The Cost of Compression: Tight Quadratic Black-Box Attacks on Sketches for $\ell_2$ Norm Estimation

Dimensionality reduction via linear sketching is a powerful and widely used technique, but it is known to be vulnerable to adversarial inputs. We study the black-box adversarial setting, where a fixed, hidden sketching matrix $A \in R^{k \times n}$ maps high-dimensional vectors $v \in R^n$ to lower-dimensional sketches $A v \in R^k$, and an adversary can query the system to obtain approximate $\ell_2$-norm estimates that are computed from the sketch. We present a universal, nonadaptive attack that, using $\tilde{O}(k^2)$ queries, either causes a failure in norm estimation or constructs an adversarial input on which the optimal estimator for the query distribution (used by the attack) fails. The attack is completely agnostic to the sketching matrix and to the estimator: it applies to any linear sketch and any query responder, including those that are randomized, adaptive, or tailored to the query distribution. Our lower bound construction tightly matches the known upper bounds of $\tildeΩ(k^2)$, achieved by specialized estimators for Johnson Lindenstrauss transforms and AMS sketches. Beyond sketching, our results uncover structural parallels to adversarial attacks in image classification, highlighting fundamental vulnerabilities of compressed representations.

cs.LG↗

arXiv2024

Diversify and Conquer: Diversity-Centric Data Selection with Iterative Refinement

Finetuning large language models on instruction data is crucial for enhancing pre-trained knowledge and improving instruction-following capabilities. As instruction datasets proliferate, selecting optimal data for effective training becomes increasingly important. This work addresses the question: How can we determine the optimal subset of data for effective training? While existing research often emphasizes local criteria like instance quality for subset selection, we argue that a global approach focused on data diversity is more critical. Our method employs k-means clustering to ensure the selected subset effectively represents the full dataset. We propose an iterative refinement method inspired by active learning techniques to resample instances from clusters, reassessing each cluster's importance and sampling weight in every training iteration. This approach reduces the effect of outliers and automatically filters out clusters containing low-quality data. Through extensive evaluation across natural language reasoning, general world knowledge, code and math reasoning tasks, and by fine-tuning models from various families, we observe consistent improvements, achieving a 7% increase over random selection and a 3.8% improvement over state-of-the-art sampling methods. Our work highlights the significance of diversity-first sampling when finetuning LLMs to enhance performance across a broad array of evaluation tasks. Our code is available at https://github.com/for-ai/iterative-data-selection.

cs.CL↗

arXiv2024

Unmasking Vulnerabilities: Cardinality Sketches under Adaptive Inputs

Cardinality sketches are popular data structures that enhance the efficiency of working with large data sets. The sketches are randomized representations of sets that are only of logarithmic size but can support set merges and approximate cardinality (i.e., distinct count) queries. When queries are not adaptive, that is, they do not depend on preceding query responses, the design provides strong guarantees of correctly answering a number of queries exponential in the sketch size $k$. In this work, we investigate the performance of cardinality sketches in adaptive settings and unveil inherent vulnerabilities. We design an attack against the ``standard'' estimators that constructs an adversarial input by post-processing responses to a set of simple non-adaptive queries of size linear in the sketch size $k$. Empirically, our attack used only $4k$ queries with the widely used HyperLogLog (HLL++)~\citep{hyperloglog:2007,hyperloglogpractice:EDBT2013} sketch. The simple attack technique suggests it can be effective with post-processed natural workloads. Finally and importantly, we demonstrate that the vulnerability is inherent as \emph{any} estimator applied to known sketch structures can be attacked using a number of queries that is quadratic in $k$, matching a generic upper bound.

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arXiv2024

Fair Active Ranking from Pairwise Preferences

We investigate the problem of probably approximately correct and fair (PACF) ranking of items by adaptively evoking pairwise comparisons. Given a set of $n$ items that belong to disjoint groups, our goal is to find an $(ε, δ)$-PACF-Ranking according to a fair objective function that we propose. We assume access to an oracle, wherein, for each query, the learner can choose a pair of items and receive stochastic winner feedback from the oracle. Our proposed objective function asks to minimize the $\ell_q$ norm of the error of the groups, where the error of a group is the $\ell_p$ norm of the error of all the items within that group, for $p, q \geq 1$. This generalizes the objective function of $ε$-Best-Ranking, proposed by Saha & Gopalan (2019). By adopting our objective function, we gain the flexibility to explore fundamental fairness concepts like equal or proportionate errors within a unified framework. Adjusting parameters $p$ and $q$ allows tailoring to specific fairness preferences. We present both group-blind and group-aware algorithms and analyze their sample complexity. We provide matching lower bounds up to certain logarithmic factors for group-blind algorithms. For a restricted class of group-aware algorithms, we show that we can get reasonable lower bounds. We conduct comprehensive experiments on both real-world and synthetic datasets to complement our theoretical findings.

cs.LG↗

arXiv2022

DeMEtRIS: Counting (near)-Cliques by Crawling

We study the problem of approximately counting cliques and near cliques in a graph, where the access to the graph is only available through crawling its vertices; thus typically seeing only a small portion of it. This model, known as the random walk model or the neighborhood query model has been introduced recently and captures real-life scenarios in which the entire graph is too massive to be stored as a whole or be scanned entirely and sampling vertices independently is non-trivial in it. We introduce DeMEtRIS: Dense Motif Estimation through Random Incident Sampling. This method provides a scalable algorithm for clique and near clique counting in the random walk model. We prove the correctness of our algorithm through rigorous mathematical analysis and extensive experiments. Both our theoretical results and our experiments show that DeMEtRIS obtains a high precision estimation by only crawling a sub-linear portion on vertices, thus we demonstrate a significant improvement over previously known results.

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arXiv2022

Improved Approximation for Fair Correlation Clustering

Correlation clustering is a ubiquitous paradigm in unsupervised machine learning where addressing unfairness is a major challenge. Motivated by this, we study Fair Correlation Clustering where the data points may belong to different protected groups and the goal is to ensure fair representation of all groups across clusters. Our paper significantly generalizes and improves on the quality guarantees of previous work of Ahmadi et al. and Ahmadian et al. as follows. - We allow the user to specify an arbitrary upper bound on the representation of each group in a cluster. - Our algorithm allows individuals to have multiple protected features and ensure fairness simultaneously across them all. - We prove guarantees for clustering quality and fairness in this general setting. Furthermore, this improves on the results for the special cases studied in previous work. Our experiments on real-world data demonstrate that our clustering quality compared to the optimal solution is much better than what our theoretical result suggests.

cs.LG↗

arXiv2021

Maximizing Agreements for Ranking, Clustering and Hierarchical Clustering via MAX-CUT

In this paper, we study a number of well-known combinatorial optimization problems that fit in the following paradigm: the input is a collection of (potentially inconsistent) local relationships between the elements of a ground set (e.g., pairwise comparisons, similar/dissimilar pairs, or ancestry structure of triples of points), and the goal is to aggregate this information into a global structure (e.g., a ranking, a clustering, or a hierarchical clustering) in a way that maximizes agreement with the input. Well-studied problems such as rank aggregation, correlation clustering, and hierarchical clustering with triplet constraints fall in this class of problems. We study these problems on stochastic instances with a hidden embedded ground truth solution. Our main algorithmic contribution is a unified technique that uses the maximum cut problem in graphs to approximately solve these problems. Using this technique, we can often get approximation guarantees in the stochastic setting that are better than the known worst case inapproximability bounds for the corresponding problem. On the negative side, we improve the worst case inapproximability bound on several hierarchical clustering formulations through a reduction to related ranking problems.

cs.DS↗

arXiv2020

The Wedge Picking Model: A dynamic graph model based on triadic closure

Social networks have become an inseparable part of human life and processing them in an efficient manner is a top priority in the study of networks. These networks are highly dynamic and they are growing incessantly. Inspired by the concept of triadic closure, we propose a probabilistic mechanism to model the evolution of these dynamic graphs. Although triadic closure is ubiquitous in social networks and its presence helps forming communities, probabilistic models encapsulating it have not been studied adequately. We theoretically analyze our model and show how to bound the growth rate of some characteristics of the graph, such as degree of vertices. Leveraging our theoretical results, we develop a scheduling subroutine to process modifications of the graph in batches. Our scheduling subroutine is then used to speed up the state-of-the-art algorithms with negligible loss in their approximation guarantees. We demonstrate the applicability of our method by applying it to the densest subgraph and tri-densest subgraph discovery problem.

cs.SI↗

arXiv2020

Fair Hierarchical Clustering

As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective.

cs.DS↗

arXiv2020

Fair Correlation Clustering

In this paper, we study correlation clustering under fairness constraints. Fair variants of $k$-median and $k$-center clustering have been studied recently, and approximation algorithms using a notion called fairlet decomposition have been proposed. We obtain approximation algorithms for fair correlation clustering under several important types of fairness constraints. Our results hinge on obtaining a fairlet decomposition for correlation clustering by introducing a novel combinatorial optimization problem. We define a fairlet decomposition with cost similar to the $k$-median cost and this allows us to obtain approximation algorithms for a wide range of fairness constraints. We complement our theoretical results with an in-depth analysis of our algorithms on real graphs where we show that fair solutions to correlation clustering can be obtained with limited increase in cost compared to the state-of-the-art (unfair) algorithms.

cs.DS↗

arXiv2019

Bisect and Conquer: Hierarchical Clustering via Max-Uncut Bisection

Hierarchical Clustering is an unsupervised data analysis method which has been widely used for decades. Despite its popularity, it had an underdeveloped analytical foundation and to address this, Dasgupta recently introduced an optimization viewpoint of hierarchical clustering with pairwise similarity information that spurred a line of work shedding light on old algorithms (e.g., Average-Linkage), but also designing new algorithms. Here, for the maximization dual of Dasgupta's objective (introduced by Moseley-Wang), we present polynomial-time .4246 approximation algorithms that use Max-Uncut Bisection as a subroutine. The previous best worst-case approximation factor in polynomial time was .336, improving only slightly over Average-Linkage which achieves 1/3. Finally, we complement our positive results by providing APX-hardness (even for 0-1 similarities), under the Small Set Expansion hypothesis.

cs.DS↗

arXiv2019

Clustering without Over-Representation

In this paper we consider clustering problems in which each point is endowed with a color. The goal is to cluster the points to minimize the classical clustering cost but with the additional constraint that no color is over-represented in any cluster. This problem is motivated by practical clustering settings, e.g., in clustering news articles where the color of an article is its source, it is preferable that no single news source dominates any cluster. For the most general version of this problem, we obtain an algorithm that has provable guarantees of performance; our algorithm is based on finding a fractional solution using a linear program and rounding the solution subsequently. For the special case of the problem where no color has an absolute majority in any cluster, we obtain a simpler combinatorial algorithm also with provable guarantees. Experiments on real-world data shows that our algorithms are effective in finding good clustering without over-representation.

cs.DS↗

arXiv2017

Further Approximations for Demand Matching: Matroid Constraints and Minor-Closed Graphs

We pursue a study of the Generalized Demand Matching problem, a common generalization of the $b$-Matching and Knapsack problems. Here, we are given a graph with vertex capacities, edge profits, and asymmetric demands on the edges. The goal is to find a maximum-profit subset of edges so the demands of chosen edges do not violate vertex capacities. This problem is APX-hard and constant-factor approximations are known. Our results fall into two categories. First, using iterated relaxation and various filtering strategies, we show with an efficient rounding algorithm if an additional matroid structure $\mathcal M$ is given and we further only allow sets $F \subseteq E$ that are independent in $\mathcal M$, the natural LP relaxation has an integrality gap of at most $\frac{25}{3} \approx 8.333$. This can be improved in various special cases, for example we improve over the 15-approximation for the previously-studied Coupled Placement problem [Korupolu et al. 2014] by giving a $7$-approximation. Using similar techniques, we show the problem of computing a minimum-cost base in $\mathcal M$ satisfying vertex capacities admits a $(1,3)$-bicriteria approximation. This improves over the previous $(1,4)$-approximation in the special case that $\mathcal M$ is the graphic matroid over the given graph [Fukanaga and Nagamochi, 2009]. Second, we show Demand Matching admits a polynomial-time approximation scheme in graphs that exclude a fixed minor. If all demands are polynomially-bounded integers, this is somewhat easy using dynamic programming in bounded-treewidth graphs. Our main technical contribution is a sparsification lemma allowing us to scale the demands to be used in a more intricate dynamic programming algorithm, followed by randomized rounding to filter our scaled-demand solution to a feasible solution.

cs.DS↗

arXiv2017

Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms

Clustering is a classic topic in optimization with $k$-means being one of the most fundamental such problems. In the absence of any restrictions on the input, the best known algorithm for $k$-means with a provable guarantee is a simple local search heuristic yielding an approximation guarantee of $9+ε$, a ratio that is known to be tight with respect to such methods. We overcome this barrier by presenting a new primal-dual approach that allows us to (1) exploit the geometric structure of $k$-means and (2) to satisfy the hard constraint that at most $k$ clusters are selected without deteriorating the approximation guarantee. Our main result is a $6.357$-approximation algorithm with respect to the standard LP relaxation. Our techniques are quite general and we also show improved guarantees for the general version of $k$-means where the underlying metric is not required to be Euclidean and for $k$-median in Euclidean metrics.

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