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Arash Amini

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11 papers

2 author rows

AAAI Conference 2026 Conference Paper

Exact Combinatorial Multi-Class Graph Cuts for Semi-Supervised Learning

Mohammad Mahdi Omati
Yasin Salajeghe
Mahshad Moradi
Arash Amini

Semi-supervised learning (SSL) on graphs is critical in applications where labeled data are scarce and costly, yet existing graph-based methods often degrade under extreme label sparsity or class imbalance, yielding trivial or unstable solutions. We introduce \textbf{CombCut}, the first exact combinatorial optimization framework for multi-class graph-based semi-supervised learning that operates directly on binary one-hot assignments, without any convex relaxation or heuristic volume constraints. By employing a minorization–maximization (MM) scheme, CombCut transforms each step into a structured linear assignment problem solved efficiently via network-flow algorithms. Total unimodularity guarantees integral iterates, and our theoretical analysis establishes both monotonic ascent of the true discrete objective and convergence of every limit point to a Karush–Kuhn–Tucker (KKT) stationary solution of the original combinatorial problem. Our approach requires no hyperparameter tuning and scales near-linearly in the number of vertices. Empirical evaluation on MNIST, Fashion-MNIST, and CIFAR-10 with as few as 1–5 labels per class shows that CombCut excels in worst-case labeling scenarios, significantly outperforming state-of-the-art graph-SSL baselines and yielding more stable and accurate label propagation under severe supervision constraints.

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NeurIPS Conference 2025 Conference Paper

A CLT for Polynomial GNNs on Community-Based Graphs

Luciano Vinas
Arash Amini

We consider the empirical distribution of the embeddings of a $k$-layer polynomial GNN on a semi-supervised node classification task and prove a central limit theorem for them. Assuming a community based model for the underlying graph, with growing average degree $\nu_n\to\infty$, we show that the empirical distribution of the centered features, when scaled by $\nu_{n}^{k-1/2}$ converge in 1-Wasserstein distance to a centered stable mixture of multivariate normal distributions. In addition, the joint empirical distribution of uncentered features and labels when normalized by $\nu_n^k$ approach that of mixture of multivariate normal distributions, with stable means and covariance matrices vanishing as $\nu_n^{-1}$. We explicitly identify the asymptotic means and covariances, showing that the mixture collapses towards a 1-D version as $k$ is increased. Our results provides a precise and nuanced lens on how oversmoothing presents itself in the large graph limit, in the sparse regime. In particular, we show that training with cross-entropy on these embeddings is asymptotically equivalent to training on these nearly collapsed Gaussian mixtures.

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TMLR Journal 2025 Journal Article

A Max-Min Approach to the Worst-Case Class Separation Problem

Mohammad Mahdi Omati
Prabhu babu
Petre Stoica
Arash Amini

In this paper, we propose a novel discriminative feature learning method based on a minorization-maximization framework for min-max (MM4MM) to address the long-standing “worst-case class separation (WCCS)” problem, which, in our design, refers to maximizing the minimum pairwise Chernoff distance between all class pairs in the low-dimensional subspace. The proposed algorithm relies on the relaxation of a semi-orthogonality constraint, which is proven to be tight at every iteration of the algorithm. To solve the worst-case class separation problem, we first introduce the vanilla version of the proposed algorithm, which requires solving a semi-definite program (SDP) at each iteration. We further simplify it to solving a quadratic program by formulating the dual of the surrogate maximization problem. We also then present reformulations of the worst-case class separation problem that enforce sparsity of the dimension-reducing matrix. The proposed algorithms are computationally efficient and are guaranteed to converge to optimal solutions. An important feature of these algorithms is that they do not require any hyperparameter tuning (except for the sparsity case, where a penalty parameter controlling sparsity must be chosen by the user). Experiments on several machine learning datasets demonstrate the effectiveness of the MM4MM approach.

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NeurIPS Conference 2025 Conference Paper

Network two-sample test for block models

Chung Kyong Nguen
Arash Amini
OSCAR HERNAN MADRID PADILLA

We consider the two-sample testing problem for networks, where the goal is to determine whether two sets of networks originated from the same stochastic model. Assuming no vertex correspondence and allowing for different numbers of nodes, we address a fundamental network testing problem that goes beyond simple adjacency matrix comparisons. We adopt the stochastic block model (SBM) for network distributions, due to their interpretability and the potential to approximate more general models. The lack of meaningful node labels and vertex correspondence translate to a graph matching challenge when developing a test for SBMs. We introduce an efficient algorithm to match estimated network parameters, allowing us to properly combine and contrast information within and across samples, leading to a powerful test. We show that the matching algorithm, and the overall test are consistent, under mild conditions on the sparsity of the networks and the sample sizes, and derive a chi-squared asymptotic null distribution for the test. Through a mixture of theoretical insights and empirical validations, including experiments with both synthetic and real-world data, this study advances robust statistical inference for complex network data.

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IROS Conference 2024 Conference Paper

Scalable Networked Feature Selection with Randomized Algorithm for Robot Navigation

Vivek Pandey
Arash Amini
Guangyi Liu 0004
Ufuk Topcu
Qiyu Sun
Kostas Daniilidis
Nader Motee

We address the problem of sparse selection of visual features for localizing a team of robots navigating in an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select a set of the most informative features.

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NeurIPS Conference 2022 Conference Paper

Target alignment in truncated kernel ridge regression

Arash Amini
Richard Baumgartner
Dai Feng

Kernel ridge regression (KRR) has recently attracted renewed interest due to its potential for explaining the transient effects, such as double descent, that emerge during neural network training. In this work, we study how the alignment between the target function and the kernel affects the performance of the KRR. We focus on the truncated KRR (TKRR) which utilizes an additional parameter that controls the spectral truncation of the kernel matrix. We show that for polynomial alignment, there is an over-aligned regime, in which TKRR can achieve a faster rate than what is achievable by full KRR. The rate of TKRR can improve all the way to the parametric rate, while that of full KRR is capped at a sub-optimal value. This shows that target alignemnt can be better leveraged by utilizing spectral truncation in kernel methods. We also consider the bandlimited alignment setting and show that the regularization surface of TKRR can exhibit transient effects including multiple descent and non-monotonic behavior. Our results show that there is a strong and quantifable relation between the shape of the alignment spectrum and the generalization performance of kernel methods, both in terms of rates and in finite samples.

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NeurIPS Conference 2021 Conference Paper

Label consistency in overfitted generalized $k$-means

Linfan Zhang
Arash Amini

We provide theoretical guarantees for label consistency in generalized $k$-means problems, with an emphasis on the overfitted case where the number of clusters used by the algorithm is more than the ground truth. We provide conditions under which the estimated labels are close to a refinement of the true cluster labels. We consider both exact and approximate recovery of the labels. Our results hold for any constant-factor approximation to the $k$-means problem. The results are also model-free and only based on bounds on the maximum or average distance of the data points to the true cluster centers. These centers themselves are loosely defined and can be taken to be any set of points for which the aforementioned distances can be controlled. We show the usefulness of the results with applications to some manifold clustering problems.

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NeurIPS Conference 2020 Conference Paper

The Potts-Ising model for discrete multivariate data

Zahra Razaee
Arash Amini

Modeling dependencies in multivariate discrete data is a challenging problem, especially in high dimensions. The Potts model is a versatile such model, suitable when each coordinate is a categorical variable. However, the full Potts model has too many parameters to be accurately fit when the number of categories is large. We introduce a variation on the Potts model that allows for general categorical marginals and Ising-type multivariate dependence. This reduces the number of parameters from $\Omega(d^2 K^2)$ in the full Potts model to $O(d^2 + Kd)$, where $K$ is the number of categories and $d$ is the dimension of the data. We show that the complexity of fitting this new Potts-Ising model is the same as that of an Ising model. In particular, adopting the neighborhood regression framework, the model can be fit by solving $d$ separate logistic regressions. We demonstrate the ability of the model to capture multivariate dependencies by comparing with existing approaches.

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NeurIPS Conference 2019 Conference Paper

Globally optimal score-based learning of directed acyclic graphs in high-dimensions

Bryon Aragam
Arash Amini
Qing Zhou

We prove that $\Omega(s\log p)$ samples suffice to learn a sparse Gaussian directed acyclic graph (DAG) from data, where $s$ is the maximum Markov blanket size. This improves upon recent results that require $\Omega(s^{4}\log p)$ samples in the equal variance case. To prove this, we analyze a popular score-based estimator that has been the subject of extensive empirical inquiry in recent years and is known to achieve state-of-the-art results. Furthermore, the approach we study does not require strong assumptions such as faithfulness that existing theory for score-based learning crucially relies on. The resulting estimator is based around a difficult nonconvex optimization problem, and its analysis may be of independent interest given recent interest in nonconvex optimization in machine learning. Our analysis overcomes the drawbacks of existing theoretical analyses, which either fail to guarantee structure consistency in high-dimensions (i. e. learning the correct graph with high probability), or rely on restrictive assumptions. In contrast, we give explicit finite-sample bounds that are valid in the important $p\gg n$ regime.

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NeurIPS Conference 2017 Conference Paper

Variable Importance Using Decision Trees

Jalil Kazemitabar
Arash Amini
Adam Bloniarz
Ameet Talwalkar

Decision trees and random forests are well established models that not only offer good predictive performance, but also provide rich feature importance information. While practitioners often employ variable importance methods that rely on this impurity-based information, these methods remain poorly characterized from a theoretical perspective. We provide novel insights into the performance of these methods by deriving finite sample performance guarantees in a high-dimensional setting under various modeling assumptions. We further demonstrate the effectiveness of these impurity-based methods via an extensive set of simulations.

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NeurIPS Conference 2013 Conference Paper

Bayesian inference as iterated random functions with applications to sequential inference in graphical models

Arash Amini
XuanLong Nguyen

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequential change point detection problem formulated via a latent variable directed graphical model. The sequential inference algorithm and its supporting theory are illustrated by simulated examples.

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