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Arash A. Amini

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6 papers
2 author rows

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6

JMLR Journal 2025 Journal Article

Step and Smooth Decompositions as Topological Clustering

  • Luciano Vinas
  • Arash A. Amini

We investigate a class of recovery problems for which observations are a noisy combination of continuous and step functions. These problems can be seen as non-injective instances of non-linear ICA with direct applications to image decontamination for magnetic resonance imaging. Alternately, the problem can be viewed as clustering in the presence of structured (smooth) contaminant. We show that a global topological property (graph connectivity) interacts with a local property (the degree of smoothness of the continuous component) to determine conditions under which the components are identifiable. Additionally, a practical estimation algorithm is provided for the case when the contaminant lies in a reproducing kernel Hilbert space of continuous functions. Algorithm effectiveness is demonstrated through a series of simulations and real-world studies. [abs] [ pdf ][ bib ] &copy JMLR 2025. ( edit, beta )

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RLC Conference 2024 Conference Paper

Graph Neural Thompson Sampling

  • Shuang Wu
  • Arash A. Amini

We consider an online decision-making problem with a reward function defined over graph-structured data. We formally formulate the problem as an instance of graph action bandit. We then propose GNN-TS, a Graph Neural Network (GNN) powered Thompson Sampling (TS) algorithm which employs a GNN approximator for estimating the mean reward function and the graph neural tangent features for uncertainty estimation. We prove that, under certain boundness assumptions on the reward function, GNN-TS achieves a state-of-the-art regret bound which is (1) sub-linear of order $\tilde{\mathcal{O}}(( \tilde{d} T)^{1/2})$ in the number of interaction rounds, $T$, and a notion of effective dimension $\tilde d$, and (2) independent of the number of graph nodes. Empirical results validate that our proposed GNN-TS exhibits competitive performance and scales well on graph action bandit problems.

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RLJ Journal 2024 Journal Article

Graph Neural Thompson Sampling

  • Shuang Wu
  • Arash A. Amini

We consider an online decision-making problem with a reward function defined over graph-structured data. We formally formulate the problem as an instance of graph action bandit. We then propose GNN-TS, a Graph Neural Network (GNN) powered Thompson Sampling (TS) algorithm which employs a GNN approximator for estimating the mean reward function and the graph neural tangent features for uncertainty estimation. We prove that, under certain boundness assumptions on the reward function, GNN-TS achieves a state-of-the-art regret bound which is (1) sub-linear of order $\tilde{\mathcal{O}}(( \tilde{d} T)^{1/2})$ in the number of interaction rounds, $T$, and a notion of effective dimension $\tilde d$, and (2) independent of the number of graph nodes. Empirical results validate that our proposed GNN-TS exhibits competitive performance and scales well on graph action bandit problems.

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ICLR Conference 2023 Conference Paper

Statistical Guarantees for Consensus Clustering

  • Zhixin Zhou
  • Gautam Dudeja
  • Arash A. Amini

Consider the problem of clustering $n$ objects. One can apply multiple algorithms to produce $N$ potentially different clustersings of the same objects, that is, partitions of the $n$ objects into $K$ groups. Even a single randomized algorithm can output different clusterings. This often happens when one samples from the posterior of a Bayesian model, or runs multiple MCMC chains from random initializations. A natural task is then to form a consensus among these different clusterings. The challenge in an unsupervised setting is that the optimal matching between clusters of different inputs is unknown. We model this problem as finding a barycenter (also known as Fr\'{e}chet mean) relative to the misclassification rate. We show that by lifting the problem to the space of association matrices, one can derive aggregation algorithms that circumvent the knowledge of the optimal matchings. We analyze the statistical performance of aggregation algorithms under a stochastic label perturbation model, and show that a $K$-means type algorithm followed by a local refinement step can achieve near optimal performance, with a rate that decays exponentially fast in $N$. Numerical experiments show the effectiveness of the proposed methods.

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JMLR Journal 2020 Journal Article

Optimal Bipartite Network Clustering

  • Zhixin Zhou
  • Arash A. Amini

We study bipartite community detection in networks, or more generally the network biclustering problem. We present a fast two-stage procedure based on spectral initialization followed by the application of a pseudo-likelihood classifier twice. Under mild regularity conditions, we establish the weak consistency of the procedure (i.e., the convergence of the misclassification rate to zero) under a general bipartite stochastic block model. We show that the procedure is optimal in the sense that it achieves the optimal convergence rate that is achievable by a biclustering oracle, adaptively over the whole class, up to constants. This is further formalized by deriving a minimax lower bound over a class of biclustering problems. The optimal rate we obtain sharpens some of the existing results and generalizes others to a wide regime of average degree growth, from sparse networks with average degrees growing arbitrarily slowly to fairly dense networks with average degrees of order $\sqrt{n}$. As a special case, we recover the known exact recovery threshold in the $\log n$ regime of sparsity. To obtain the consistency result, as part of the provable version of the algorithm, we introduce a sub-block partitioning scheme that is also computationally attractive, allowing for distributed implementation of the algorithm without sacrificing optimality. The provable algorithm is derived from a general class of pseudo-likelihood biclustering algorithms that employ simple EM type updates. We show the effectiveness of this general class by numerical simulations. [abs] [ pdf ][ bib ] &copy JMLR 2020. ( edit, beta )

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JMLR Journal 2019 Journal Article

Matched Bipartite Block Model with Covariates

  • Zahra S. Razaee
  • Arash A. Amini
  • Jingyi Jessica Li

Community detection or clustering is a fundamental task in the analysis of network data. Many real networks have a bipartite structure which makes community detection challenging. In this paper, we consider a model which allows for matched communities in the bipartite setting, in addition to node covariates with information about the matching. We derive a simple fast algorithm for fitting the model based on variational inference ideas and show its effectiveness on both simulated and real data. A variation of the model to allow for degree-correction is also considered, in addition to a novel approach to fitting such degree-corrected models. [abs] [ pdf ][ bib ] &copy JMLR 2019. ( edit, beta )

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