We investigate the classification performance of graph neural networks with graph-polynomial features, poly-GNNs, on the problem of semi-supervised node classification. We analyze poly-GNNs under a general contextual stochastic block model (CSBM) by providing a sharp characterization of the rate of separation between classes in their output node representations. A question of interest is whether this rate depends on the depth of the network k, i.e., whether deeper networks can achieve a faster separation? We provide a negative answer to this question: for a sufficiently large graph, a depth k>1 poly-GNN exhibits the same rate of separation as a depth k=1 counterpart. Our analysis highlights and quantifies the impact of “graph noise” in deep GNNs and shows how noise in the graph structure can dominate other sources of signal in the graph, negating any benefit further aggregation provides. Our analysis also reveals subtle differences between even and odd-layered GNNs in how the feature noise propagates.
@article{vinas2024sharp,
title = {Sharp Bounds for Poly-{GNN}s and the Effect of Graph Noise},
author = {Vinas, Luciano and Amini, Arash A.},
journal = {Preprint},
year = {2024},
url = {https://arxiv.org/abs/2407.19567}
}
Network two-sample test for block models
Chung Kyong Nguen, Oscar Hernan Madrid Padilla, Arash A. Amini · PreprintarXivdoi
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.
@article{nguen2024network,
title = {Network two-sample test for block models},
author = {Chung Kyong Nguen and Oscar Hernan Madrid Padilla and Arash A. Amini},
year = {2024},
doi = {10.48550/arXiv.2406.06014},
url = {https://arxiv.org/abs/2406.06014},
primaryclass = {math.ST}
}
Bayesian Community Detection for Networks with Covariates
Luyi Shen, Arash Amini, Nathaniel Josephs, Lizhen Lin · BAdoi
@article{shen2024bayesian,
title = {{Bayesian Community Detection for Networks with Covariates}},
author = {Luyi Shen and Arash Amini and Nathaniel Josephs and Lizhen Lin},
journal = {Bayesian Analysis},
pages = {1 -- 28},
year = {2024},
publisher = {International Society for Bayesian Analysis},
doi = {10.1214/24-BA1415}
}
@article{ye2024federated,
title = {Federated Learning of Generalized Linear Causal Networks},
author = {Ye, Qiaoling and Amini, Arash A. and Zhou, Qing},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
pages = {1-14},
year = {2024},
doi = {10.1109/TPAMI.2024.3381860}
}
Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
Arash Amini, Marina Paez, Lizhen Lin · BAarXivdoicode
@article{AminiPaezLin2024,
title = {{Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks}},
author = {Arash Amini and Marina Paez and Lizhen Lin},
journal = {Bayesian Analysis},
volume = {19},
number = {1},
pages = {319 -- 345},
year = {2024},
publisher = {International Society for Bayesian Analysis},
doi = {10.1214/22-BA1355}
}
2023
Learning non-graphical conditional independence structures via the neighbourhood lattice
Arash A. Amini, Bryon Aragam, Qing Zhou · Preprint
@article{nb-lat-graphoid,
title = {Learning non-graphical conditional independence structures via the neighbourhood lattice},
author = {Arash A. Amini and Bryon Aragam and and Qing Zhou},
journal = {Preprint},
year = {2023}
}
Simplifying GNN Performance with Low Rank Kernel Models
@article{VinasAmini2023,
title = {Step and Smooth Decompositions as Topological Clustering},
author = {Vinas, Luciano and Amini, Arash A.},
journal = {Preprint},
year = {2023},
url = {https://arxiv.org/abs/2311.05756}
}
Nested stochastic block model for simultaneously clustering networks and nodes
Nathaniel Josephs, Arash A Amini, Marina Paez, Lizhen Lin · PreprintarXiv
@article{josephs2023nested,
title = {Nested stochastic block model for simultaneously clustering networks and nodes},
author = {Josephs, Nathaniel and Amini, Arash A and Paez, Marina and Lin, Lizhen},
journal = {Preprint},
year = {2023}
}
Statistical Guarantees for Consensus Clustering
Zhixin Zhou, Gautam Dudeja, Arash A. Amini · ICLR
@inproceedings{label-agg,
title = {Statistical Guarantees for Consensus Clustering},
author = {Zhixin Zhou and Gautam Dudeja and Arash A. Amini},
booktitle = {ICLR},
year = {2023}
}
Adjusted Chi-Square Test for Degree-Corrected Block Models
@article{ZhangAmini2023,
title = {Adjusted Chi-Square Test for Degree-Corrected Block Models},
author = {Zhang, Linfan and Amini, Arash A.},
journal = {The Annals of Statistics},
volume = {51},
number = {6},
pages = {2366--2385},
year = {2023},
doi = {10.1214/23-AOS2329}
}
Performance evaluation of automotive dealerships using grouped mixture of regressions
Haidar Almohri, Ratna Babu Chinnam, Arash A. Amini · ESA
@article{almohri2023performance,
title = {Performance evaluation of automotive dealerships using grouped mixture of regressions},
author = {Almohri, Haidar and Chinnam, Ratna Babu and Amini, Arash A.},
journal = {Expert Systems with Applications},
volume = {213},
pages = {119266},
year = {2023},
publisher = {Elsevier}
}
2022
Finding quadruply imaged quasars with machine learning. I. Methods
A. Akhazhanov, A. More, A. Amini, C. Hazlett, T. Treu, S. Birrer, A. Shajib, P. Schechter, C. Lemon, B. Nord, M. Aguena, S. Allam, …, et al. · MNRASarXivpdflink
@article{akhazhanov2021finding,
title = {Finding quadruply imaged quasars with machine learning. I. Methods},
author = {A. Akhazhanov and A. More and A. Amini and C. Hazlett and T. Treu and S. Birrer and A. Shajib and P. Schechter and C. Lemon and B. Nord and M. Aguena and S. Allam and F. Andrade-Oliveira and J. Annis and D. Brooks and E. Buckley-Geer and D. L. Burke and A. Carnero Rosell and M. Carrasco Kind and J. Carretero and A. Choi and C. Conselice and M. Costanzi and L. N. da Costa and M. E. S. Pereira and J. De Vicente and S. Desai and J. P. Dietrich and P. Doel and S. Everett and I. Ferrero and D. A. Finley and B. Flaugher and J. Frieman and J. García-Bellido and D. W. Gerdes and D. Gruen and R. A. Gruendl and J. Gschwend and G. Gutierrez and S. R. Hinton and D. L. Hollowood and K. Honscheid and D. J. James and A. G. Kim and K. Kuehn and N. Kuropatkin and O. Lahav and M. Lima and H. Lin and M. A. G. Maia and M. March and F. Menanteau and R. Miquel and R. Morgan and A. Palmese and F. Paz-Chinchón and A. Pieres and A. A. Plazas Malagón and E. Sanchez and V. Scarpine and S. Serrano and I. Sevilla-Noarbe and M. Smith and M. Soares-Santos and E. Suchyta and M. E. C. Swanson and G. Tarle and C. To and T. N. Varga and J. Weller},
journal = {Monthly Notices of the Royal Astronomical Society},
volume = {513},
number = {2},
pages = {2407--2421},
year = {2022},
publisher = {Oxford University Press},
eprint = {2109.09781},
archiveprefix = {arXiv},
primaryclass = {astro-ph.CO}
}
@inproceedings{amini2022perfectness,
title = {On perfectness in Gaussian graphical models},
author = {Amini, Arash and Aragam, Bryon and Zhou, Qing},
booktitle = {International Conference on Artificial Intelligence and Statistics},
pages = {7505--7517},
year = {2022},
organization = {PMLR}
}
Target alignment in truncated kernel ridge regression
Arash A Amini, Richard Baumgartner, Dai Feng · NeurIPSarXivcode
@inproceedings{amini2022target,
title = {Target alignment in truncated kernel ridge regression},
author = {Amini, Arash A and Baumgartner, Richard and Feng, Dai},
booktitle = {NeurIPS},
year = {2022}
}
A non-graphical representation of conditional independence via the neighbourhood lattice
Arash A Amini, Bryon Aragam, Qing Zhou · PreprintarXiv
@article{amini2022non,
title = {A non-graphical representation of conditional independence via the neighbourhood lattice},
author = {Amini, Arash A and Aragam, Bryon and Zhou, Qing},
journal = {Preprint},
year = {2022}
}
2021
Spectrally-truncated kernel ridge regression and its free lunch
@article{kernelconcen:annals,
title = {{Concentration of kernel matrices with application to kernel spectral clustering}},
author = {Arash A. Amini and Zahra S. Razaee},
journal = {The Annals of Statistics},
volume = {49},
number = {1},
pages = {531 -- 556},
year = {2021},
publisher = {Institute of Mathematical Statistics},
doi = {10.1214/20-AOS1967},
url = {https://doi.org/10.1214/20-AOS1967}
}
Label consistency in overfitted generalized k-means
@article{zhang2021label,
title = {Label consistency in overfitted generalized k-means},
author = {Zhang, Linfan and Amini, Arash A.},
journal = {Neural Information Processing Systems (NeurIPS)},
year = {2021}
}
2020
Approximate Identification of the Optimal Epidemic Source in Complex Networks
We consider the problem of identifying the source of a network epidemic from a complete snapshot of the infected nodes. We take a fully statistical approach and derive novel recursions to compute the Bayes optimal solution, under a heterogeneous susceptible-infected (SI) epidemic model. Our analysis is time and rate independent, and holds for general network topologies. We then provide two highly scalable algorithms for solving these recursions, a mean-field approximation and a greedy approach, and evaluate their performance on real and synthetic networks. Previous work on the problem has mostly focused on tree-like network topologies. Real networks are far from tree-like and an emphasis will be given to networks with high transitivity, such as social networks and those with communities. We show that on such networks, our approaches significantly outperform popular geometric and spectral centrality measures, most of which perform no better than random guessing.
@inproceedings{approx-epidem,
title = {Approximate Identification of the Optimal Epidemic Source in Complex Networks},
author = {Kazemitabar, S. Jalil and Amini, Arash A.},
editor = {Masuda, Naoki and Goh, Kwang-Il and Jia, Tao and Yamanoi, Junichi and Sayama, Hiroki},
booktitle = {Proceedings of NetSci-X 2020: Sixth International Winter School and Conference on Network Science},
pages = {107--125},
year = {2020},
publisher = {Springer International Publishing},
address = {Cham},
isbn = {978-3-030-38965-9}
}
@article{zhou2020optimal,
title = {Optimal bipartite network clustering},
author = {Zhou, Zhixin and Amini, Arash A.},
journal = {Journal of Machine Learning Research},
volume = {21},
number = {40},
pages = {1--68},
year = {2020}
}
Optimizing regularized Cholesky score for order-based learning of Bayesian networks
Qiaoling Ye, Arash A. Amini, Qing Zhou · TPAMIarXivlink
@article{dagarcs:IEEE,
title = {Optimizing regularized Cholesky score for order-based learning of Bayesian networks},
author = {Qiaoling Ye and Arash A. Amini and Qing Zhou},
journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
year = {2020},
publisher = {IEEE}
}
The Potts-Ising model for discrete multivariate data
@article{razaee2020potts,
title = {The Potts-Ising model for discrete multivariate data},
author = {Razaee, Zahra and Amini, Arash A.},
journal = {Advances in Neural Information Processing Systems},
volume = {33},
year = {2020}
}
Generalized Autoregressive Linear Models for Discrete High-Dimensional Data
Parthe Pandit, Mojtaba Sahraee-Ardakan, Arash A. Amini, Sundeep Rangan, Alyson K. Fletcher · JSAITdoi
@article{pandit2020generalized,
title = {Generalized Autoregressive Linear Models for Discrete High-Dimensional Data},
author = {Pandit, Parthe and Sahraee-Ardakan, Mojtaba and Amini, Arash A. and Rangan, Sundeep and Fletcher, Alyson K.},
journal = {IEEE Journal on Selected Areas in Information Theory},
volume = {1},
number = {3},
pages = {884-896},
year = {2020},
doi = {10.1109/JSAIT.2020.3041714}
}
On the properties of the toxicity index and its statistical efficiency
Zahra S Razaee, Arash A. Amini, Márcio A Diniz, Mourad Tighiouart, Greg Yothers, André Rogatko · Stat Medpdflink
@article{razaee2020properties,
title = {On the properties of the toxicity index and its statistical efficiency},
author = {Razaee, Zahra S and Amini, Arash A. and Diniz, M{\'a}rcio A and Tighiouart, Mourad and Yothers, Greg and Rogatko, Andr{\'e}},
journal = {Statistics in Medicine},
pages = {1--18},
year = {2020},
publisher = {Wiley Online Library}
}
2019
Globally optimal score-based learning of directed acyclic graphs in high-dimensions
@inproceedings{aragam2019globally,
title = {Globally optimal score-based learning of directed acyclic graphs in high-dimensions},
author = {Aragam, Bryon and Amini, Arash and Zhou, Qing},
booktitle = {Advances in Neural Information Processing Systems},
pages = {4452--4464},
year = {2019}
}
Matched Bipartite Block Model with Covariates.
Zahra S Razaee, Arash A. Amini, Jingyi Jessica Li · JMLRarXivpdflinkcode
@article{Razaee2017,
title = {Matched Bipartite Block Model with Covariates.},
author = {Razaee, Zahra S and Amini, Arash A. and Li, Jingyi Jessica},
journal = {Journal of Machine Learning Research},
volume = {20},
number = {34},
pages = {1--44},
year = {2019}
}
Analysis of spectral clustering algorithms for community detection: the general bipartite setting
@article{sc-review,
title = {Analysis of spectral clustering algorithms for community detection: the general bipartite setting},
author = {Zhixin Zhou and Arash A. Amini},
journal = {Journal of Machine Learning Research},
volume = {20},
number = {47},
pages = {1-47},
year = {2019},
url = {http://jmlr.org/papers/v20/18-170.html}
}
Efficient Network Epidemic Inference with Application to Source Identification
S. Jalil Kazemitabar, Arash A. Amini · Working paper
@article{is-epidem,
title = {Efficient Network Epidemic Inference with Application to Source Identification},
author = {S. Jalil Kazemitabar and Arash A. Amini},
journal = {Working paper},
year = {2019-}
}
Exact slice sampler for Hierarchical Dirichlet Processes
Arash A. Amini, Marina Paez, Lizhen Lin, Zahra S. Razaee · Tech ReportarXivcode
We propose an exact slice sampler for Hierarchical Dirichlet process (HDP) and its associated mixture models (Teh et al., 2006). Although there are existing MCMC algorithms for sampling from the HDP, a slice sampler has been missing from the literature. Slice sampling is well-known for its desirable properties including its fast mixing and its natural potential for parallelization. On the other hand, the hierarchical nature of HDPs poses challenges to adopting a full-fledged slice sampler that automatically truncates all the infinite measures involved without ad-hoc modifications. In this work, we adopt the powerful idea of Bayesian variable augmentation to address this challenge. By introducing new latent variables, we obtain a full factorization of the joint distribution that is suitable for slice sampling. Our algorithm has several appealing features such as (1) fast mixing; (2) remaining exact while allowing natural truncation of the underlying infinite-dimensional measures, as in (Kalli et al., 2011), resulting in updates of only a finite number of necessary atoms and weights in each iteration; and (3) being naturally suited to parallel implementations. The underlying principle for joint factorization of the full likelihood is simple and can be applied to many other settings, such as designing sampling algorithms for general dependent Dirichlet process (DDP) models.
@article{hdp:slice,
title = {Exact slice sampler for Hierarchical Dirichlet Processes},
author = {Arash A. Amini and Marina Paez and Lizhen Lin and Zahra S. Razaee},
journal = {Technical Report}
}
Sparse Multivariate Bernoulli Processes in High Dimensions
We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with spiking or binary valued data. We also allow the process to depend on its past up to a lag p, for a general $p \geq 1$, allowing for more realistic modeling in many applications. We propose and analyze an $\ell_1$-regularized maximum likelihood (ML) estimator under the assumption that the parameter tensor is approximately sparse. Rigorous analysis of such estimators is made challenging by the dependent and non-Gaussian nature of the process as well as the presence of the nonlinearities and multi-level feedback. We derive precise upper bounds on the mean-squared estimation error in terms of the number of samples, dimensions of the process, the lag $p$ and other key statistical properties of the model. The ideas presented can be used in the rigorous high-dimensional analysis of regularized $M$-estimators for other sparse nonlinear and non-Gaussian processes with long-range dependence.
@inproceedings{mbp:ar,
title = {Sparse Multivariate Bernoulli Processes in High Dimensions},
author = {Pandit, Parthe and Sahraee-Ardakan, Mojtaba and Amini, Arash and Rangan, Sundeep and Fletcher, Alyson K.},
editor = {Chaudhuri, Kamalika and Sugiyama, Masashi},
booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics},
volume = {89},
pages = {457--466},
year = {2019},
publisher = {PMLR},
series = {Proceedings of Machine Learning Research},
url = {https://proceedings.mlr.press/v89/pandit19a.html}
}
On the support recovery of marginal regression
S. Jalil Kazemitabar, Arash A. Amini, Ameet Talwalkar · Tech ReportarXiv
Leading methods for support recovery in high-dimensional regression, such as Lasso, have been well-studied and their limitations in the context of correlated design have been characterized with precise incoherence conditions. In this work, we present a similar treatment of selection consistency for marginal regression (MR), a computationally efficient family of methods with connections to decision trees. Selection based on marginal regression is also referred to as covariate screening or independence screening and is a popular approach in applied work, especially in ultra high-dimensional settings. We identify the underlying factors—which we denote as \emph{MR incoherence}—affecting MR's support recovery performance. Our near complete characterization provides a much more nuanced and optimistic view of MR in comparison to previous works. To ground our results, we provide a broad taxonomy of results for leading feature selection methods, relating the behavior of Lasso, OMP, SIS, and MR. We also lay the foundation for interesting generalizations of our analysis, e.g., to non-linear feature selection methods and to more general regression frameworks such as a general additive models.
@article{mr:supp,
title = {On the support recovery of marginal regression},
author = {S. Jalil Kazemitabar and Arash A. Amini and Ameet Talwalkar},
journal = {Technical Report},
eprint = {1903.09488v1}
}
The neighborhood lattice for encoding partial correlations in a Hilbert space
Arash A. Amini, Bryon Aragam, Qing Zhou · Tech ReportarXiv
Neighborhood regression has been a successful approach in graphical and structural equation modeling, with applications to learning undirected and directed graphical models. We extend these ideas by defining and studying an algebraic structure called the neighborhood lattice based on a generalized notion of neighborhood regression. We show that this algebraic structure has the potential to provide an economic encoding of all conditional independence statements in a Gaussian distribution (or conditional uncorrelatedness in general), even in the cases where no graphical model exists that could "perfectly" encode all such statements. We study the computational complexity of computing these structures and show that under a sparsity assumption, they can be computed in polynomial time, even in the absence of the assumption of perfectness to a graph. On the other hand, assuming perfectness, we show how these neighborhood lattices may be "graphically" computed using the separation properties of the so-called partial correlation graph. We also draw connections with directed acyclic graphical models and Bayesian networks. We derive these results using an abstract generalization of partial uncorrelatedness, called partial orthogonality, which allows us to use algebraic properties of projection operators on Hilbert spaces to significantly simplify and extend existing ideas and arguments. Consequently, our results apply to a wide range of random objects and data structures, such as random vectors, data matrices, and functions.
@article{lattice:hilbert,
title = {The neighborhood lattice for encoding partial correlations in a Hilbert space},
author = {Arash A. Amini and Bryon Aragam and Qing Zhou},
eprint = {1711.00991v2}
}
@article{sdp:sbm:aos,
title = {{On semidefinite relaxations for the block model}},
author = {A. A. Amini and E. Levina},
journal = {The Annals of Statistics},
volume = {46},
number = {1},
pages = {149-179},
year = {2018},
archiveprefix = {arXiv}
}
Conditional chi-square test for degree-corrected block models
Linfan Zhang, Arash A. Amini · Working paper
@article{cctest,
title = {Conditional chi-square test for degree-corrected block models},
author = {Linfan Zhang and Arash A. Amini},
journal = {Working paper},
year = {2018-}
}
2017
Partial correlation graphs and the neighborhood lattice
A. A. Amini, B. Aragam, Q. Zhou · Working paper
@article{pcg:working,
title = {Partial correlation graphs and the neighborhood lattice},
author = {A. A. Amini and B. Aragam and Q. Zhou},
journal = {Working paper},
year = {2017-}
}
Efficient community detection via low rank semidefinite programming
Bowei Yan, Purna Sarkar, Arash A. Amini · Working paper
@article{sdp:lowrank,
title = {Efficient community detection via low rank semidefinite programming},
author = {Bowei Yan and Purna Sarkar and Arash A. Amini},
journal = {Working paper},
year = {2017-}
}
Variable Importance Using Decision Trees
Jalil Kazemitabar, Arash A. Amini, Adam Bloniarz, Ameet S Talwalkar · NeurIPSpdflinksupplement
@inproceedings{dstump,
title = {Variable Importance Using Decision Trees},
author = {Kazemitabar, Jalil and Amini, Arash A. and Bloniarz, Adam and Talwalkar, Ameet S},
editor = {I. Guyon and U. V. Luxburg and S. Bengio and H. Wallach and R. Fergus and S. Vishwanathan and R. Garnett},
booktitle = {Advances in Neural Information Processing Systems 30},
pages = {425--434},
year = {2017},
publisher = {Curran Associates, Inc.},
url = {http://papers.nips.cc/paper/6646-variable-importance-using-decision-trees.pdf}
}
Structured regression models for high-dimensional spatial spectroscopy data
Arash A. Amini, Elizaveta Levina, Kerby A. Shedden · EJSarXivdoi
@article{AmLeSh2017,
title = {Structured regression models for high-dimensional spatial spectroscopy data},
author = {Arash A. Amini and Elizaveta Levina and Kerby A. Shedden},
journal = {Electron. J. Statist.},
volume = {11},
number = {2},
pages = {4151-4178},
year = {2017},
doi = {10.1214/17-EJS1301},
issn = {1935-7524}
}
Partial correlation graphs and the neighborhood lattice
Arash A. Amini, Bryon Aragam, Qing Zhou · Tech ReportarXiv
We define and study partial correlation graphs (PCGs) with variables in a general Hilbert space and their connections to generalized neighborhood regression, without making any distributional assumptions. Using operator-theoretic arguments, and especially the properties of projection operators on Hilbert spaces, we show that these neighborhood regressions have the algebraic structure of a lattice, which we call a neighborhood lattice. This lattice property significantly reduces the number of conditions one has to check when testing all partial correlation relations among a collection of variables. In addition, we generalize the notion of perfectness in graphical models for a general PCG to this Hilbert space setting, and establish that almost all Gram matrices are perfect. Under this perfectness assumption, we show how these neighborhood lattices may be "graphically" computed using separation properties of PCGs. We also discuss extensions of these ideas to directed models, which present unique challenges compared to their undirected counterparts. Our results have implications for multivariate statistical learning in general, including structural equation models, subspace clustering, and dimension reduction. For example, we discuss how to compute neighborhood lattices efficiently and furthermore how they can be used to reduce the sample complexity of learning directed acyclic graphs. Our work demonstrates that this abstract viewpoint via projection operators significantly simplifies existing ideas and arguments from the graphical modeling literature, and furthermore can be used to extend these ideas to more general nonparametric settings.
@article{pcg,
title = {Partial correlation graphs and the neighborhood lattice},
author = {Arash A. Amini and Bryon Aragam and Qing Zhou},
eprint = {1711.00991v1}
}
2016
Soft-label M-estimators in community detection
Arash A. Amini · Working paper
@article{soft:label,
title = {Soft-label M-estimators in community detection},
author = {Arash A. Amini},
journal = {Working paper},
year = {2016-}
}
Attribute-efficient online sparse regression
Ehsan Ebrahimzadeh, Arash A. Amini · Working paper
@article{online:sp:reg,
title = {Attribute-efficient online sparse regression},
author = {Ehsan Ebrahimzadeh and Arash A. Amini},
journal = {Working paper},
year = {2016-}
}
2015
Identifiability of Gaussian DAGs in the equal-variance case: A linear-algebraic proof
A. A. Amini · Tech Report
@article{dag:ident,
title = {Identifiability of Gaussian DAGs in the equal-variance case: A linear-algebraic proof},
author = {A. A. Amini},
journal = {Technical Report},
year = {2015}
}
Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression
Bryon Aragam, Arash A. Amini, Qing Zhou · Tech ReportarXiv
We study a family of regularized score-based estimators for learning the structure of a directed acyclic graph (DAG) for a multivariate normal distribution from high-dimensional data with $p\gg n$. Our main results establish support recovery guarantees and deviation bounds for a family of penalized least-squares estimators under concave regularization without assuming prior knowledge of a variable ordering. These results apply to a variety of practical situations that allow for arbitrary nondegenerate covariance structures as well as many popular regularizers including the MCP, SCAD, $\ell_{0}$ and $\ell_{1}$. The proof relies on interpreting a DAG as a recursive linear structural equation model, which reduces the estimation problem to a series of neighbourhood regressions. We provide a novel statistical analysis of these neighbourhood problems, establishing uniform control over the superexponential family of neighbourhoods associated with a Gaussian distribution. We then apply these results to study the statistical properties of score-based DAG estimators, learning causal DAGs, and inferring conditional independence relations via graphical models. Our results yield—for the first time—finite-sample guarantees for structure learning of Gaussian DAGs in high-dimensions via score-based estimation.
@article{dag:highd,
title = {Learning Directed Acyclic Graphs with Penalized Neighbourhood Regression},
author = {Bryon Aragam and Arash A. Amini and Qing Zhou},
year = {2015},
eprint = {1511.08963v3}
}
2013
Bayesian inference as iterated random functions with applications to sequential inference in graphical models
@article{irf:arxiv,
title = {{Bayesian inference as iterated random functions with applications to sequential inference in graphical models}},
author = {Amini, A. A. and Nguyen, X.},
journal = {Preprint},
year = {2013},
eprint = {1311.0072}
}
Bayesian inference as iterated random functions with applications to sequential inference in graphical models
@inproceedings{irf:nips,
title = {{Bayesian inference as iterated random functions with applications to sequential inference in graphical models}},
author = {Amini, A. A. and Nguyen, X.},
booktitle = {Neural Information Processing Systems (NIPS)},
year = {2013}
}
Pseudo-likelihood methods for community detection in large sparse networks
A. A. Amini, A. Chen, P. J. Bickel, E. Levina · AOSarXivdoicode
@article{pl:aos,
title = {{Pseudo-likelihood methods for community detection in large sparse networks}},
author = {Amini, A. A. and Chen, A. and Bickel, P. J. and Levina, E.},
journal = {The Annals of Statistics},
volume = {41},
number = {4},
pages = {2097--2122},
year = {2013},
doi = {10.1214/13-AOS1138},
url = {http://adsabs.harvard.edu/abs/2012arXiv1207.2340A http://projecteuclid.org/euclid.aos/1382547514},
issn = {0090-5364}
}
Sequential Detection of Multiple Change Points in Networks: A Graphical Model Approach
@article{mcp:it,
title = {{Sequential Detection of Multiple Change Points in Networks: A Graphical Model Approach}},
author = {Amini, A. A. and Nguyen, X.},
journal = {IEEE Transactions on Information Theory},
volume = {59},
number = {9},
pages = {5824--5841},
year = {2013},
doi = {10.1109/TIT.2013.2264716},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6518132},
issn = {0018-9448}
}
2012
Message-passing sequential detection of multiple change points in networks
@inproceedings{mcp:isit,
title = {{Message-passing sequential detection of multiple change points in networks}},
author = {Nguyen, X. and Amini, A. A. and Rajagopal, R.},
booktitle = {IEEE International Symposium on Information Theory (ISIT)},
pages = {2007--2011},
year = {2012},
doi = {10.1109/ISIT.2012.6283653},
url = {http://ieeexplore.ieee.org/lpdocs/epic03/wrapper.htm?arnumber=6283653},
isbn = {978-1-4673-2579-0}
}
Approximation properties of certain operator-induced norms on Hilbert spaces
@article{approx12,
title = {{Approximation properties of certain operator-induced norms on Hilbert spaces}},
author = {Amini, A. A. and Wainwright, M. J.},
journal = {Journal of Approximation Theory},
volume = {164},
number = {2},
pages = {320--345},
year = {2012},
doi = {10.1016/j.jat.2011.11.002},
url = {http://linkinghub.elsevier.com/retrieve/pii/S0021904511001821},
issn = {00219045}
}
Sampled forms of functional PCA in reproducing kernel Hilbert spaces
@article{fpca:aos,
title = {{Sampled forms of functional PCA in reproducing kernel Hilbert spaces}},
author = {Amini, A. A. and Wainwright, M. J.},
journal = {The Annals of Statistics},
volume = {40},
number = {5},
pages = {2483--2510},
year = {2012},
doi = {10.1214/12-AOS1033},
url = {http://projecteuclid.org/euclid.aos/1359987528},
issn = {0090-5364}
}
2009
High-dimensional analysis of semidefinite relaxations for sparse principal components
@article{sdp:aos,
title = {{High-dimensional analysis of semidefinite relaxations for sparse principal components}},
author = {Amini, A. A. and Wainwright, M. J.},
journal = {The Annals of Statistics},
volume = {37},
number = {5B},
pages = {2877--2921},
year = {2009},
doi = {10.1214/08-AOS664},
url = {http://projecteuclid.org/euclid.aos/1247836672},
issn = {0090-5364}
}
2008
High-dimensional analysis of semidefinite relaxations for sparse principal components
@inproceedings{sdp:isit,
title = {{High-dimensional analysis of semidefinite relaxations for sparse principal components}},
author = {Amini, A. A. and Wainwright, M. J.},
booktitle = {IEEE International Symposium on Information Theory (ISIT)},
pages = {2454--2458},
year = {2008},
url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=4595432},
isbn = {9781424425716}
}
2006
A fast method for sparse component analysis based on iterative detection-projection
A. A. Amini, M. Babai-Zadeh, C. Jutten · MaxEnt
@inproceedings{Amini2006a,
title = {{A fast method for sparse component analysis based on iterative detection-projection}},
author = {Amini, A. A. and Babai-Zadeh, M. and Jutten, C.},
booktitle = {Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt)},
year = {2006}
}
A new approach for sparse decomposition and sparse source separation
A. A. Amini, M. Babaie-Zadeh, C. Jutten · EUSIPCOlink
@inproceedings{Amini2006,
title = {{A new approach for sparse decomposition and sparse source separation}},
author = {Amini, A. A. and Babaie-Zadeh, M. and Jutten, C.},
booktitle = {European Signal Processing Conference (EUSIPCO)},
pages = {2--6},
year = {2006},
url = {http://sharif.edu/~mbzadeh/PublicOfficial/2006/EUSIPCO2006.pdf}
}