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Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers [article]

Wei Zhou and Xin He and Wei Zhong and Junhui Wang
2021 arXiv   pre-print
To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm.  ...  This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean.  ...  its parents is a quadratic function of its conditional mean.  ... 
arXiv:2111.01560v1 fatcat:oaytygqwb5helo6ewwclwfkutq

Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layers

Wei Zhou, Xin He, Wei Zhong, Junhui Wang
To facilitate learning, we introduce a novel concept of topological layers, and develop an efficient DAG learning algorithm.  ...  This paper studies a special class of non-Gaussian DAG models, where the conditional variance of each node given its parents is a quadratic function of its conditional mean.  ...  Following a similar treatment as in Park and Raskutti [2018] , Park and Park [2019] , we assume that the underlying topological layers have been learned by the proposed algorithm and using Theorem S1  ... 
doi:10.6084/m9.figshare.19651412.v1 fatcat:epbk2yvj75c3he2z6av7g2m3vq

Integer Programming for Learning Directed Acyclic Graphs from Continuous Data [article]

Hasan Manzour, Simge Küçükyavuz, Ali Shojaie
2019 arXiv   pre-print
Learning directed acyclic graphs (DAGs) from data is a challenging task both in theory and in practice, because the number of possible DAGs scales superexponentially with the number of nodes.  ...  We use the penalized negative log-likelihood score function with both ℓ_0 and ℓ_1 regularizations and propose a new mixed-integer quadratic optimization (MIQO) model, referred to as a layered network (  ...  More generally, B defines a directed graph G(B) on m nodes such that arc (j, k) appears in G(B) if and only if β jk = 0. Let σ 2 k denote the variance of δ k ; k = 1, 2, , . . . , m.  ... 
arXiv:1904.10574v1 fatcat:wtq3g3vdjbcrtdkkjluuhiv4kq

Learning Sparse Nonparametric DAGs [article]

Xun Zheng, Chen Dan, Bryon Aragam, Pradeep Ravikumar, Eric P. Xing
2020 arXiv   pre-print
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data.  ...  Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM  ...  Acknowledgements We acknowledge the support of NSF via IIS-1909816, OAC-1934584, ONR via N000141812861, NSF IIS1563887 and DARPA/AFRL FA87501720152.  ... 
arXiv:1909.13189v2 fatcat:g7no2lsnnvhdngl4tgmojqusbe

Stay on path: PCA along graph paths [article]

Megasthenis Asteris, Anastasios Kyrillidis, Alexandros G. Dimakis, Han-Gyol Yi and, Bharath Chandrasekaran
2015 arXiv   pre-print
In particular, we consider the following setting: given a directed acyclic graph G on p vertices corresponding to variables, the non-zero entries of the extracted principal component must coincide with  ...  We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph.  ...  In this paper we enforce additional structure on the support of principal components. Consider a directed acyclic graph (DAG) G = (V, E) on p vertices.  ... 
arXiv:1506.02344v2 fatcat:lb4q5qeqfzgzbndnqkrmsokeoi

Connecting the Dots: Identifying Network Structure via Graph Signal Processing [article]

Gonzalo Mateos, Santiago Segarra, Antonio G. Marques, Alejandro Ribeiro
2018 arXiv   pre-print
This tutorial offers an overview of graph learning methods developed to bridge the aforementioned gap, by using information available from graph signals to infer the underlying graph topology.  ...  A number of arguably more nascent topics are also briefly outlined, including inference of dynamic networks, nonlinear models of pairwise interaction, as well as extensions to directed graphs and their  ...  topological states representing the layers of the graph [58].  ... 
arXiv:1810.13066v1 fatcat:7ub2dgol7vhtxnwwgelficghz4

Learning from Few Positives: a Provably Accurate Metric Learning Algorithm to Deal with Imbalanced Data

Rémi Viola, Rémi Emonet, Amaury Habrard, Guillaume Metzler, Marc Sebban
2020 Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence  
Unlike the state-of-the-art methods, our algorithm MLFP, for Metric Learning from Few Positives, learns a new representation that is used only when a test query is compared to a minority training example  ...  Extensive experiments conducted on several imbalanced datasets show the effectiveness of our method.  ...  This allows us to consider functions on graphs of different sizes without obtaining infinite dimensional spaces and infinitely complex functions that would be impossible to learn via a finite number of  ... 
doi:10.24963/ijcai.2020/294 dblp:conf/ijcai/DasoulasSSV20 fatcat:zivvyy4k6jaipduk437ysirl2u

Kernel-based Graph Learning from Smooth Signals: A Functional Viewpoint [article]

Xingyue Pu, Siu Lun Chau, Xiaowen Dong, Dino Sejdinovic
2020 arXiv   pre-print
The functional learning increases the robustness of graph learning against missing and incomplete information in the graph signals.  ...  The problem of graph learning concerns the construction of an explicit topological structure revealing the relationship between nodes representing data entities, which plays an increasingly important role  ...  We have shown the effectiveness and efficiency of the proposed method, via extensive synthetic and real-world experiments, demonstrating its usefulness in learning a meaningful topology from noisy, incomplete  ... 
arXiv:2008.10065v1 fatcat:vpyt4einyfewtam6xx5rl7676a

Efficient Neural Causal Discovery without Acyclicity Constraints [article]

Phillip Lippe, Taco Cohen, Efstratios Gavves
2022 arXiv   pre-print
In this paper, we present ENCO, an efficient structure learning method for directed, acyclic causal graphs leveraging observational and interventional data.  ...  Consequently, we can provide convergence guarantees of ENCO under mild conditions without constraining the score function with respect to acyclicity.  ...  ., the University of Amsterdam and the allowance Top consortia for Knowledge and Innovation (TKIs) from the Netherlands Ministry of Economic Affairs and Climate Policy.  ... 
arXiv:2107.10483v3 fatcat:zha7qzbxpjfrxd4pg3xviyn4va

Reinforcement Learning with Chromatic Networks for Compact Architecture Search [article]

Xingyou Song, Krzysztof Choromanski, Jack Parker-Holder, Yunhao Tang, Wenbo Gao, Aldo Pacchiano, Tamas Sarlos, Deepali Jain, Yuxiang Yang
2021 arXiv   pre-print
By defining the combinatorial search space of NAS to be the set of different edge-partitionings (colorings) into same-weight classes, we represent compact architectures via efficient learned edge-partitionings  ...  For several RL tasks, we manage to learn colorings translating to effective policies parameterized by as few as 17 weight parameters, providing >90 over state-of-the-art compact policies based on Toeplitz  ...  The core concept is that different architectures can be embedded into combinatorial space, where they correspond to different subgraphs of the given acyclic directed base graph G (DAG).  ... 
arXiv:1907.06511v4 fatcat:i4d5rlvqfzgrnkgah5hlvdwhla

Optimization Models for Machine Learning: A Survey [article]

Claudio Gambella, Bissan Ghaddar, Joe Naoum-Sawaya
2020 arXiv   pre-print
The strengths and the shortcomings of these models are discussed and potential research directions and open problems are highlighted.  ...  Such models can benefit from the advancement of numerical optimization techniques which have already played a distinctive role in several machine learning settings.  ...  Acknowledgement We are very grateful to four anonymous referees for their valuable feedback and comments that helped improve the content and presentation of the paper.  ... 
arXiv:1901.05331v4 fatcat:3bwfbl34rrf2tkpqeidl5hfoxu

Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks [article]

Simge Kucukyavuz, Ali Shojaie, Hasan Manzour, Linchuan Wei, Hao-Hsiang Wu
2022 arXiv   pre-print
Bayesian Networks (BNs) represent conditional probability relations among a set of random variables (nodes) in the form of a directed acyclic graph (DAG), and have found diverse applications in knowledge  ...  The central problem can be modeled as a mixed-integer program with an objective function composed of a convex quadratic loss function and a regularization penalty subject to linear constraints.  ...  Conclusion In this paper, we study the problem of learning an optimal directed acyclic graph (DAG) from continuous observational data, where the causal effect among the random variables is linear.  ... 
arXiv:2005.14346v3 fatcat:p7wq3ezqpjfnnbx5s4w6fpozdm

A Gentle Introduction to Deep Learning for Graphs [article]

Davide Bacciu, Federico Errica, Alessio Micheli, Marco Podda
2019 arXiv   pre-print
This work is designed as a tutorial introduction to the field of deep learning for graphs.  ...  The adaptive processing of graph data is a long-standing research topic which has been lately consolidated as a theme of major interest in the deep learning community.  ...  Specifically, FastGCN samples t nodes at each layervia importance sampling, so that the variance of the gradient estimator is reduced.  ... 
arXiv:1912.12693v1 fatcat:lww6akhmuvbe5hu335hl7ggghu

Bottleneck Time Minimization for Distributed Iterative Processes: Speeding Up Gossip-Based Federated Learning on Networked Computers [article]

Mehrdad Kiamari, Bhaskar Krishnamachari
2021 arXiv   pre-print
graph.  ...  Furthermore, we derive the expected value of bottleneck time. Finally, we apply our proposed scheme on gossip-based federated learning as an application of iterative processes.  ...  Any views, opinions, and/or findings expressed are those of the author(s) and should not be interpreted as representing the official views or policies of the Department of Defense or the U.S.  ... 
arXiv:2106.15048v1 fatcat:63lthounljbhpjft2wmscisxzq

Survey on graph embeddings and their applications to machine learning problems on graphs

Ilya Makarov, Dmitrii Kiselev, Nikita Nikitinsky, Lovro Subelj
2021 PeerJ Computer Science  
Using the constructed feature spaces, many machine learning problems on graphs can be solved via standard frameworks suitable for vectorized feature representation.  ...  machine learning problems on graphs.  ...  ., 2019) compares different topology-based sampling algorithms (node, edge and random walks) in terms of bias and variance of learned GCN model.  ... 
doi:10.7717/peerj-cs.357 pmid:33817007 pmcid:PMC7959646 fatcat:ntronyrbgfbedez5dks6h4hoq4
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