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How Many Pairwise Preferences Do We Need to Rank A Graph Consistently?
[article]
2019
arXiv
pre-print
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Our proposed algorithm, Pref-Rank, predicts the underlying ranking using an SVM based approach over the chosen embedding of the product graph, and is the first to provide statistical consistency on two ...
We also report experimental evaluations on different synthetic and real datasets, where our algorithm is shown to outperform the state-of-the-art methods. ...
] which relates optimum SVM objective to Lóvasz-ϑ. ...
arXiv:1811.02161v2
fatcat:qh5cx27zancm5ljit2hup4al5y
Graph Kernels: A Survey
[article]
2019
arXiv
pre-print
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Finally, we discuss key applications of graph kernels, and outline some challenges that remain to be addressed. ...
Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. ...
Then, the Lovász ϑ kernel is defined as followŝ k(G, G ) = S∈L S ∈L δ(|S|, |S |) 1 Z |S| k ϑ S (G), ϑ S (G ) (44)
SVM-ϑ Kernel The SVM-ϑ kernel is very related to the Lovász ϑ kernel (Johansson et ...
arXiv:1904.12218v1
fatcat:shfa4lw4eja2rayvubrph6me3m
How Many Pairwise Preferences Do We Need to Rank a Graph Consistently?
2019
PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE
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Our proposed algorithm, Pref-Rank, predicts the underlying ranking using an SVM based approach using the chosen embedding of the product graph, and is the first to provide statistical consistency on two ...
O(n4/3) for union of k-cliques, or O(n5/3) for random and power law graphs etc.—a quantity much smaller than the fundamental limit of Ω(n2) for large n. ...
This work is partially supported by an Amazon grant to the Department of CSA, IISc and Qualcomm travel grant. ...
doi:10.1609/aaai.v33i01.33014830
fatcat:tmwe2bnue5cqbnfefis4xpxydm
Graph Kernels: A Survey
2021
The Journal of Artificial Intelligence Research
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Finally, we discuss key applications of graph kernels, and outline some challenges that remain to be addressed. ...
Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. ...
Then, the Lovász ϑ kernel is defined as follows k(G, G ) = S∈L S ∈L δ(|S|, |S |) 1 Ẑ|S| k ϑ S (G), ϑ S (G ) (40
SVM-ϑ Kernel The SVM-ϑ kernel is closely related to the Lovász ϑ kernel (Johansson et ...
doi:10.1613/jair.1.13225
fatcat:o7whugpf3rd7hf7g7e7gcxhoyi
Lovasz Convolutional Networks
[article]
2019
arXiv
pre-print
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We analyse local and global properties of graphs and demonstrate settings where LCNs tend to work better than GCNs. ...
In this work, we propose Lovasz Convolutional Network (LCNs) which are capable of incorporating global graph properties. LCNs achieve this by utilizing Lovasz's orthonormal embeddings of the nodes. ...
Jethava et al. (2013) show an interesting connection between Lovász ϑ function and one class SVMs. Jain et al. (2016) propose Recurrent Neural Networks (RNN) for graphs. ...
arXiv:1805.11365v3
fatcat:i3zjynz6b5ffpelcrbz6uwdq3y
Higher Order Fused Regularization for Supervised Learning with Grouped Parameters
[chapter]
2015
Lecture Notes in Computer Science
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We define the HOF penalty as the Lovász extension of a submodular higher-order potential function, which encourages parameters in a group to take similar estimated values when used as a regularizer. ...
We investigate the empirical performance of the proposed algorithm by using synthetic and real-world data. ...
This formulation includes well-known regularized supervised learning problems such as Lasso, logistic regression [17] , elastic net [36] , and SVM [28] . ...
doi:10.1007/978-3-319-23528-8_36
fatcat:mqhksrve5zck3mzxzvn7uqb27i
Random Coordinate Descent Methods for Minimizing Decomposable Submodular Functions
[article]
2015
arXiv
pre-print
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Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. ...
In this paper, we use random coordinate descent methods to obtain algorithms with faster linear convergence rates and cheaper iteration costs. ...
Lovász showed that a set function F is submodular if and only if its Lovász extension f is convex [9] . ...
arXiv:1502.02643v1
fatcat:ei3auk3muzgpdiupnfbad5fi5y
The Latent Bernoulli-Gauss Model for Data Analysis
[article]
2010
arXiv
pre-print
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The model is applied to MAP estimation, clustering, feature selection and collaborative filtering and fares favorably with the state-of-the-art latent-variable models. ...
We present the LBG model in sec. 2 and its applications in sec. 2.3. ...
The optimal mapping is obtained by the Kuhn-Munkres algorithm (Lovasz & Plummer, 1986) . We compared our results with those of MOU, pLSI and LDA. ...
arXiv:1007.0660v1
fatcat:3itascqvn5cj5ci4zhqblxfuyy
GraKeL: A Graph Kernel Library in Python
[article]
2020
arXiv
pre-print
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The problem of accurately measuring the similarity between graphs is at the core of many applications in a variety of disciplines. ...
It is simple to use and can be naturally combined with scikit-learn's modules to build a complete machine learning pipeline for tasks such as graph classification and clustering. ...
It is used for solving the semidefinite programming formulation that computes the Lovász number ϑ of a graph (Andersen et al., 2013). ...
arXiv:1806.02193v2
fatcat:6kriueyit5c2hjqzmrzmfnidxe
AN EFFICIENT REPRESENTATION OF 3D BUILDINGS: APPLICATION TO THE EVALUATION OF CITY MODELS
2021
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
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Most modeling methods focus on 3D buildings with Very High Resolution overhead data (images and/or 3D point clouds). ...
The experiments show for both feature extraction strategy strong and complementary results (F-score > 74% for most labels). ...
SVM ϑ Kernel (STK) This kernel takes only the graph structure into account and is agnostic to attributes. It is a tractable version of the Lovász ϑ kernel (Johansson et al., 2014) . ...
doi:10.5194/isprs-archives-xliii-b2-2021-329-2021
fatcat:cuqaeqzln5hvpmi66xd6kjr22e
Stochastic subGradient Methods with Linear Convergence for Polyhedral Convex Optimization
[article]
2016
arXiv
pre-print
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2015 pre-print arXiv:1510.01444v4 fatcat:l4j44gzybvaqfc7s7n3us4pdnaOther Versions
Its applications in machine learning include ℓ_1 constrained or regularized piecewise linear loss minimization and submodular function minimization. ...
To the best of our knowledge, this is the first result on the linear convergence rate of stochastic subgradient methods for non-smooth and non-strongly convex optimization problems. ...
Acknolwedgements We thank James Renegar for pointing out the connection to his work and for his valuable comments on the difference between the two work. ...
arXiv:1510.01444v5
fatcat:3u3w4374e5cqhgjfa6aan6oyue
Graph Drawing via Gradient Descent, (GD)^2
[article]
2020
arXiv
pre-print
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We provide quantitative and qualitative evidence of the effectiveness of (GD)^2 with experimental data and a functional prototype: . ...
Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other ...
The loss reaches its minimum at 0 when the SVM classifier f w,b : x → xw + b predicts node i and j to be greater than 1 and node k and l to be less than −1. ...
arXiv:2008.05584v1
fatcat:u3ybexyzpzb5zf63l3spbapbbq
Safe Element Screening for Submodular Function Minimization
[article]
2018
arXiv
pre-print
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Submodular functions are discrete analogs of convex functions, which have applications in various fields, including machine learning and computer vision. ...
However, in large-scale applications, solving Submodular Function Minimization (SFM) problems remains challenging. ...
SVM [20, 29] . ...
arXiv:1805.08527v4
fatcat:b7wci3icirb5nieef7hjqdbwly
Partition-wise Linear Models
[article]
2014
arXiv
pre-print
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Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. ...
Our key ideas are 1) assigning linear models not to regions but to partitions (region-specifiers) and representing region-specific linear models by linear combinations of partition-specific models, and ...
, λ θ' , σ in LDKL, C in FaLK-SVM, and C, γ in RBF-SVM. 10 We used a scikit-learn package. http://scikit-learn.org/ 11 We used a libsvm package. ...
arXiv:1410.8675v1
fatcat:oh33dc24yfgvjfhrr755d6dffq
A study in Rashomon curves and volumes: A new perspective on generalization and model simplicity in machine learning
[article]
2021
arXiv
pre-print
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2020 pre-print arXiv:1908.01755v2 fatcat:lzafipvlvvefxc6oqbosov347mOther Versions
We consider the Rashomon set - the set of almost-equally-accurate models for a given problem - and study its properties and the types of models it could contain. ...
In this work, we study how the Rashomon effect can be useful for understanding the relationship between training and test performance, and the possibility that simple-yet-accurate models exist for many ...
Acknowledgments We thank Theja Tulabandhula, Aaron Fisher, Zhi Chen, and Fulton Wang for comments on the manuscript. ...
arXiv:1908.01755v3
fatcat:zwzifjshubamrfcf4s5hzcumjm
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