Filters








67 Hits in 3.7 sec

How Many Pairwise Preferences Do We Need to Rank A Graph Consistently? [article]

Aadirupa Saha, Rakesh Shivanna, Chiranjib Bhattacharyya
2019 arXiv   pre-print
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]

Giannis Nikolentzos and Giannis Siglidis and Michalis Vazirgiannis
2019 arXiv   pre-print
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?

Aadirupa Saha, Rakesh Shivanna, Chiranjib Bhattacharyya
2019 PROCEEDINGS OF THE THIRTIETH AAAI CONFERENCE ON ARTIFICIAL INTELLIGENCE AND THE TWENTY-EIGHTH INNOVATIVE APPLICATIONS OF ARTIFICIAL INTELLIGENCE CONFERENCE  
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

Giannis Nikolentzos, Giannis Siglidis, Michalis Vazirgiannis
2021 The Journal of Artificial Intelligence Research  
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]

Prateek Yadav, Madhav Nimishakavi, Naganand Yadati, Shikhar Vashishth, Arun Rajkumar, Partha Talukdar
2019 arXiv   pre-print
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]

Koh Takeuchi, Yoshinobu Kawahara, Tomoharu Iwata
2015 Lecture Notes in Computer Science  
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]

Alina Ene, Huy L. Nguyen
2015 arXiv   pre-print
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]

Amnon Shashua, Gabi Pragier
2010 arXiv   pre-print
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]

Giannis Siglidis, Giannis Nikolentzos, Stratis Limnios, Christos Giatsidis, Konstantinos Skianis, Michalis Vazirgiannis
2020 arXiv   pre-print
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

O. Ennafii, A. Le Bris, F. Lafarge, C. Mallet
2021 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
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]

Tianbao Yang, Qihang Lin
2016 arXiv   pre-print
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]

Reyan Ahmed, Felice De Luca, Sabin Devkota, Stephen Kobourov, Mingwei Li
2020 arXiv   pre-print
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]

Weizhong Zhang, Bin Hong, Lin Ma, Wei Liu, Tong Zhang
2018 arXiv   pre-print
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]

Hidekazu Oiwa, Ryohei Fujimaki
2014 arXiv   pre-print
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]

Lesia Semenova, Cynthia Rudin, Ronald Parr
2021 arXiv   pre-print
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
« Previous Showing results 1 — 15 out of 67 results