Graph Construction from Data using Non Negative Kernel regression (NNK Graphs)

Shekkizhar, Sarath; Ortega, Antonio

doi:10.48550/arxiv.1910.09383

Cited by 7 publications

(14 citation statements)

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“…SUPPLEMENTARY MATERIAL A. Proof of Proposition (1) Lemma 1 ( [44]). The quadratic optimization problem of (7) satisfies active constraints set 4 .…”

Section: Discussion and Future Workmentioning

confidence: 99%

DeepNNK: Explaining deep models and their generalization using polytope interpolation

Shekkizhar,

Ortega

2020

Preprint

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Modern machine learning systems based on neural networks have shown great success in learning complex data patterns while being able to make good predictions on unseen data points. However, the limited interpretability of these systems hinders further progress and application to several domains in the real world. This predicament is exemplified by time consuming model selection and the difficulties faced in predictive explainability, especially in the presence of adversarial examples. In this paper, we take a step towards better understanding of neural networks by introducing a local polytope interpolation method. The proposed Deep Non Negative Kernel regression (NNK) interpolation framework is non parametric, theoretically simple and geometrically intuitive. We demonstrate instance based explainability for deep learning models and develop a method to identify models with good generalization properties using leave one out estimation. Finally, we draw a rationalization to adversarial and generative examples which are inevitable from an interpolation view of machine learning.

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“…SUPPLEMENTARY MATERIAL A. Proof of Proposition (1) Lemma 1 ( [44]). The quadratic optimization problem of (7) satisfies active constraints set 4 .…”

Section: Discussion and Future Workmentioning

confidence: 99%

DeepNNK: Explaining deep models and their generalization using polytope interpolation

Shekkizhar,

Ortega

2020

Preprint

Self Cite

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“…We now consider a more recent sparsity-based method. We choose NNK (Non Negative Kernel regression) [6], due to its simplicity and its demonstrated results on semisupervised learning tasks. This method can be interpreted as producing representations with orthogonal approximation errors, which in turn favors sparser representations.…”

Section: Sparsity-based Methodsmentioning

confidence: 99%

“…Many recent works have therefore considered the problem of inferring the topology (i.e. the edges) of the graph based on nodal observations [4,5,6]; see also [7] for a recent tutorial treatment. Inferring a graph structure can be performed in a task-agnostic manner, where only unsupervised observations This work was supported in part by the Brittany region and by the NSF award CCF-1750428.…”

Section: Introductionmentioning

confidence: 99%

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Graph topology inference benchmarks for machine learning

Lassance¹,

Gripon²,

Mateos³

2020

Preprint

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Graphs are nowadays ubiquitous in the fields of signal processing and machine learning. As a tool used to express relationships between objects, graphs can be deployed to various ends: (i) clustering of vertices, (ii) semi-supervised classification of vertices, (iii) supervised classification of graph signals, and (iv) denoising of graph signals. However, in many practical cases graphs are not explicitly available and must therefore be inferred from data. Validation is a challenging endeavor that naturally depends on the downstream task for which the graph is learnt. Accordingly, it has often been difficult to compare the efficacy of different algorithms. In this work, we introduce several ease-to-use and publicly released benchmarks specifically designed to reveal the relative merits and limitations of graph inference methods. We also contrast some of the most prominent techniques in the literature.

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“…Many recent works have tackled the problem of inferring the graph topology using graph signals [71,119,146]; see also [108] for a recent tutorial treatment. Inferring a graph structure can be performed in a task-agnostic manner, i.e., labeling data is not used.…”

Section: Inferring Graph Topology From Signalsmentioning

confidence: 99%

Graphs for deep learning representations

Lassance¹

2020

Preprint

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Ces dernières années, les méthodes d'apprentissage profond ont atteint l'état de l'art dans une vaste gamme de tâches d'apprentissage automatique, y compris la classification d'images et la traduction automatique. Ces architectures sont assemblées pour résoudre des tâches d'apprentissage automatique de bout en bout. Afin d'atteindre des performances de haut niveau, ces architectures nécessitent souvent d'un très grand nombre de paramètres.Les conséquences indésirables sont multiples, et pour y remédier, il est souhaitable de pouvoir compreendre ce qui se passe à l'intérieur des architectures d'apprentissage profond.Il est difficile de le faire en raison de: i) la dimension élevée des représentations, and ii) la stochasticité du processus de formation. Dans cette thèse, nous étudions ces architectures en introduisant un formalisme à base de graphes, s'appuyant notamment sur les récents progrès du traitement de signaux sur graphe (TSG). À savoir, nous utilisons des graphes pour représenter les espaces latents des réseaux neuronaux profonds. Nous montrons que ce formalisme des graphes nous permet de répondre à diverses questions, notamment: i) mesurer des capacités de généralisation, ii) réduire la quantité de des choix arbitraires dans la conception du processus d'apprentissage, iii) améliorer la robustesse aux petites ix x RÉSUMÉ perturbations ajoutées sur les entrées, and iv) réduire la complexité des calculs.

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Graph Construction from Data using Non Negative Kernel regression (NNK Graphs)

Cited by 7 publications

References 0 publications

DeepNNK: Explaining deep models and their generalization using polytope interpolation

DeepNNK: Explaining deep models and their generalization using polytope interpolation

Graph topology inference benchmarks for machine learning

Graphs for deep learning representations

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