Instructional Material
Online Graph Learning from Social Interactions
Shumovskaia, Valentina, Ntemos, Konstantinos, Vlaski, Stefan, Sayed, Ali H.
Social learning algorithms provide models for the formation of opinions over social networks resulting from local reasoning and peer-to-peer exchanges. Interactions occur over an underlying graph topology, which describes the flow of information and relative influence between pairs of agents. For a given graph topology, these algorithms allow for the prediction of formed opinions. In this work, we study the inverse problem. Given a social learning model and observations of the evolution of beliefs over time, we aim at identifying the underlying graph topology. The learned graph allows for the inference of pairwise influence between agents, the overall influence agents have over the behavior of the network, as well as the flow of information through the social network. The proposed algorithm is online in nature and can adapt dynamically to changes in the graph topology or the true hypothesis.
From graph cuts to isoperimetric inequalities: Convergence rates of Cheeger cuts on data clouds
Trillos, Nicolas Garcia, Murray, Ryan, Thorpe, Matthew
In this work we study statistical properties of graph-based clustering algorithms that rely on the optimization of balanced graph cuts, the main example being the optimization of Cheeger cuts. We consider proximity graphs built from data sampled from an underlying distribution supported on a generic smooth compact manifold $M$. In this setting, we obtain high probability convergence rates for both the Cheeger constant and the associated Cheeger cuts towards their continuum counterparts. The key technical tools are careful estimates of interpolation operators which lift empirical Cheeger cuts to the continuum, as well as continuum stability estimates for isoperimetric problems. To our knowledge the quantitative estimates obtained here are the first of their kind.
Deep Learning Prerequisites: Linear Regression in Python
Deep Learning Prerequisites: Linear Regression in Python Data science: Learn linear regression from scratch and build your own working program in Python for data analysis. BESTSELLER 22,535 students enrolled Created by Lazy Programmer Inc. ย English [Auto-generated], Spanish [Auto-generated] Preview this course ย - GET COUPON CODE Free Coupon Discount Udemy Online Courses
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