A Sharp Lower Bound for Mixed-membership
نویسندگان
چکیده
The goal is to estimate {πi, 1 ≤ i ≤ n} (i.e., membership estimation). We model the network with the degree-corrected mixed membership (DCMM) model [8]. Since for many natural networks, the degrees have an approximate power-law tail, we allow severe degree heterogeneity in our model. For any membership estimation {π̂i, 1 ≤ i ≤ n}, since each πi is a probability mass function, it is natural to measure the errors by the average `-norm 1 n n ∑
منابع مشابه
An Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
متن کاملThe Structure of Bhattacharyya Matrix in Natural Exponential Family and Its Role in Approximating the Variance of a Statistics
In most situations the best estimator of a function of the parameter exists, but sometimes it has a complex form and we cannot compute its variance explicitly. Therefore, a lower bound for the variance of an estimator is one of the fundamentals in the estimation theory, because it gives us an idea about the accuracy of an estimator. It is well-known in statistical inference that the Cram&eac...
متن کاملA Sharp Sufficient Condition for Sparsity Pattern Recovery
Sufficient number of linear and noisy measurements for exact and approximate sparsity pattern/support set recovery in the high dimensional setting is derived. Although this problem as been addressed in the recent literature, there is still considerable gaps between those results and the exact limits of the perfect support set recovery. To reduce this gap, in this paper, the sufficient con...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کاملRESOLUTION METHOD FOR MIXED INTEGER LINEAR MULTIPLICATIVE-LINEAR BILEVEL PROBLEMS BASED ON DECOMPOSITION TECHNIQUE
In this paper, we propose an algorithm base on decomposition technique for solvingthe mixed integer linear multiplicative-linear bilevel problems. In actuality, this al-gorithm is an application of the algorithm given by G. K. Saharidis et al for casethat the rst level objective function is linear multiplicative. We use properties ofquasi-concave of bilevel programming problems and decompose th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017