Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts. Being amazed by the incredible power of machine learning, a lot of us have become unfaithful to statistics. Our focus has narrowed down to exploring machine learning. We fail to understand that machine learning is only one way to solve real world problems. In several situations, it does not help us solve business problems, even though there is data involved in these problems. To say the least, knowledge of statistics will allow you to work on complex analytical problems, irrespective of the size of data. In 1770s, Thomas Bayes introduced'Bayes Theorem'.

Mussmann, Stephen (Purdue University) | Moore, John (Purdue University) | Pfeiffer, Joseph John (Purdue University) | Neville, Jennifer (Purdue University)

Due to the recent availability of large complex networks, considerable analysis has focused on understanding and characterizing the properties of these networks. Scalable generative graph models focus on modeling distributions of graphs that match real world network properties and scale to large datasets. Much work has focused on modeling networks with a power law degree distribution, clustering, and small diameter. In network analysis, the assortativity statistic is defined as the correlation between the degrees of linked nodes in the network. The assortativity measure can distinguish between types of networks---social networks commonly exhibit positive assortativity, in contrast to biological or technological networks that are typically disassortative. Despite this, little work has focused on scalable graph models that capture assortativity in networks. The contributions of our work are twofold. First, we prove that an unbounded number of pairs of networks exist with the same degree distribution and assortativity, yet different joint degree distributions. Thus, assortativity as a network measure cannot distinguish between graphs with complex (non-linear) dependence in their joint degree distributions. Motivated by this finding, we introduce a generative graph model that explicitly estimates and models the joint degree distribution. Our Binned Chung Lu method accurately captures both the joint degree distribution and assortativity, while still matching characteristics such as the degree distribution and clustering coefficients. Further, our method has subquadratic learning and sampling methods that enable scaling to large, real world networks. We evaluate performance compared to other scalable graph models on six real world networks, including a citation network with over 14 million edges.

I hope you liked my previous posts. Today I am going to talk on an important topic; that is Probability Distribution. Well, it's like you are trying to assume or predict something in a scientific way. Now the question is Probability on what? First concentrate on 2 kind of variables: 1. Discrete (Example like coin toss, rolling die, counting person etc.) Now the question is why do we need to learn probability distribution?