Are web users really Markovian?

Abstract

User modeling on the Web has rested on the fundamental assumption of Markovian behavior -a user's next action depends only on her current state, and not the history leading up to the current state. This forms the underpinning of PageRank web ranking, as well as a number of techniques for targeting advertising to users. In this work we examine the validity of this assumption, using data from a number of Web settings. Our main result invokes statistical order estimation tests for Markov chains to establish that Web users are not, in fact, Markovian. We study the extent to which the Markovian assumption is invalid, and derive a number of avenues for further research.

Memory in network flows and its effects on spreading dynamics and community detection

“…In principle, we could go to any order n for higher accuracy. In practice, however, higher-order Markov models are more complex and demand many long pathways to statistically separate real effects of memory from insufficient data 15 . For the air-traffic data, we have enough long pathways to measure the entropy rate of a higher-order Markov model.…”

“…Recent work has indicated that a first-order Markov model may fail to adequately predict real dynamics 15,20,23,26 . That is, real dynamics often have at least one-step memory, which conventional network analysis cannot capture.…”

“…When going from rankings based on counting links to measuring the average visit frequency of a random walker on a standard network,that is, calculating the PageRank 6 , the importance of neighbours becomes evident. Similarly, when going to PageRank on a network with secondorder memory, the amount of flow received from neighbours also depends on the flow's origin 15,48 . We define a generalized secondorder PageRank as the stationary solution of equation (6) …”

“…Shannon 10 introduced higher-order memory models in 1948, and there is a substantial body of work on analysing memory effects in, for example, time-series analysis for forecasting financial markets 11 , correlated random walks for predicting animal movements 12 and exponential random graph models for capturing social networks 13 . Moreover, there is recent evidence that memory is necessary for accurately predicting web traffic 14,15 , for improving search and navigation in information networks [16][17][18] and for capturing important phenomena in the spread of information [19][20][21][22][23] and epidemics [24][25][26][27][28][29] . Nevertheless, little is known about memory effects on community detection, ranking and spreading analysis, three principal methods in network science.…”

Evolution properties of online user preference diversity

“…Inspired by these questions, we investigate the evolution properties of online user preference diversity, where the preference diversity is measured by the variation coefficient. Firstly, we rescale each user life span to an standard time interval (see Methods), which has been used for the domain analysis of various online settings [32][33][34][35]. Comparing with the null model, the empirical results indicate that, for movies and reviews, the diversity of user preference increases initially and then decreases to a small value.…”