Choice decisions made by users of online applications can suffer from biases due to the users' level of engagement. For instance, low engagement users may make random choices with no concern for the quality of items offered. This biased choice data can corrupt estimates of user preferences for items. However, one can correct for these biases if additional behavioral data is utilized. To do this we construct a new choice engagement time model which captures the impact of user engagement on choice decisions and response times associated with these choice decisions. Response times are the behavioral data we choose because they are easily measured by online applications and reveal information about user engagement. To test our model we conduct online polls with subject populations that have different levels of engagement and measure their choice decisions and response times. We have two main empirical findings. First, choice decisions and response times are correlated, with strong preferences having faster response times than weak preferences. Second, low user engagement is manifested through more random choice data and faster response times. Both of these phenomena are captured by our choice engagement time model and we find that this model fits the data better than traditional choice models. Our work has direct implications for online applications. It lets these applications remove the bias of low engagement users when estimating preferences for items. It also allows for the segmentation of users according to their level of engagement, which can be useful for targeted advertising or marketing campaigns.
Models were also developed which viewed the information accumulation process as a random walk . The random walk modeled the relative information accumulation of each item, whereas previous models had focused on independent information accumulation processes for each item. The drift of the walk depends on the item utilities and there are decision thresholds above and below the starting point of the process. An item is chosen when one of these thresholds is hit by the process, and the item chosen depends on whether the upper or lower threshold is hit first. A continuous time version of these models known as the drift diffusion model was proposed by @cite_0 , where the information accumulation process is modeled as a one dimensional Brownian motion. The drift diffusion model has been successful at modeling phenomena seen in empirical data . However, a challenge posed by the drift diffusion model is the lack of a simple closed form expression for the likelihood function of the response times. To overcome this, approximations have been developed to allow for easier model estimation . Recent work has extended the drift diffusion model to multi-item choice decisions .
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Diffusion is known to be an important process governing the behaviours observed in network environments like social networks, contact networks, etc. For modeling the diffusion process, the Independent Cascade Model (IC Model) is commonly adopted and algorithms have been proposed for recovering the hidden diffusion network based on observed cascades. However, the IC Model assumes the effects of multiple neighbors on a node to be independent and does not consider the structural diversity of nodes' neighbourhood. In this paper, we propose an extension of the IC Model with the community structure of node neighbours incorporated. We derive an expectation maximization (EM) algorithm to infer the model parameters. To evaluate the effectiveness and efficiency of the proposed method, we compared it with the IC model and its variants that do not consider the structural properties. Our empirical results based on the MemeTracker dataset, shows that after incorporating the structural diversity, there is a significant improvement in the modelling accuracy, with reasonable increase in run-time. Estimation of parameters of a diffusion based on discrete time observations poses a difficult problem due to the lack of a closed form expression for the likelihood. From a Bayesian computational perspective it can be casted as a missing data problem where the diffusion bridges in between discrete-time observations are missing. The computational problem can then be dealt with using a Markov-chain Monte-Carlo method known as data-augmentation. If unknown parameters appear in the diffusion coefficient, direct implementation of data-augmentation results in a Markov chain that is reducible. Furthermore, data-augmentation requires efficient sampling of diffusion bridges, which can be difficult, especially in the multidimensional case. We present a general framework to deal with with these problems that does not rely on discretisation. The construction generalises previous approaches and sheds light on the assumptions necessary to make these approaches work. We define a random-walk type Metropolis-Hastings sampler for updating diffusion bridges. Our methods are illustrated using guided proposals for sampling diffusion bridges. These are Markov processes obtained by adding a guiding term to the drift of the diffusion. We give general guidelines on the construction of these proposals and introduce a time change and scaling of the guided proposal that reduces discretisation error. Numerical examples demonstrate the performance of our methods. Predicting the diffusion of information on social networks is a key problem for applications like Opinion Leader Detection, Buzz Detection or Viral Marketing. Many recent diffusion models are direct extensions of the Cascade and Threshold models, initially proposed for epidemiology and social studies. In such models, the diffusion process is based on the dynamics of interactions between neighbor nodes in the network (the social pressure), and largely ignores important dimensions as the content of the piece of information diffused. We propose here a new family of probabilistic models that aims at predicting how a content diffuses in a network by making use of additional dimensions: the content of the piece of information diffused, user's profile and willingness to diffuse. These models are illustrated and compared with other approaches on two blog datasets. The experimental results obtained on these datasets show that taking into account the content of the piece of information diffused is important to accurately model the diffusion process. The stochastic block model (SBM) with two communities, or equivalently the planted bisection model, is a popular model of random graph exhibiting a cluster behaviour. In the symmetric case, the graph has two equally sized clusters and vertices connect with probability @math within clusters and @math across clusters. In the past two decades, a large body of literature in statistics and computer science has focused on providing lower-bounds on the scaling of @math to ensure exact recovery. In this paper, we identify a sharp threshold phenomenon for exact recovery: if @math and @math are constant (with @math ), recovering the communities with high probability is possible if @math and impossible if @math . In particular, this improves the existing bounds. This also sets a new line of sight for efficient clustering algorithms. While maximum likelihood (ML) achieves the optimal threshold (by definition), it is in the worst-case NP-hard. This paper proposes an efficient algorithm based on a semidefinite programming relaxation of ML, which is proved to succeed in recovering the communities close to the threshold, while numerical experiments suggest it may achieve the threshold. An efficient algorithm which succeeds all the way down to the threshold is also obtained using a partial recovery algorithm combined with a local improvement procedure.