We introduce region-based explanations (RbX), a novel, model-agnostic method to generate local explanations of scalar outputs from a black-box prediction model using only query access. RbX is based on a greedy algorithm for building a convex polytope that approximates a region of feature space where model predictions are close to the prediction at some target point. This region is fully specified by the user on the scale of the predictions, rather than on the scale of the features. The geometry of this polytope -specifically the change in each coordinate necessary to escape the polytope -quantifies the local sensitivity of the predictions to each of the features. These "escape distances" can then be standardized to rank the features by local importance. RbX is guaranteed to satisfy a "sparsity" axiom, which requires that features which do not enter into the prediction model are assigned zero importance. At the same time, real data examples and synthetic experiments show how RbX can more readily detect all locally relevant features than existing methods.
The rapid growth of social media has been witnessed during recent years as a result of the prevalence of the internet. This trend brings an increasing interest in simulating social media which can provide valuable insights to both academic researchers and businesses. In this paper, we present a step-by-step approach of using Hawkes process, a self-activating stochastic process, to simulate Twitter activities and demonstrate how this model can be utilized to evaluate the chance of extremely rare web crises. Another goal of this research is to introduce a new strategy that implements Hawkes process on graph structures. Overall, we intend to extend the current Hawkes process to a wider range of scenarios and, in particular, create a more realistic simulation of Twitter activities by incorporating the actual user status and following-follower interactions between users.
CCS CONCEPTS• Mathematics of computing → Stochastic processes; Maximum likelihood estimation; • General and reference → Estimation.
The latent order book of [Donier et al., 2015, A fully consistent, minimal model for nonlinear market impact, Quantitative Finance 15(7), 1109–1121] is one of the most promising agent-based models for market impact. This work extends the minimal model by allowing agents to exhibit mean-reversion, a commonly observed pattern in real markets. This modification leads to new order book dynamics, which we explicitly study and analyze. Underlying our analysis is a mean-field assumption that views the order book through its average density. We show how price impact develops in this new model, providing a flexible family of solutions that can potentially be calibrated to real data. While no closed-form solution is provided, we complement our theoretical investigation with extensive numerical results, including a simulation scheme for the entire order book.
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