In this paper, we introduce Max Markov Chain (MMC), a novel model for sequential data with sparse correlations among the state variables.It may also be viewed as a special class of approximate models for High-order Markov Chains (HMCs).MMC is desirable for domains where the sparse correlations are long-term and vary in their temporal stretches.Although generally intractable, parameter optimization for MMC can be solved analytically.However, based on this result,we derive an approximate solution that is highly efficient empirically.When compared with HMC and approximate HMC models, MMCcombines better sample efficiency, model parsimony, and an outstanding computational advantage.Such a quality allows MMC to scale to large domainswhere the competing models would struggle to perform.We compare MMC with several baselines with synthetic and real-world datasets to demonstrate MMC as a valuable alternative for stochastic modeling.
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PrivTrace: Differentially Private Trajectory Synthesis by Adaptive Markov Models
Publishing trajectory data (individual’s movement information) is very useful, but it also raises privacy concerns. To handle the privacy concern, in this paper, we apply differential privacy, the standard technique for data privacy, together with Markov chain model, to generate synthetic trajectories. We notice that existing studies all use Markov chain model and thus propose a framework to analyze the usage of the Markov chain model in this problem. Based on the analysis, we come up with an effective algorithm PrivTrace that uses the first-order and second-order Markov model adaptively. We evaluate PrivTrace and existing methods on synthetic and real-world datasets to demonstrate the superiority of our method.
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- Award ID(s):
- 2220433
- PAR ID:
- 10467378
- Publisher / Repository:
- USENIX
- Date Published:
- ISBN:
- 978-1-939133-37-3
- Format(s):
- Medium: X
- Location:
- Anaheim, CA, USA
- Sponsoring Org:
- National Science Foundation
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