Differentially Private Learning of Markov Chains: Near-Optimal Sample Complexity for Item and User Level Privacy
Researchers give near-optimal private bounds for learning Markov chain transition matrices.
The paper studies differentially private estimation of a discrete ergodic Markov chain's transition matrix from N independent trajectories of length T, under maximum row-wise L1 error and arbitrary initial distributions. The bounds depend on the number of states, minimum stationary probability, and pseudo-spectral gap, which control coverage and mixing. Item-level privacy separates the costs of sampling, state occupancy, mixing, and privacy. For sufficiently long trajectories, user-level privacy reduces to private product-distribution estimation, with nearly tight large-T bounds and new optimal user-level bounds for products of discrete distributions.
- The task is private estimation of a discrete ergodic Markov transition matrix.
- Bounds depend on stationary probability and the pseudo-spectral gap.
- User-level privacy reduces long trajectories to private product-distribution estimation.
- Item-level bounds are tight up to a non-private term.
From the original article
1 min read at arxiv.orgSequential data such as documents, conversations, and trajectories are naturally partitioned across users, motivating privacy guarantees that protect each user's entire trajectory. We initiate the study of privately estimating the transition matrix of a discrete ergodic Markov chain from N independent trajectories of length T, with arbitrary initial distributions, under maximum row-wise ell 1 error.
By Devansh Gupta · arxiv.org
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