Name
Abstract | ||
|---|---|---|
This paper studies the problem of learning the probability distribution P-X of a discrete random variable X using indirect and sequential samples. At each time step, we choose one of the possible K functions, g(1,) . . . , g(K) and observe the corresponding sample g(i)(X). The goal is to estimate the probability distribution of X by using a minimum number of such sequential samples. This problem has several real-world applications including inference under non-precise information and privacy-preserving statistical estimation. We establish necessary and sufficient conditions on the functions g(1,) . . . , g(K) under which asymptotically consistent estimation is possible. We also derive lower bounds on the estimation error as a function of total samples and show that it is order-wise achievable. Leveraging these results, we propose an iterative algorithm that i) chooses the function to observe at each step based on past observations; and ii) combines the obtained samples to estimate p(X). The performance of this algorithm is investigated numerically under various scenarios, and shown to outperform baseline approaches. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1109/allerton.2018.8635924 | 2018 56TH ANNUAL ALLERTON CONFERENCE ON COMMUNICATION, CONTROL, AND COMPUTING (ALLERTON) |
Keywords | DocType | Volume |
distribution learning,hidden random variable,indirect samples,sequential decision-making | Conference | abs/1808.05334 |
ISSN | Citations | PageRank |
2474-0195 | 0 | 0.34 |
References | Authors | |
12 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Samarth Gupta | 1 | 13 | 5.60 |
| Gauri Joshi | 2 | 308 | 29.70 |
| Osman Yagan | 3 | 430 | 43.65 |