Sequential Mode Estimation with Oracle Queries

Shah, Dhruti; Choudhury, Tuhinangshu; Karamchandani, Nikhil; Gopalan, Aditya

doi:10.1609/aaai.v34i04.6018

Cited by 6 publications

(16 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We omit this generalisation, noting that it can be handled quite easily by the methods proposed in the paper. In fact, our version with = 0 exactly matches the problem defined by Shah et al [2], whose algorithms and analysis are our primary baseline. Shah et al [2] effectively "settle" the PAC mode estimation problem from a theoretical perspective.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, our version with = 0 exactly matches the problem defined by Shah et al [2], whose algorithms and analysis are our primary baseline. Shah et al [2] effectively "settle" the PAC mode estimation problem from a theoretical perspective. First they show the following lower bound.…”

Section: Introductionmentioning

confidence: 99%

“…First they show the following lower bound. Theorem 1 (Lower bound [2]). Fix δ ∈ (0, 1), K ≥ 2, and a δ-correct stopping rule L. On each problem instance P = (p, v, K), the expected number of samples observed by L is at least…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

PAC Mode Estimation using PPR Martingale Confidence Sequences

Jain¹,

Shah²,

Gupta³

et al. 2021

Preprint

View full text Add to dashboard Cite

We consider the problem of correctly identifying the mode of a discrete distribution P with sufficiently high probability by observing a sequence of i.i.d. samples drawn according to P. This problem reduces to the estimation of a single parameter when P has a support set of size K = 2. Noting the efficiency of prior-posterior-ratio (PPR) martingale confidence sequences [1] for handling this special case, we propose a generalisation to mode estimation, in which P may take K ≥ 2 values. We observe that the "one-versus-one" principle yields a more efficient generalisation than the "one-versus-rest" alternative. Our resulting stopping rule, denoted PPR-ME, is optimal in its sample complexity up to a logarithmic factor. Moreover, PPR-ME empirically outperforms several other competing approaches for mode estimation. We demonstrate the gains offered by PPR-ME in two practical applications: (1) sample-based forecasting of the winner in indirect election systems, and (2) efficient verification of smart contracts in permissionless blockchains. * Equal contribution Preprint. Under review.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

PAC Mode Estimation using PPR Martingale Confidence Sequences

Jain¹,

Shah²,

Gupta³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Closer to the problem studied in this paper, the problem of mode estimation was originally studied in [13,14] with the focus on statistical properties of various estimators such as consistency. More recently, the instance-optimal sample complexity of mode estimation for any discrete distribution was derived in [15]. Our formulation differs from this line of work in the non-i.i.d.…”

Section: Introductionmentioning

confidence: 99%

“…The same mode identification problem was considered in the fixed confidence setting recently in[15].…”

mentioning

confidence: 99%

Sequential Community Mode Estimation

Jain¹,

Goenka²,

Bapna³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We consider a population, partitioned into a set of communities, and study the problem of identifying the largest community within the population via sequential, random sampling of individuals. There are multiple sampling domains, referred to as boxes, which also partition the population. Each box may consist of individuals of different communities, and each community may in turn be spread across multiple boxes. The learning agent can, at any time, sample (with replacement) a random individual from any chosen box; when this is done, the agent learns the community the sampled individual belongs to, and also whether or not this individual has been sampled before. The goal of the agent is to minimize the probability of mis-identifying the largest community in a fixed budget setting, by optimizing both the sampling strategy as well as the decision rule. We propose and analyse novel algorithms for this problem, and also establish information theoretic lower bounds on the probability of error under any algorithm. In several cases of interest, the exponential decay rates of the probability of error under our algorithms are shown to be optimal up to constant factors. The proposed algorithms are further validated via simulations on real-world datasets.

show abstract