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arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

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14 results for “good-turing”

Mean-Squared Accuracy of Good-Turing Estimatorstat.ML

This study calculates the maximum error of a famous estimation method.

problem Estimating rare items not seen in a sample.

method Characterizes the maximal mean-squared error of the Good-Turing estimator.

result Characterizes the maximal mean-squared error of the Good-Turing estimator.

Good-Turing estimator sample coverage missing mass mean-squared error

2021-04-14abs ↗pdf ↗

An interpretable Good--Turing restart criterion for k-means++cs.LG

A new restart criterion for k-means++ improves clustering quality and adapts to data difficulty.

problem Arbitrary restart counts in k-means++ lead to inconsistent results and wasted computation.

method GTRC combines Good-Turing estimates, bounds, and user-specified tolerance to dynamically decide restarts.

result GTRC achieves clustering quality comparable to fixed restart counts, varying restarts based on data difficulty.

k-means++restart criterion Good-Turing clustering quality data difficulty

2026-07-09abs ↗pdf ↗

Blind-Spot Mass: A Good-Turing Framework for Quantifying Deployment Coverage Risk in Machine Learning Systemscs.LG

A framework to quantify deployment risk in ML systems, especially for rare states.

problem Under-supported rare states in ML models lead to unreliable performance in unseen data.

method Blind-Spot Mass (B_n(tau)) using Good-Turing unseen-species estimation.

result Identifies and quantifies the risk of under-supported states in ML models.

Good-Turing deployment coverage machine learning coverage risk rare states

2026-04-06abs ↗pdf ↗

Divergence Frontiers for Generative Models: Sample Complexity, Quantization Effects, and Frontier Integralsstat.ML

New tools quantify deep generative models' performance.

problem Measuring the quality-diversity trade-off in deep generative models.

method Established non-asymptotic bounds on sample complexity and introduced frontier integrals.

result Smoothed estimators improve convergence rates of divergence frontiers.

divergence frontiers sample complexity quantization effects frontier integrals good-turing

2021-06-15abs ↗pdf ↗

On consistent estimation of the missing massmath.ST

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$ -th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannes…

2018-06-25abs ↗pdf ↗

Just Wing It: Near-Optimal Estimation of Missing Mass in a Markovian Sequencestat.ML

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

problem Estimating missing mass in Markovian sequences.

method Windowed Good-Turing (WingIt) estimator.

result Risk decays as

\widetilde{O}(\mathsf{T_{mix}}/n)

, independent of state space size.

Markov chains Good-Turing estimator mixing time stationary mass sequence models

2024-04-08abs ↗pdf ↗

Instance-Optimality for Private KL Distribution Estimationstat.ML

Private KL distribution estimation improved with instance-optimality.

problem Minimizing KL divergence between true and estimated distributions.

method Construct minimax optimal private estimators, then focus on instance-optimality.

result Achieved instance-optimality up to constant factors for KL estimation.

KL divergence private estimation instance-optimality Good-Turing estimator differential privacy

2025-05-29abs ↗pdf ↗

How good is Good-Turing for Markov samples?cs.IT

GT estimator shows convergence for Markov samples, improving i.i.d. results.

problem Estimating missing mass in Markov samples.

method Analyzed convergence of Good-Turing estimator for Markov samples, considering spectral properties of transition matrices.

result The convergence of the GT estimator for Markov samples depends on the spectral properties of the transition matrices, leading to a new minimax rate of

1/(nβ^5)

for rank-2 Markov chains.

Good-Turing estimator Markov samples missing mass spectral properties minimax rate

2021-02-03abs ↗pdf ↗

Estimating stationary mass, frequency by frequencystat.ML

Estimates stationary mass and frequency from non-i.i.d. data.

problem Estimating stationary mass and frequency from non-i.i.d. data.

method Combines plug-in estimator with WingIt modification for exponentially

α

-mixing processes.

result Universal consistency in

n

for total variation distance estimation.

stationary distribution exponentially $α$-mixing Good-Turing estimator WingIt Poissonization

2025-03-17abs ↗pdf ↗

How Much is Unseen Depends Chiefly on Information About the Seencs.LG

Estimates missing data points in classifier inputs based on training data.

problem Estimating the proportion of unseen data points in classifier inputs.

method Characterizes the expected missing mass in terms of the sample and uses optimization to find nearly unbiased estimators with minimized MSE.

result Found estimators with MSE roughly 80% of the Good-Turing estimator's, improving over 93% of runs.

missing mass classifier inputs training data exponential decay mean-squared error

2024-02-08abs ↗pdf ↗

Optimal discovery with probabilistic expert advice: finite time analysis and macroscopic optimalitycs.LG

We consider an original problem that arises from the issue of security analysis of a power system and that we name optimal discovery with probabilistic expert advice. We address it with an algorithm based on the optimistic paradigm and on the Good-Turing missing mass estimator. We prove two different regret bounds on t…

2012-07-22abs ↗pdf ↗

Conformal Inference for Open-Set and Imbalanced Classificationstat.ML

Paper develops a new method for open-set and imbalanced classification with valid prediction sets.

problem Tackles open-set and imbalanced classification with new prediction methods.

method Develops a new family of conformal p-values and a selective sample splitting algorithm.

result Valid prediction sets with valid coverage in open-set scenarios and informative predictions under extreme class imbalance.

conformal inference open-set classification imbalanced data selective sample splitting valid prediction sets

2025-10-14abs ↗pdf ↗

Outperforming Good-Turing: Preliminary Reportstat.ML

Estimating a large alphabet probability distribution from a limited number of samples is a fundamental problem in machine learning and statistics. A variety of estimation schemes have been proposed over the years, mostly inspired by the early work of Laplace and the seminal contribution of Good and Turing. One of the b…

2018-07-06abs ↗pdf ↗

The Broad Optimality of Profile Maximum Likelihoodstat.ML

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide range of learning tasks. In particular, for every alphabet size $k$ and desired…

2019-06-10abs ↗pdf ↗