相关论文: An Illuminating Counterexample
It is argued that systematically unbiassing estimators is not always justified and can be counter-productive. On the contrary, a general rule is given to build a (slightly) biased but consistent estimator which is always closer to the value…
Several problems in statistics involve the combination of high-variance unbiased estimators with low-variance estimators that are only unbiased under strong assumptions. A notable example is the estimation of causal effects while combining…
Eliciting relevance judgments for ranking evaluation is labor-intensive and costly, motivating careful selection of which documents to judge. Unlike traditional approaches that make this selection deterministically, probabilistic sampling…
We present new counterexamples, which provide stronger limitations to sums-differences statements than were previously known. The main idea is to consider non-uniform probability measures.
We address the problem of existence of unbiased constrained parameter estimators. We show that if the constrained set of parameters is compact and the hypothesized distributions are absolutely continuous with respect to one another, then…
We give a counterexample to a recently conjectured variant of the Penrose inequality.
Law enforcement acquires costly evidence with the aim of securing the conviction of a defendant, who is convicted if a decision-maker's belief exceeds a certain threshold. Either law enforcement or the decision-maker is biased and is…
The paper presents a counterexample to the Hodge conjecture.
We provide a comparative study of several widely used off-policy estimators (Empirical Average, Basic Importance Sampling and Normalized Importance Sampling), detailing the different regimes where they are individually suboptimal. We then…
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
This paper contains two finite-sample results concerning the sign test. First, we show that the sign-test is unbiased with independent, non-identically distributed data for both one-sided and two-sided hypotheses. The proof for the…
We discuss a construction that gives counterexamples to various questions of unique determination of convex bodies.
Due to the potential benefits of parallelization, designing unbiased Monte Carlo estimators, primarily in the setting of randomized multilevel Monte Carlo, has recently become very popular in operations research and computational…
Unsupervised contrastive learning has shown significant performance improvements in recent years, often approaching or even rivaling supervised learning in various tasks. However, its learning mechanism is fundamentally different from…
Computer vision algorithms, e.g. for face recognition, favour groups of individuals that are better represented in the training data. This happens because of the generalization that classifiers have to make. It is simpler to fit the…
A variety of methods exist to explain image classification models. However, whether they provide any benefit to users over simply comparing various inputs and the model's respective predictions remains unclear. We conducted a user study…
The article provides a counterexample to a conjecture by Blocki-Zwonek.
Estimators for mutual information are typically biased. However, in the case of the Kozachenko-Leonenko estimator for metric spaces, a type of nearest neighbour estimator, it is possible to calculate the bias explicitly.
In [2] the author claims to provide a counterexample to a result in a recent paper [1]. In this note, we prove that the details of his example is false and this example is compatible with our result in [1] and so is not a countreexample.