arXiv subjects

Rianne de Heide

Publications and source records attributed to Rianne de Heide.

15 recordsLinked to original sources

arXiv2026

Statistical reduction before the target is known: two boundary results

Suppose that the eventual use of data is not known when the data are reduced or collected. This note considers two simple boundary cases. In a finite statistical experiment, a statistic preserves the Bayes risk for every finite later decision problem if and only if it is sufficient. Hence, when the minimal sufficient statistic is one-to-one, exact preservation of all later decision problems permits no nontrivial reduction. We then consider adaptive sampling from $m$ independent Gaussian streams when an external query specifies the coordinate to be classified only after sampling stops. Under coordinatewise error control, the optimal symmetric average sample size is exactly $m$ times the one-coordinate optimum. A change-of-measure argument gives the corresponding pointwise lower bound in terms of binary relative entropy.

math.ST↗

arXiv2026

Where Does the Union Bound Go? Best-Arm Identification and Strong FWER Control

In fixed-confidence best-arm identification, proofs often use a union bound across the competing arms. From a multiple-testing point of view this can look puzzling: if the best arm is unique, only one hypothesis of the form ``arm $i$ is best'' can be true. Why then should there be a Bonferroni-type factor of $K-1$? The answer is that there are two natural ways to orient the hypotheses. In one orientation, best-arm identification is literally a strong familywise-error-rate (FWER) problem with $K-1$ true nulls. In the opposite orientation, exactly one null is true, but a pairwise implementation can falsely reject that one null through any of $K-1$ comparisons. Thus the multiplicity has not disappeared; it just pops up in different places. This note makes the equivalence explicit in the terminology of both communities.

stat.ME↗

arXiv2026

Dynamic $e$-closure for online hypotheses with any-time-valid evidence: closure principles and projective mergers

Many modern testing problems are sequential along two axes: new hypotheses may arrive over time, while evidence for hypotheses already under consideration continues to evolve and may be inspected at arbitrary stopping times. We develop dynamic $e$-closure for this setting. At a global stopping time the active true-null intersection is random. Future-extension coherence allows its certificate to be compared with that of a fixed terminal intersection, yielding simultaneous stopped-FDR control. If the certificates are also time-monotone, the resulting closure controls simultaneous SupFDR and is setwise persistent. Conversely, every procedure satisfying either criterion is contained in a dynamic closure generated by canonical normalized-loss processes. For pointwise mergers, fixed-dimensional admissibility is equivalent to ordinary arbitrary-dependence $e$-merging. Coherence across horizons then forces a single globally summable weight sequence and exact neutrality under padding by the $e$-value one; on a countably infinite hypothesis universe, this rules out nontrivial symmetric mergers in the admissible pointwise class. The theory extends from FDP to bounded losses that are monotone in the possible true-null configuration and local in the reported action. We also give a coherence counterexample, persistent constructions, and a globally valid shared-control model.

math.ST↗

arXiv2026

Bringing Closure to False Discovery Rate Control: A General Principle for Multiple Testing

We present a novel necessary and sufficient principle for multiple testing methods controlling an expected loss. This principle asserts that every such multiple testing method is a special case of a general closed testing procedure based on e-values. It generalizes the Closure Principle, known to underlie all methods controlling familywise error and tail probabilities of false discovery proportions, to a large class of error rates -- in particular to the false discovery rate (FDR). By writing existing methods as special cases of this procedure, we can achieve uniform improvements, as we demonstrate for the e-Benjamini-Hochberg and the Benjamini-Yekutieli procedures, and the self-consistent method of Su (2018). We also show that methods derived using our novel e-Closure Principle generally control their error rate not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher. Moreover, because all multiple testing methods for the expected loss error metrics covered by our framework are derived from the same procedure, researchers may even choose the error metric post hoc. Under certain conditions, this flexibility even extends to post hoc choice of the nominal error rate.

stat.ME↗

arXiv2025

The e-Partitioning Principle of False Discovery Rate Control

We present a novel necessary and sufficient principle for False Discovery Rate (FDR) control. This e-Partitioning Principle says that a procedure controls FDR if and only if it is a special case of a general e-Partitioning procedure. By writing existing methods as special cases of this procedure, we can achieve uniform improvements of these methods, and we show this in particular for the eBH, BY and Su methods. We also show that methods developed using the $e$-Partitioning Principle have several valuable properties. They generally control FDR not just for one rejected set, but simultaneously over many, allowing post hoc flexibility for the researcher in the final choice of the rejected hypotheses. Under some conditions, they also allow for post hoc adjustment of the error rate, choosing the FDR level $α$ post hoc, or switching to familywise error control after seeing the data. In addition, e-Partitioning allows FDR control methods to exploit logical relationships between hypotheses to gain power.

math.ST↗

arXiv2025

Carefree multiple testing with e-processes

E-processes enable hypothesis testing with ongoing data collection while maintaining Type I error control. However, when testing multiple hypotheses simultaneously, current $e$-value based multiple testing methods such as e-BH are not invariant to the order in which data are gathered for the different $e$-processes. This can lead to undesirable situations, e.g., where a hypothesis rejected at time $t$ is no longer rejected at time $t+1$ after choosing to gather more data for one or more $e$-processes unrelated to that hypothesis. We argue that multiple testing methods should always work with suprema of $e$-processes. We provide an example to illustrate that e-BH does not control the FDR, at level $α$ when applied to suprema of $e$-processes. From the same example we see that the FWER is not controlled with averaging, and also closed e-BH does not control the FDR. We show that adjusters can be used to ensure FDR-sup control with e-BH under arbitrary dependence.

math.ST↗

arXiv2023

Attribution-based Explanations that Provide Recourse Cannot be Robust

Different users of machine learning methods require different explanations, depending on their goals. To make machine learning accountable to society, one important goal is to get actionable options for recourse, which allow an affected user to change the decision $f(x)$ of a machine learning system by making limited changes to its input $x$. We formalize this by providing a general definition of recourse sensitivity, which needs to be instantiated with a utility function that describes which changes to the decisions are relevant to the user. This definition applies to local attribution methods, which attribute an importance weight to each input feature. It is often argued that such local attributions should be robust, in the sense that a small change in the input $x$ that is being explained, should not cause a large change in the feature weights. However, we prove formally that it is in general impossible for any single attribution method to be both recourse sensitive and robust at the same time. It follows that there must always exist counterexamples to at least one of these properties. We provide such counterexamples for several popular attribution methods, including LIME, SHAP, Integrated Gradients and SmoothGrad. Our results also cover counterfactual explanations, which may be viewed as attributions that describe a perturbation of $x$. We further discuss possible ways to work around our impossibility result, for instance by allowing the output to consist of sets with multiple attributions, and we provide sufficient conditions for specific classes of continuous functions to be recourse sensitive. Finally, we strengthen our impossibility result for the restricted case where users are only able to change a single attribute of $x$, by providing an exact characterization of the functions $f$ to which impossibility applies.

stat.ML↗

arXiv2023

E-Statistics, Group Invariance and Anytime Valid Testing

We study worst-case-growth-rate-optimal (GROW) e-statistics for hypothesis testing between two group models. It is known that under a mild condition on the action of the underlying group G on the data, there exists a maximally invariant statistic. We show that among all e-statistics, invariant or not, the likelihood ratio of the maximally invariant statistic is GROW, both in the absolute and in the relative sense, and that an anytime-valid test can be based on it. The GROW e-statistic is equal to a Bayes factor with a right Haar prior on G. Our treatment avoids nonuniqueness issues that sometimes arise for such priors in Bayesian contexts. A crucial assumption on the group G is its amenability, a well-known group-theoretical condition, which holds, for instance, in scale-location families. Our results also apply to finite-dimensional linear regression.

math.ST↗

arXiv2023

Safe Testing

We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values are safe, i.e. they preserve Type-I error guarantees, under such optional continuation. We define growth-rate optimality (GRO) as an analogue of power in an optional continuation context, and we show how to construct GRO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GRO e-values take the form of Bayes factors with special priors. We illustrate the theory using several classic examples including a one-sample safe t-test and the 2 x 2 contingency table. Sharing Fisherian, Neymanian and Jeffreys-Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools.

math.ST↗

arXiv2022

Top Two Algorithms Revisited

Top Two algorithms arose as an adaptation of Thompson sampling to best arm identification in multi-armed bandit models (Russo, 2016), for parametric families of arms. They select the next arm to sample from by randomizing among two candidate arms, a leader and a challenger. Despite their good empirical performance, theoretical guarantees for fixed-confidence best arm identification have only been obtained when the arms are Gaussian with known variances. In this paper, we provide a general analysis of Top Two methods, which identifies desirable properties of the leader, the challenger, and the (possibly non-parametric) distributions of the arms. As a result, we obtain theoretically supported Top Two algorithms for best arm identification with bounded distributions. Our proof method demonstrates in particular that the sampling step used to select the leader inherited from Thompson sampling can be replaced by other choices, like selecting the empirical best arm.

stat.ML↗

arXiv2021

Bandits with many optimal arms

We consider a stochastic bandit problem with a possibly infinite number of arms. We write $p^*$ for the proportion of optimal arms and $Δ$ for the minimal mean-gap between optimal and sub-optimal arms. We characterize the optimal learning rates both in the cumulative regret setting, and in the best-arm identification setting in terms of the problem parameters $T$ (the budget), $p^*$ and $Δ$. For the objective of minimizing the cumulative regret, we provide a lower bound of order $Ω(\log(T)/(p^*Δ))$ and a UCB-style algorithm with matching upper bound up to a factor of $\log(1/Δ)$. Our algorithm needs $p^*$ to calibrate its parameters, and we prove that this knowledge is necessary, since adapting to $p^*$ in this setting is impossible. For best-arm identification we also provide a lower bound of order $Ω(\exp(-cTΔ^2 p^*))$ on the probability of outputting a sub-optimal arm where $c>0$ is an absolute constant. We also provide an elimination algorithm with an upper bound matching the lower bound up to a factor of order $\log(T)$ in the exponential, and that does not need $p^*$ or $Δ$ as parameter. Our results apply directly to the three related problems of competing against the $j$-th best arm, identifying an $ε$ good arm, and finding an arm with mean larger than a quantile of a known order.

cs.LG↗

arXiv2021

Safe-Bayesian Generalized Linear Regression

We study generalized Bayesian inference under misspecification, i.e. when the model is 'wrong but useful'. Generalized Bayes equips the likelihood with a learning rate $η$. We show that for generalized linear models (GLMs), $η$-generalized Bayes concentrates around the best approximation of the truth within the model for specific $η\neq 1$, even under severely misspecified noise, as long as the tails of the true distribution are exponential. We derive MCMC samplers for generalized Bayesian lasso and logistic regression and give examples of both simulated and real-world data in which generalized Bayes substantially outperforms standard Bayes.

math.ST↗

arXiv2021

Why optional stopping can be a problem for Bayesians

Recently, optional stopping has been a subject of debate in the Bayesian psychology community. Rouder (2014) argues that optional stopping is no problem for Bayesians, and even recommends the use of optional stopping in practice, as do Wagenmakers et al. (2012). This article addresses the question whether optional stopping is problematic for Bayesian methods, and specifies under which circumstances and in which sense it is and is not. By slightly varying and extending Rouder's (2014) experiments, we illustrate that, as soon as the parameters of interest are equipped with default or pragmatic priors - which means, in most practical applications of Bayes factor hypothesis testing - resilience to optional stopping can break down. We distinguish between three types of default priors, each having their own specific issues with optional stopping, ranging from no-problem-at-all (Type 0 priors) to quite severe (Type II priors).

stat.ME↗

arXiv2020

Optional Stopping with Bayes Factors: a categorization and extension of folklore results, with an application to invariant situations

It is often claimed that Bayesian methods, in particular Bayes factor methods for hypothesis testing, can deal with optional stopping. We first give an overview, using elementary probability theory, of three different mathematical meanings that various authors give to this claim: (1) stopping rule independence, (2) posterior calibration and (3) (semi-) frequentist robustness to optional stopping. We then prove theorems to the effect that these claims do indeed hold in a general measure-theoretic setting. For claims of type (2) and (3), such results are new. By allowing for non-integrable measures based on improper priors, we obtain particularly strong results for the practically important case of models with nuisance parameters satisfying a group invariance (such as location or scale). We also discuss the practical relevance of (1)--(3), and conclude that whether Bayes factor methods actually perform well under optional stopping crucially depends on details of models, priors and the goal of the analysis.

math.ST↗

arXiv2019

Fixed-Confidence Guarantees for Bayesian Best-Arm Identification

We investigate and provide new insights on the sampling rule called Top-Two Thompson Sampling (TTTS). In particular, we justify its use for fixed-confidence best-arm identification. We further propose a variant of TTTS called Top-Two Transportation Cost (T3C), which disposes of the computational burden of TTTS. As our main contribution, we provide the first sample complexity analysis of TTTS and T3C when coupled with a very natural Bayesian stopping rule, for bandits with Gaussian rewards, solving one of the open questions raised by Russo (2016). We also provide new posterior convergence results for TTTS under two models that are commonly used in practice: bandits with Gaussian and Bernoulli rewards and conjugate priors.

cs.LG↗