Minimal Assumptions Research Articles

On a Holm-related MTP for rejecting at least k hypotheses: general validity, optimality property, confidence regions, and applications.

This article concerns p-value-based multiple testing procedures (MTPs) that can be used in a confirmatory clinical study under minimal assumptions in case the requirement for study-success is that at least k out of m primary/important hypotheses become rejected. Recently, a simple, generally valid Holm-type MTP was discussed that can be used for such a requirement for any k from one to m. It can only reject at least k (or zero) hypotheses, but this increases the power to reject k or more hypotheses compared to Holm's step-down MTP. The present article provides a simple formulation and proof of strong family-wise error rate (FWER) control for a stepwise MTP that is sharper in that for any k strictly between one and m it: (a) always rejects at least as much, and (b) can potentially reject fewer than k hypotheses. This sharper MTP too is generally valid, without any assumption about logical or stochastic relationships. It has a gatekeeping step, followed by m steps where ordered primary p-values are compared to critical constants and rejections are made in a step-down manner. These constants have the optimality property that under a natural monotonicity restriction, they cannot be increased without losing the general strong FWER control. Confidence regions like those for Holm's MTP are provided. Applications are discussed in connection with three interesting approaches proposed earlier for confirmatory studies: (a) the Superiority-Noninferiority approach; (b) Fallback tests for co-primary endpoints; and (c) Multistage gatekeeping MTPs that utilize so-called k-truncated Holm MTPs in some stages.

Interpolation of derivatives and ultradifferentiable regularity

AbstractInterpolation inequalities for functions allow to bound derivatives of intermediate order by bounds for the derivatives of order 0 and . We review various interpolation inequalities for ‐norms () in arbitrary finite dimensions. They allow us to study ultradifferentiable regularity by lacunary estimates in a comprehensive way, striving for minimal assumptions on the weights.

The MeerKAT Pulsar Timing Array: Maps of the gravitational wave sky with the 4.5-yr data release

ABSTRACT In an accompanying publication, the MeerKAT Pulsar Timing Array (MPTA) Collaboration reports tentative evidence for the presence of a stochastic gravitational wave background, following observations of similar signals from the European and Indian Pulsar Timing Arrays, the North American Nanohertz Observatory for Gravitational Waves, the Parkes Pulsar Timing Array, and the Chinese Pulsar Timing Array. If such a gravitational wave background signal originates from a population of inspiraling supermassive black hole binaries, the signal may be anisotropically distributed in the sky. In this paper, we evaluate the anisotropy of the MPTA signal using a spherical harmonic decomposition. We discuss complications arising from the covariance between pulsar pairs and the regularization of the Fisher matrix. Applying our method to the $4.5 \hbox{-}\text{yr}$ data set, we obtain two forms of sky maps for the three most sensitive MPTA frequency bins between $7 \ {\rm and} \ 21 \, {\rm nHz}$. Our ‘clean maps’ estimate the distribution of gravitational wave strain power with minimal assumptions. Our radiometer maps answer the question: Is there a statistically significant point source? We find a noteworthy hotspot in the $7 \, \mathrm{nHz}$ clean map with a p-factor of $p=0.015$ (not including trial factors). Future observations are required to determine if this hotspot is of astrophysical origin.

Certifying temporal correlations

Self-testing has been established as a major approach for quantum device certification based on experimental statistics with minimal assumptions. However, despite more than 20 years of research effort, most of the self-testing protocols are restricted to spatial scenarios (Bell scenarios), without many temporal generalizations known. Under the scenario of sequential measurements performed on a single quantum system, semi-definite optimization-based techniques have been applied to bound sequential measurement inequalities. Building upon this formalism, we show that the optimizer matrix that saturates such sequential inequalities is unique and, moreover, this uniqueness is robust to small deviations from the quantum bound. Furthermore, we consider a generalized scenario in the presence of quantum channels and highlight analogies to the structure of Bell and sequential inequalities using the pseudo-density matrix formalism. These analogies allow us to show a practical use of maximal violations of sequential inequalities in the form of certification of quantum channels up to isometries.

Mine Your Own Anatomy: Revisiting Medical Image Segmentation With Extremely Limited Labels.

Recent studies on contrastive learning have achieved remarkable performance solely by leveraging few labels in the context of medical image segmentation. Existing methods mainly focus on instance discrimination and invariant mapping (i.e., pulling positive samples closer and negative samples apart in the feature space). However, they face three common pitfalls: (1) tailness: medical image data usually follows an implicit long-tail class distribution. Blindly leveraging all pixels in training hence can lead to the data imbalance issues, and cause deteriorated performance; (2) consistency: it remains unclear whether a segmentation model has learned meaningful and yet consistent anatomical features due to the intra-class variations between different anatomical features; and (3) diversity: the intra-slice correlations within the entire dataset have received significantly less attention. This motivates us to seek a principled approach for strategically making use of the dataset itself to discover similar yet distinct samples from different anatomical views. In this paper, we introduce a novel semi-supervised 2D medical image segmentation framework termed Mine yOur owNAnatomy (MONA), and make three contributions. First, prior work argues that every pixel equally matters to the model training; we observe empirically that this alone is unlikely to define meaningful anatomical features, mainly due to lacking the supervision signal. We show two simple solutions towards learning invariances-through the use of stronger data augmentations and nearest neighbors. Second, we construct a set of objectives that encourage the model to be capable of decomposing medical images into a collection of anatomical features in an unsupervised manner. Lastly, we both empirically and theoretically, demonstrate the efficacy of our MONA on three benchmark datasets with different labeled settings, achieving new state-of-the-art under different labeled semi-supervised settings. MONA makes minimal assumptions on domain expertise, and hence constitutes a practical and versatile solution in medical image analysis. We provide the PyTorch-like pseudo-code in supplementary.

Barycentric and pairwise Rényi quantum leakage with application to privacy-utility trade-off

Barycentric and pairwise quantum Rényi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e. they do not make any assumptions on the eavesdropper’s attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality and unitary invariance. The barycentric quantum Rényi leakage can be computed by solving a semi-definite program; the pairwise quantum Rényi leakage possesses an explicit formula. The barycentric and pairwise quantum Rényi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum α -mutual information, the accessible information and the Holevo’s information. Furthermore, differentially private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e. information leakage can only be reduced, if the performance degradation grows larger and vice versa .

Test for comparing the associations of multiple exposures with a common outcome

IntroductionWith advancement of medicine, alternative exposures or interventions are emerging with respect to a common outcome, and there are needs to formally test the difference in the associations of multiple exposures. MethodsThe paper proposes a duplication method-based multivariate Wald test in the Cox proportional hazard regression model to test the difference in the associations of multiple exposures with a same outcome. This method applies to continuous or categorical exposures. For illustration, the method was applied to compare the associations between alignment to two different dietary patterns (Alternative Healthy Eating Index-2010 [AHEI-2010] and reversed empirical dietary inflammatory pattern [rEDIP]), either as continuous or quartile exposures, and incident chronic diseases, defined as a composite of cardiovascular disease, cancer, and diabetes, in the Health Professional Follow-up Study (HPFS). Relevant sample codes in R that implement the proposed approach are provided. The present analysis was conducted in 2024. ResultsWith a median follow-up of 22 years, there were a total of 14,427 chronic disease incidences among N=43,185 men included in the HPFS analysis. The hazard ratios (HRs) [95% confidence interval] per increment from the 10th to the 90th percentile for incident chronic disease were 0.83 [0.79, 0.87] for AHEI-2010 and 0.76 [0.73, 0.80] for rEDIP. Although the 95% CIs were overlapped for each exposure, the proposed test was well powered to detect the difference (p=0.005). ConclusionsThe proposed duplication-method-based approach offers a flexible, formal statistical test for heterogeneity in the associations of multiple exposures with the common outcome with minimal assumptions.

Robust-less-fragile: Tackling systemic risk and financial contagion in a macro agent-based model

We extend the Schumpeter meeting Keynes (K+S) agent-based model by introducing an evolving interbank network in the money market. Banks are exposed to counterparty risk and evaluate interbank positions using a network valuation (NEVA) clearing mechanism, which ensures systemic risk minimization with minimal assumptions on banks’ behavior. The model can replicate several stylized facts about the topology of the interbank network and the dynamics of banks’ balance sheets. The model encompasses financial contagion and systemic risk, allowing us to study the interactions between micro- and macro-prudential policies. Our results suggest that the introduction of a micro-prudential regulation also accounting for the network structure can reduce the incidence of systemic risk events. We also find that, in presence of a two-pillar regulatory framework – grounded on a Basel III macro-prudential regulation and a NEVA-based micro-prudential one –, there is no trade-off between financial stability and macroeconomic performance. This points towards the possibility of designing a regulatory framework able to achieve financial stability without overly stringent capital requirements.

Non-parametric identification of single-lined binary candidates in young clusters using single-epoch spectroscopy

Binarity plays a crucial role in star formation and evolution. Consequently, identifying binary stars is essential to deepening our understanding of these processes. We propose a method to investigate the observed radial velocity distribution of massive stars in young clusters with the goal of identifying binary systems. We reconstruct the radial velocity distribution using a three-layer hierarchical Bayesian non-parametric approach; non-parametric methods are data-driven models able to infer arbitrary probability densities under minimal mathematical assumptions. When applying our statistical framework, it is possible to identify variable stars and binary systems because these deviate significantly from the expected intrinsic Gaussian distribution for radial velocities. We tested our method with the massive star-forming region within the giant H$_ II $ region M17. We are able to confidently identify binaries and variable stars with as little as single-epoch observations. The distinction between variable and binary stars improves significantly when introducing additional epochs.

Uncertainty-aware genomic deep learning with knowledge distillation.

Deep neural networks (DNNs) have advanced predictive modeling for regulatory genomics, but challenges remain in ensuring the reliability of their predictions and understanding the key factors behind their decision making. Here we introduce DEGU (Distilling Ensembles for Genomic Uncertainty-aware models), a method that integrates ensemble learning and knowledge distillation to improve the robustness and explainability of DNN predictions. DEGU distills the predictions of an ensemble of DNNs into a single model, capturing both the average of the ensemble's predictions and the variability across them, with the latter representing epistemic (or model-based) uncertainty. DEGU also includes an optional auxiliary task to estimate aleatoric, or data-based, uncertainty by modeling variability across experimental replicates. By applying DEGU across various functional genomic prediction tasks, we demonstrate that DEGU-trained models inherit the performance benefits of ensembles in a single model, with improved generalization to out-of-distribution sequences and more consistent explanations of cis-regulatory mechanisms through attribution analysis. Moreover, DEGU-trained models provide calibrated uncertainty estimates, with conformal prediction offering coverage guarantees under minimal assumptions. Overall, DEGU paves the way for robust and trustworthy applications of deep learning in genomics research.

Mapping the spectrotemporal regions influencing perception of French stop consonants in noise

Understanding how speech sounds are decoded into linguistic units has been a central research challenge over the last century. This study follows a reverse-correlation approach to reveal the acoustic cues listeners use to categorize French stop consonants in noise. Compared to previous methods, this approach ensures an unprecedented level of detail with only minimal theoretical assumptions. Thirty-two participants performed a speech-in-noise discrimination task based on natural /aCa/ utterances, with C = /b/, /d/, /g/, /p/, /t/, or /k/. The trial-by-trial analysis of their confusions enabled us to map the spectrotemporal information they relied on for their decisions. In place-of-articulation contrasts, the results confirmed the critical role of formant consonant-vowel transitions, used by all participants, and, to a lesser extent, vowel-consonant transitions and high-frequency release bursts. Similarly, for voicing contrasts, we validated the prominent role of the voicing bar cue, with some participants also using formant transitions and burst cues. This approach revealed that most listeners use a combination of several cues for each task, with significant variability within the participant group. These insights shed new light on decades-old debates regarding the relative importance of cues for phoneme perception and suggest that research on acoustic cues should not overlook individual variability in speech perception.

Gold’s Value as an Investment

Abstract This paper presents an approach for pricing gold from investors’ perspective. The model is based on no-arbitrage principles with minimal structural assumptions. There is no need to specify investor preferences. When fitted to match 10-year real U.S. Treasury rates, the model can replicate the salient fluctuations in the time series of gold prices since 2007. The model is also able to capture key patterns of CME Comex gold futures prices. The model implies that the majority of the value of gold is due to its role as an investment asset. (JEL G12, G13)

The impact of the cosmological constant on past and future star formation

ABSTRACT We present an extended analytical model for cosmic star formation, with the aim of investigating the impact of cosmological parameters on the star formation history within the $\Lambda$CDM paradigm. Constructing an ensemble of flat $\Lambda$CDM models where the cosmological constant varies between $\Lambda = 0$ and $10^5$ times the observed value, $\Lambda _{\rm obs}$, we find that the fraction of cosmic baryons that are converted into stars over the entire history of the universe peaks at $\sim$ 27 per cent for $0.01 \lesssim \Lambda /\Lambda _{\rm obs} \lesssim 1$. We explain, from first principles, that the decline of this asymptotic star formation efficiency for lower and higher values of $\Lambda$ is driven, respectively, by the astrophysics of star formation, and by the suppression of cosmic structure formation. However, the asymptotic efficiency declines slowly as $\Lambda$ increases, falling below 5 per cent only for $\Lambda \gt 100 \, \Lambda _{\rm obs}$. Making the minimal assumption that the probability of generating observers is proportional to this efficiency, and following Weinberg in adopting a flat prior on $\Lambda$, the median posterior value of $\Lambda$ is $539 \, \Lambda _{\rm obs}$. Furthermore, the probability of observing $\Lambda \le \Lambda _{\rm obs}$ is only 0.5 per cent. Although this work has not considered recollapsing models with $\Lambda \lt 0$, the indication is thus that $\Lambda _{\rm obs}$ appears to be unreasonably small compared to the predictions of the simplest multiverse ensemble. This poses a challenge for anthropic reasoning as a viable explanation for cosmic coincidences and the apparent fine-tuning of the Universe: either the approach is invalid or more parameters than $\Lambda$ alone must vary within the ensemble.

Robust Principal Component Analysis: A Median of Means Approach.

Principal component analysis (PCA) is a fundamental tool for data visualization, denoising, and dimensionality reduction. It is widely popular in statistics, machine learning, computer vision, and related fields. However, PCA is well-known to fall prey to outliers and often fails to detect the true underlying low-dimensional structure within the dataset. Following the Median of Means (MoM) philosophy, recent supervised learning methods have shown great success in dealing with outlying observations without much compromise to their large sample theoretical properties. This article proposes a PCA procedure based on the MoM principle. Called the MoMPCA, the proposed method is not only computationally appealing but also achieves optimal convergence rates under minimal assumptions. In particular, we explore the nonasymptotic error bounds of the obtained solution via the aid of the Rademacher complexities while granting absolutely no assumption on the outlying observations. The derived concentration results are not dependent on the dimension because the analysis is conducted in a separable Hilbert space, and the results only depend on the fourth moment of the underlying distribution in the corresponding norm. The proposal's efficacy is also thoroughly showcased through simulations and real data applications.

Contraction rate estimates of stochastic gradient kinetic Langevin integrators

In previous work, we introduced a method for determining convergence rates for integration methods for the kinetic Langevin equation for M-▽Lipschitz m-log-concave densities [Leimkuhler et al., SIAM J. Numer. Anal. 62 (2024) 1226–1258]. In this article, we exploit this method to treat several additional schemes including the method of Brunger, Brooks and Karplus (BBK) and stochastic position/velocity Verlet. We introduce a randomized midpoint scheme for kinetic Langevin dynamics, inspired by the recent scheme of Bou-Rabee and Marsden [arXiv:2211.11003, 2022]. We also extend our approach to stochastic gradient variants of these schemes under minimal extra assumptions. We provide convergence rates of O(m/M), with explicit stepsize restriction, which are of the same order as the stability thresholds for Gaussian targets and are valid for a large interval of the friction parameter. We compare the contraction rate estimates of many kinetic Langevin integrators from molecular dynamics and machine learning. Finally, we present numerical experiments for a Bayesian logistic regression example.

Public transport across models and scales: A case study of the Munich network.

The use of public transport systems is a striking example of complex human behavior. Modeling, planning, and managing public transport is a major future challenge considering the drastically accelerated population growth in many urban areas. The desire to design sustainable cities that can cope with a dynamically increasing demand requires models for transport networks since we are not able to perform real-life experiments before constructing additional infrastructure. Yet, there is a fundamental challenge in the modeling process: we have to understand which basic principles apply to the design of transit networks. In this work, we are going to compare three scientific methods to understand human behavior in public transport modeling: agent-based models, centralized optimization-based models, and minimal physics-based models. As a case study, we focus on the transport network in Munich, Germany. We show that there are certain universal macroscopic emergent features of public transport that arise regardless of the model chosen. In particular, we can obtain with minimal basic assumptions a common and robust distribution for the individual passenger in-vehicle time as well as for several other distributions. Yet, there are other more microscopic features that differ between the individual and centralized organization and/or that cannot be reproduced by a minimal nonlocal random-walk type model. Finally, we cross-validate our results with observed public transport data. In summary, our results provide a key understanding of the basic assumptions that have to underlie transport modeling for human behavior in future sustainable cities.

Estimating false alarm rates of sub-dominant quasi-normal modes in GW190521

Abstract A major aim of gravitational wave astronomy is to test observationally the Kerr nature of black holes. The strongest such test, with minimal additional assumptions, is provided by observations of multiple ringdown modes, also known as black hole spectroscopy. For the gravitational wave merger event GW190521, we have previously claimed the detection of two ringdown modes emitted by the remnant black hole. In this paper we provide further evidence for the detection of multiple ringdown modes from this event. We analyse the recovery of simulated gravitational wave signals designed to replicate the ringdown properties of GW190521. We quantify how often our detection statistic reports strong evidence for a sub-dominant $(\ell,m,n)=(3,3,0)$ ringdown mode, even when no such mode is present in the simulated signal. We find this only occurs with a probability $\sim 0.02$, which is consistent with a Bayes factor of $56 \pm 1$ (1$\sigma$ uncertainty) found for GW190521. We also quantify our agnostic analysis of GW190521, in which no relationship is assumed between ringdown modes, and find that only 1 in 250 simulated signals without a $(3,3,0)$ mode yields a result as significant as GW190521. Conversely, we verify that when simulated signals do have an observable $(3,3,0)$ mode they consistently yield a strong evidence and significant agnostic results. We also find that constraints on deviations from the $(3,3,0)$ mode on GW190521-like signals with a $(3,3,0)$ mode are consistent with what was obtained from our previous analysis of GW190521. Our results support our previous conclusion that the gravitational wave signal from GW190521 contains an observable sub-dominant $(\ell,m,n)=(3,3,0)$ mode.

One for all? Assessing the quality of Italian hospital care with the “benefit of the doubt” composite indicator methods

Quality assessment in healthcare systems is challenging due to the multidimensional nature of healthcare services. This study evaluates the overall quality provided by hospitals using composite indicators under the Benefit of the Doubt (BoD) approach, which determines the weights of the indicators with minimal assumptions. We used data from 2015-2020 for Italian Local Health Authorities (LHAs) for 21 outcome measures, applying various non-parametric methods to address aggregation and weighting challenges. Our results show that the BoD measures are robust and effectively capture the dynamics of the quality of LHA, even during external shocks such as the COVID-19 pandemic. This research highlights the importance of methodological choices in the construction of composite indicators and demonstrates the effectiveness of the BoD approach in providing a comprehensive measure of healthcare quality.

The Motivic Anabelian Geometry of Local Heights on Abelian Varieties

We study the problem of describing local components of Néron–Tate height functions on abelian varieties over characteristic 0 0 local fields as functions on spaces of torsors under various realisations of the 2 2 -step unipotent motivic fundamental group of the G m \mathbb G_m -torsor corresponding to the defining line bundle. To this end, we present three main theorems giving such a description in terms of the Q ℓ \mathbb Q_\ell - and Q p \mathbb Q_p -pro-unipotent étale realisations when the base field is p p -adic, and in terms of the R \mathbb R -pro-unipotent Betti–de Rham realization when the base field is archimedean. In the course of proving the p p -adic instance of these theorems, we develop a new technique for studying local nonabelian Bloch–Kato Selmer sets, working with certain explicit cosimplicial group models for these sets and using methods from homotopical algebra. Among other uses, these models enable us to construct a pro-unipotent generalization of the Bloch–Kato exponential sequence under minimal assumptions.

Save the five: Meeting Taurek's challenge

AbstractSix people are in trouble. We can save five of them or just the sixth. What should we do? John Taurek defends a radical view: We are not required to save the greater number. Taurek has persuaded some. But even the unpersuaded agree that Taurek poses a deep and important challenge: From where does the priority of the many derive? It seems difficult, or even impossible, to convince someone who denies the importance of the numbers… to care about the numbers. That's what this paper aims to do. It will argue that the priority of the many follows, with minimal other assumptions, from something all should accept: the modest premise that if we can improve one person's chance of survival—without affecting anyone else—we should.