We study the decay of correlation between locally constrained independent random variables in the local lemma regimes. the distribution defined by constraint satisfaction problems (CSPs) in the local lemma regime. For atomically constrained independent random variables of sufficiently large domains, we show that a decay of correlation property holds up to the local lemma condition $pD^{2+o(1)}\lesssim 1$, asymptotically matching the sampling threshold for constraint satisfaction solutions [BGG+19,GGW22]. This provides evidence for the conjectured $pD^2\lesssim 1$ threshold for the "sampling Lov\'{a}sz local lemma". We use a recursively-constructed coupling to bound the correlation decay. Our approach completely dispenses with the "freezing" paradigm originated from Beck [Bec91], which was commonly used to deal with the non-self-reducibility of the local lemma regimes, and hence can bypass the current technical barriers due to the use of $\{2,3\}$-trees.
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Defining the effect of exposure of interest and selecting an appropriate estimation method are prerequisite for causal inference. Understanding the ways in which association between heatwaves (i.e., consecutive days of extreme high temperature) and an outcome depends on whether adjustment was made for temperature and how such adjustment was conducted, is limited. This paper aims to investigate this dependency, demonstrate that temperature is a confounder in heatwave-outcome associations, and introduce a new modeling approach to estimate a new heatwave-outcome relation: E[R(Y)|HW=1, Z]/E[R(Y)|T=OT, Z], where HW is a daily binary variable to indicate the presence of a heatwave; R(Y) is the risk of an outcome, Y; T is a temperature variable; OT is optimal temperature; and Z is a set of confounders including typical confounders but also some types of T as a confounder. We recommend characterization of heatwave-outcome relations and careful selection of modeling approaches to understand the impacts of heatwaves under climate change. We demonstrate our approach using real-world data for Seoul, which suggests that the total effect of heatwaves may be larger than what may be inferred from the extant literature. An R package, HEAT (Heatwave effect Estimation via Adjustment for Temperature), was developed and made publicly available.
Neuro-evolutionary methods have proven effective in addressing a wide range of tasks. However, the study of the robustness and generalisability of evolved artificial neural networks (ANNs) has remained limited. This has immense implications in the fields like robotics where such controllers are used in control tasks. Unexpected morphological or environmental changes during operation can risk failure if the ANN controllers are unable to handle these changes. This paper proposes an algorithm that aims to enhance the robustness and generalisability of the controllers. This is achieved by introducing morphological variations during the evolutionary process. As a results, it is possible to discover generalist controllers that can handle a wide range of morphological variations sufficiently without the need of the information regarding their morphologies or adaptation of their parameters. We perform an extensive experimental analysis on simulation that demonstrates the trade-off between specialist and generalist controllers. The results show that generalists are able to control a range of morphological variations with a cost of underperforming on a specific morphology relative to a specialist. This research contributes to the field by addressing the limited understanding of robustness and generalisability in neuro-evolutionary methods and proposes a method by which to improve these properties.
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear differential equation characterisation of the probability density function is given. This is used to derive a Stein-type differential identity relating to the expectation with respect to the gamma difference distribution of a general twice differentiable function $g(x)$. Choosing $g(x) = x^k$ gives a second order recurrence for the positive integer moments, which are also shown to permit evaluations in terms of ${}_2 F_1$ hypergeometric polynomials. A hypergeometric function evaluation is given for the absolute continuous moments. Specialising the gamma difference distribution gives the variance gamma distribution. Results of the type obtained herein have previously been obtained for this distribution, allowing for comparisons to be made.
We consider the problem of sequential change detection, where the goal is to design a scheme for detecting any changes in a parameter or functional $\theta$ of the data stream distribution that has small detection delay, but guarantees control on the frequency of false alarms in the absence of changes. In this paper, we describe a simple reduction from sequential change detection to sequential estimation using confidence sequences: we begin a new $(1-\alpha)$-confidence sequence at each time step, and proclaim a change when the intersection of all active confidence sequences becomes empty. We prove that the average run length is at least $1/\alpha$, resulting in a change detection scheme with minimal structural assumptions~(thus allowing for possibly dependent observations, and nonparametric distribution classes), but strong guarantees. Our approach bears an interesting parallel with the reduction from change detection to sequential testing of Lorden (1971) and the e-detector of Shin et al. (2022).
Leverage score sampling is crucial to the design of randomized algorithms for large-scale matrix problems, while the computation of leverage scores is a bottleneck of many applications. In this paper, we propose a quantum algorithm to accelerate this useful method. The speedup is at least quadratic and could be exponential for well-conditioned matrices. We also prove some quantum lower bounds, which suggest that our quantum algorithm is close to optimal. As an application, we propose a new quantum algorithm for rigid regression problems with vector solution outputs. It achieves polynomial speedups over the best classical algorithm known. In this process, we give an improved randomized algorithm for rigid regression.
Mediation analysis is widely used in health science research to evaluate the extent to which an intermediate variable explains an observed exposure-outcome relationship. However, the validity of analysis can be compromised when the exposure is measured with error. Motivated by the Health Professionals Follow-up Study (HPFS), we investigate the impact of exposure measurement error on assessing mediation with a survival outcome, based on the Cox proportional hazards outcome model. When the outcome is rare and there is no exposure-mediator interaction, we show that the uncorrected estimators of the natural indirect and direct effects can be biased into either direction, but the uncorrected estimator of the mediation proportion is approximately unbiased as long as the measurement error is not large or the mediator-exposure association is not strong. We develop ordinary regression calibration and risk set regression calibration approaches to correct the exposure measurement error-induced bias when estimating mediation effects and allowing for an exposure-mediator interaction in the Cox outcome model. The proposed approaches require a validation study to characterize the measurement error process. We apply the proposed approaches to the HPFS (1986-2016) to evaluate extent to which reduced body mass index mediates the protective effect of vigorous physical activity on the risk of cardiovascular diseases, and compare the finite-sample properties of the proposed estimators via simulations.
Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine-learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A postprocessing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.
We examine the tension between academic impact - the volume of citations received by publications - and scientific disruption. Intuitively, one would expect disruptive scientific work to be rewarded by high volumes of citations and, symmetrically, impactful work to also be disruptive. A number of recent studies have instead shown that such intuition is often at odds with reality. In this paper, we break down the relationship between impact and disruption with a detailed correlation analysis in two large data sets of publications in Computer Science and Physics. We find that highly disruptive papers tend to be cited at higher rates than average. Contrastingly, the opposite is not true, as we do not find highly impactful papers to be particularly disruptive. Notably, these results qualitatively hold even within individual scientific careers, as we find that - on average - an author's most disruptive work tends to be well cited, whereas their most cited work does not tend to be disruptive. We discuss the implications of our findings in the context of academic evaluation systems, and show how they can contribute to reconcile seemingly contradictory results in the literature.
The notion that algorithmic systems should be "transparent" and "explainable" is common in the many statements of consensus principles developed by governments, companies, and advocacy organizations. But what exactly do policy and legal actors want from these technical concepts, and how do their desiderata compare with the explainability techniques developed in the machine learning literature? In hopes of better connecting the policy and technical communities, we provide case studies illustrating five ways in which algorithmic transparency and explainability have been used in policy settings: specific requirements for explanations; in nonbinding guidelines for internal governance of algorithms; in regulations applicable to highly regulated settings; in guidelines meant to increase the utility of legal liability for algorithms; and broad requirements for model and data transparency. The case studies span a spectrum from precise requirements for specific types of explanations to nonspecific requirements focused on broader notions of transparency, illustrating the diverse needs, constraints, and capacities of various policy actors and contexts. Drawing on these case studies, we discuss promising ways in which transparency and explanation could be used in policy, as well as common factors limiting policymakers' use of algorithmic explainability. We conclude with recommendations for researchers and policymakers.
Given an observational study with $n$ independent but heterogeneous units, our goal is to learn the counterfactual distribution for each unit using only one $p$-dimensional sample per unit containing covariates, interventions, and outcomes. Specifically, we allow for unobserved confounding that introduces statistical biases between interventions and outcomes as well as exacerbates the heterogeneity across units. Modeling the conditional distribution of the outcomes as an exponential family, we reduce learning the unit-level counterfactual distributions to learning $n$ exponential family distributions with heterogeneous parameters and only one sample per distribution. We introduce a convex objective that pools all $n$ samples to jointly learn all $n$ parameter vectors, and provide a unit-wise mean squared error bound that scales linearly with the metric entropy of the parameter space. For example, when the parameters are $s$-sparse linear combination of $k$ known vectors, the error is $O(s\log k/p)$. En route, we derive sufficient conditions for compactly supported distributions to satisfy the logarithmic Sobolev inequality. As an application of the framework, our results enable consistent imputation of sparsely missing covariates.
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