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Nearest-neighbor methods have become popular in statistics and play a key role in statistical learning. Important decisions in nearest-neighbor methods concern the variables to use (when many potential candidates exist) and how to measure the dissimilarity between units. The first decision depends on the scope of the application while second depends mainly on the type of variables. Unfortunately, relatively few options permit to handle mixed-type variables, a situation frequently encountered in practical applications. The most popular dissimilarity for mixed-type variables is derived as the complement to one of the Gower's similarity coefficient. It is appealing because ranges between 0 and 1, being an average of the scaled dissimilarities calculated variable by variable, handles missing values and allows for a user-defined weighting scheme when averaging dissimilarities. The discussion on the weighting schemes is sometimes misleading since it often ignores that the unweighted "standard" setting hides an unbalanced contribution of the single variables to the overall dissimilarity. We address this drawback following the recent idea of introducing a weighting scheme that minimizes the differences in the correlation between each contributing dissimilarity and the resulting weighted Gower's dissimilarity. In particular, this note proposes different approaches for measuring the correlation depending on the type of variables. The performances of the proposed approaches are evaluated in simulation studies related to classification and imputation of missing values.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work we present a higher-order GNN model trained to predict the fourth-order stiffness tensor of periodic strut-based lattices. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate the benefits of the encoded equivariance and energy conservation in terms of predictive performance and reduced training requirements.

A popular method for variance reduction in observational causal inference is propensity-based trimming, the practice of removing units with extreme propensities from the sample. This practice has theoretical grounding when the data are homoscedastic and the propensity model is parametric (Yang and Ding, 2018; Crump et al. 2009), but in modern settings where heteroscedastic data are analyzed with non-parametric models, existing theory fails to support current practice. In this work, we address this challenge by developing new methods and theory for sample trimming. Our contributions are three-fold: first, we describe novel procedures for selecting which units to trim. Our procedures differ from previous work in that we trim not only units with small propensities, but also units with extreme conditional variances. Second, we give new theoretical guarantees for inference after trimming. In particular, we show how to perform inference on the trimmed subpopulation without requiring that our regressions converge at parametric rates. Instead, we make only fourth-root rate assumptions like those in the double machine learning literature. This result applies to conventional propensity-based trimming as well and thus may be of independent interest. Finally, we propose a bootstrap-based method for constructing simultaneously valid confidence intervals for multiple trimmed sub-populations, which are valuable for navigating the trade-off between sample size and variance reduction inherent in trimming. We validate our methods in simulation, on the 2007-2008 National Health and Nutrition Examination Survey, and on a semi-synthetic Medicare dataset and find promising results in all settings.

The intermittent intake of treatment is commonly seen in patients with chronic disease. For example, patients with atrial fibrillation may need to discontinue the oral anticoagulants when they experience a certain surgery and re-initiate the treatment after the surgery. As another example, patients may skip a few days before they refill a treatment as planned. This treatment dispensation information (i.e., the time at which a patient initiates and refills a treatment) is recorded in the electronic healthcare records or claims database, and each patient has a different treatment dispensation. Current methods to estimate the effects of such treatments censor the patients who re-initiate the treatment, which results in information loss or biased estimation. In this work, we present methods to estimate the effect of treatments on failure time outcomes by taking all the treatment dispensation information. The developed methods are based on the continuous-time structural failure time model, where the dependent censoring is tackled by inverse probability of censoring weighting. The estimators are doubly robust and locally efficient.

A discrete spatial lattice can be cast as a network structure over which spatially-correlated outcomes are observed. A second network structure may also capture similarities among measured features, when such information is available. Incorporating the network structures when analyzing such doubly-structured data can improve predictive power, and lead to better identification of important features in the data-generating process. Motivated by applications in spatial disease mapping, we develop a new doubly regularized regression framework to incorporate these network structures for analyzing high-dimensional datasets. Our estimators can easily be implemented with standard convex optimization algorithms. In addition, we describe a procedure to obtain asymptotically valid confidence intervals and hypothesis tests for our model parameters. We show empirically that our framework provides improved predictive accuracy and inferential power compared to existing high-dimensional spatial methods. These advantages hold given fully accurate network information, and also with networks which are partially misspecified or uninformative. The application of the proposed method to modeling COVID-19 mortality data suggests that it can improve prediction of deaths beyond standard spatial models, and that it selects relevant covariates more often.

We analyze the optimized adaptive importance sampler (OAIS) for performing Monte Carlo integration with general proposals. We leverage a classical result which shows that the bias and the mean-squared error (MSE) of the importance sampling scales with the $\chi^2$-divergence between the target and the proposal and develop a scheme which performs global optimization of $\chi^2$-divergence. While it is known that this quantity is convex for exponential family proposals, the case of the general proposals has been an open problem. We close this gap by utilizing the nonasymptotic bounds for stochastic gradient Langevin dynamics (SGLD) for the global optimization of $\chi^2$-divergence and derive nonasymptotic bounds for the MSE by leveraging recent results from non-convex optimization literature. The resulting AIS schemes have explicit theoretical guarantees that are uniform-in-time.

Understanding fluid movement in multi-pored materials is vital for energy security and physiology. For instance, shale (a geological material) and bone (a biological material) exhibit multiple pore networks. Double porosity/permeability models provide a mechanics-based approach to describe hydrodynamics in aforesaid porous materials. However, current theoretical results primarily address steady-state response, and their counterparts in the transient regime are still wanting. The primary aim of this paper is to fill this knowledge gap. We present three principal properties -- with rigorous mathematical arguments -- that the solutions under the double porosity/permeability model satisfy in the transient regime: backward-in-time uniqueness, reciprocity, and a variational principle. We employ the ``energy method'' -- by exploiting the physical total kinetic energy of the flowing fluid -- to establish the first property and Cauchy-Riemann convolutions to prove the next two. The results reported in this paper -- that qualitatively describe the dynamics of fluid flow in double-pored media -- have (a) theoretical significance, (b) practical applications, and (c) considerable pedagogical value. In particular, these results will benefit practitioners and computational scientists in checking the accuracy of numerical simulators. The backward-in-time uniqueness lays a firm theoretical foundation for pursuing inverse problems in which one predicts the prescribed initial conditions based on data available about the solution at a later instance.

Survey sampling plays an important role in the efficient allocation and management of resources. The essence of survey sampling lies in acquiring a sample of data points from a population and subsequently using this sample to estimate the population parameters of the targeted response variable, such as environmental-related metrics or other pertinent factors. Practical limitations imposed on survey sampling necessitate prudent consideration of the number of samples attainable from the study areas, given the constraints of a fixed budget. To this end, researchers are compelled to employ sampling designs that optimize sample allocations to the best of their ability. Generally, probability sampling serves as the preferred method, ensuring an unbiased estimation of population parameters. Evaluating the efficiency of estimators involves assessing their variances and benchmarking them against alternative baseline approaches, such as simple random sampling. In this study, we propose a novel model-assisted unbiased probability sampling method that leverages Bayesian optimization for the determination of sampling designs. As a result, this approach can yield in estimators with more efficient variance outcomes compared to the conventional estimators such as the Horvitz-Thompson. Furthermore, we test the proposed method in a simulation study using an empirical dataset covering plot-level tree volume from central Finland. The results demonstrate statistically significant improved performance for the proposed method when compared to the baseline.

This paper aims to front with dimensionality reduction in regression setting when the predictors are a mixture of functional variable and high-dimensional vector. A flexible model, combining both sparse linear ideas together with semiparametrics, is proposed. A wide scope of asymptotic results is provided: this covers as well rates of convergence of the estimators as asymptotic behaviour of the variable selection procedure. Practical issues are analysed through finite sample simulated experiments while an application to Tecator's data illustrates the usefulness of our methodology.