亚洲男人的天堂2018av,欧美草比,久久久久久免费视频精选,国色天香在线看免费,久久久久亚洲av成人片仓井空

We introduce the nested stochastic block model (NSBM) to cluster a collection of networks while simultaneously detecting communities within each network. NSBM has several appealing features including the ability to work on unlabeled networks with potentially different node sets, the flexibility to model heterogeneous communities, and the means to automatically select the number of classes for the networks and the number of communities within each network. This is accomplished via a Bayesian model, with a novel application of the nested Dirichlet process (NDP) as a prior to jointly model the between-network and within-network clusters. The dependency introduced by the network data creates nontrivial challenges for the NDP, especially in the development of efficient samplers. For posterior inference, we propose several Markov chain Monte Carlo algorithms including a standard Gibbs sampler, a collapsed Gibbs sampler, and two blocked Gibbs samplers that ultimately return two levels of clustering labels from both within and across the networks. Extensive simulation studies are carried out which demonstrate that the model provides very accurate estimates of both levels of the clustering structure. We also apply our model to two social network datasets that cannot be analyzed using any previous method in the literature due to the anonymity of the nodes and the varying number of nodes in each network.

We generalize signature Gr\"obner bases, previously studied in the free algebra over a field or polynomial rings over a ring, to ideals in the mixed algebra $R[x_1,...,x_k]\langle y_1,\dots,y_n \rangle$ where $R$ is a principal ideal domain. We give an algorithm for computing them, combining elements from the theory of commutative and noncommutative (signature) Gr\"obner bases, and prove its correctness. Applications include extensions of the free algebra with commutative variables, e.g., for homogenization purposes or for performing ideal theoretic operations such as intersections, and computations over $\mathbb{Z}$ as universal proofs over fields of arbitrary characteristic. By extending the signature cover criterion to our setting, our algorithm also lifts some technical restrictions from previous noncommutative signature-based algorithms, now allowing, e.g., elimination orderings. We provide a prototype implementation for the case when $R$ is a field, and show that our algorithm for the mixed algebra is more efficient than classical approaches using existing algorithms.

In biomedical studies, longitudinal processes are collected till time-to-event, sometimes on nested timescales (example, days within months). Most of the literature in joint modeling of longitudinal and time-to-event data has focused on modeling the mean or dispersion of the longitudinal process with the hazard for time-to-event. However, based on the motivating studies, it may be of interest to investigate how the cycle-level {\it geometric features} (such as the curvature, location and height of a peak), of a cyclical longitudinal process is associated with the time-to-event being studied. We propose a shared parameter joint model for a cyclical longitudinal process and a discrete survival time, measured on nested timescales, where the cycle-varying geometric feature is modeled through a linear mixed effects model and a proportional hazards model for the discrete survival time. The proposed approach allows for prediction of survival probabilities for future subjects based on their available longitudinal measurements. Our proposed model and approach is illustrated through simulation and analysis of Stress and Time-to-Pregnancy, a component of Oxford Conception Study. A joint modeling approach was used to assess whether the cycle-specific geometric features of the lutenizing hormone measurements, such as its peak or its curvature, are associated with time-to-pregnancy (TTP).

We present a deterministic algorithm for the efficient evaluation of imaginary time diagrams based on the recently introduced discrete Lehmann representation (DLR) of imaginary time Green's functions. In addition to the efficient discretization of diagrammatic integrals afforded by its approximation properties, the DLR basis is separable in imaginary time, allowing us to decompose diagrams into linear combinations of nested sequences of one-dimensional products and convolutions. Focusing on the strong coupling bold-line expansion of generalized Anderson impurity models, we show that our strategy reduces the computational complexity of evaluating an $M$th-order diagram at inverse temperature $\beta$ from $\mathcal{O}(\beta^{2M-1})$ for a direct quadrature to $\mathcal{O}(M \log^{M+1} \beta)$, with controllable high-order accuracy. We benchmark our algorithm using third-order expansions for multi-band impurity problems with off-diagonal hybridization and spin-orbit coupling, presenting comparisons with exact diagonalization and quantum Monte Carlo approaches. In particular, we perform a self-consistent dynamical mean-field theory calculation for a three-band Hubbard model with strong spin-orbit coupling representing a minimal model of Ca$_2$RuO$_4$, demonstrating the promise of the method for modeling realistic strongly correlated multi-band materials. For expansions of low and intermediate order, in which diagrams can be enumerated, our method provides an efficient, straightforward, and robust black-box evaluation procedure. In this sense, it fills a gap between diagrammatic approximations of the lowest order, which are simple and inexpensive but inaccurate, and those based on Monte Carlo sampling of high-order diagrams.

Intensive care occupancy is an important indicator of health care stress that has been used to guide policy decisions during the COVID-19 pandemic. Toward reliable decision-making as a pandemic progresses, estimating the rates at which patients are admitted to and discharged from hospitals and intensive care units (ICUs) is crucial. Since individual-level hospital data are rarely available to modelers in each geographic locality of interest, it is important to develop tools for inferring these rates from publicly available daily numbers of hospital and ICU beds occupied. We develop such an estimation approach based on an immigration-death process that models fluctuations of ICU occupancy. Our flexible framework allows for immigration and death rates to depend on covariates, such as hospital bed occupancy and daily SARS-CoV-2 test positivity rate, which may drive changes in hospital ICU operations. We demonstrate via simulation studies that the proposed method performs well on noisy time series data and apply our statistical framework to hospitalization data from the University of California, Irvine (UCI) Health and Orange County, California. By introducing a likelihood-based framework where immigration and death rates can vary with covariates, we find, through rigorous model selection, that hospitalization and positivity rates are crucial covariates for modeling ICU stay dynamics and validate our per-patient ICU stay estimates using anonymized patient-level UCI hospital data.

Randomized trials balance all covariates on average and provide the gold standard for estimating treatment effects. Chance imbalances nevertheless exist more or less in realized treatment allocations and intrigue an important question: what should we do in case the treatment groups differ with respect to some important baseline characteristics? A common strategy is to conduct a {\it preliminary test} of the balance of baseline covariates after randomization, and invoke covariate adjustment for subsequent inference if and only if the realized allocation fails some prespecified criterion. Although such practice is intuitive and popular among practitioners, the existing literature has so far only evaluated its properties under strong parametric model assumptions in theory and simulation, yielding results of limited generality. To fill this gap, we examine two strategies for conducting preliminary test-based covariate adjustment by regression, and evaluate the validity and efficiency of the resulting inferences from the randomization-based perspective. As it turns out, the preliminary-test estimator based on the analysis of covariance can be even less efficient than the unadjusted difference in means, and risks anticonservative confidence intervals based on normal approximation even with the robust standard error. The preliminary-test estimator based on the fully interacted specification is on the other hand less efficient than its counterpart under the {\it always-adjust} strategy, and yields overconservative confidence intervals based on normal approximation. Based on theory and simulation, we echo the existing literature and do not recommend the preliminary-test procedure for covariate adjustment in randomized trials.

Predictions under hypothetical interventions are estimates of what a person's risk of an outcome would be if they were to follow a particular treatment strategy, given their individual characteristics. Such predictions can give important input to medical decision making. However, evaluating predictive performance of interventional predictions is challenging. Standard ways of evaluating predictive performance do not apply when using observational data, because prediction under interventions involves obtaining predictions of the outcome under conditions that are different to those that are observed for a subset of individuals in the validation dataset. This work describes methods for evaluating counterfactual predictive performance of predictions under interventions for time-to-event outcomes. This means we aim to assess how well predictions would match the validation data if all individuals had followed the treatment strategy under which predictions are made. We focus on counterfactual performance evaluation using longitudinal observational data, and under treatment strategies that involve sustaining a particular treatment regime over time. We introduce an estimation approach using artificial censoring and inverse probability weighting which involves creating a validation dataset that mimics the treatment strategy under which predictions are made. We extend measures of calibration, discrimination (c-index and cumulative/dynamic AUC) and overall prediction error (Brier score) to allow assessment of counterfactual performance. The methods are evaluated using a simulation study, including scenarios in which the methods should detect poor performance. Applying our methods in the context of liver transplantation shows that our procedure allows quantification of the performance of predictions supporting crucial decisions on organ allocation.

Population size estimation based on the capture-recapture experiment is an interesting problem in various fields including epidemiology, criminology, demography, etc. In many real-life scenarios, there exists inherent heterogeneity among the individuals and dependency between capture and recapture attempts. A novel trivariate Bernoulli model is considered to incorporate these features, and the Bayesian estimation of the model parameters is suggested using data augmentation. Simulation results show robustness under model misspecification and the superiority of the performance of the proposed method over existing competitors. The method is applied to analyse real case studies on epidemiological surveillance. The results provide interesting insight on the heterogeneity and dependence involved in the capture-recapture mechanism. The methodology proposed can assist in effective decision-making and policy formulation.

We define simple variants of zip trees, called zip-zip trees, which provide several advantages over zip trees, including overcoming a bias that favors smaller keys over larger ones. We analyze zip-zip trees theoretically and empirically, showing, e.g., that the expected depth of a node in an $n$-node zip-zip tree is at most $1.3863\log n-1+o(1)$, which matches the expected depth of treaps and binary search trees built by uniformly random insertions. Unlike these other data structures, however, zip-zip trees achieve their bounds using only $O(\log\log n)$ bits of metadata per node, w.h.p., as compared to the $\Theta(\log n)$ bits per node required by treaps. In fact, we even describe a ``just-in-time'' zip-zip tree variant, which needs just an expected $O(1)$ number of bits of metadata per node. Moreover, we can define zip-zip trees to be strongly history independent, whereas treaps are generally only weakly history independent. We also introduce \emph{biased zip-zip trees}, which have an explicit bias based on key weights, so the expected depth of a key, $k$, with weight, $w_k$, is $O(\log (W/w_k))$, where $W$ is the weight of all keys in the weighted zip-zip tree. Finally, we show that one can easily make zip-zip trees partially persistent with only $O(n)$ space overhead w.h.p.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.