In assessing prediction accuracy of multivariable prediction models, optimism corrections are essential for preventing biased results. However, in most published papers of clinical prediction models, the point estimates of the prediction accuracy measures are corrected by adequate bootstrap-based correction methods, but their confidence intervals are not corrected, e.g., the DeLong's confidence interval is usually used for assessing the C-statistic. These naive methods do not adjust for the optimism bias and do not account for statistical variability in the estimation of parameters in the prediction models. Therefore, their coverage probabilities of the true value of the prediction accuracy measure can be seriously below the nominal level (e.g., 95%). In this article, we provide two generic bootstrap methods, namely (1) location-shifted bootstrap confidence intervals and (2) two-stage bootstrap confidence intervals, that can be generally applied to the bootstrap-based optimism correction methods, i.e., the Harrell's bias correction, 0.632, and 0.632+ methods. In addition, they can be widely applied to various methods for prediction model development involving modern shrinkage methods such as the ridge and lasso regressions. Through numerical evaluations by simulations, the proposed confidence intervals showed favourable coverage performances. Besides, the current standard practices based on the optimism-uncorrected methods showed serious undercoverage properties. To avoid erroneous results, the optimism-uncorrected confidence intervals should not be used in practice, and the adjusted methods are recommended instead. We also developed the R package predboot for implementing these methods (//github.com/nomahi/predboot). The effectiveness of the proposed methods are illustrated via applications to the GUSTO-I clinical trial.
相關內容
Variable selection methods are widely used in molecular biology to detect biomarkers or to infer gene regulatory networks from transcriptomic data. Methods are mainly based on the high-dimensional Gaussian linear regression model and we focus on this framework for this review. We propose a comparison study of variable selection procedures from regularization paths by considering three simulation settings. In the first one, the variables are independent allowing the evaluation of the methods in the theoretical framework used to develop them. In the second setting, two structures of the correlation between variables are considered to evaluate how biological dependencies usually observed affect the estimation. Finally, the third setting mimics the biological complexity of transcription factor regulations, it is the farthest setting from the Gaussian framework. In all the settings, the capacity of prediction and the identification of the explaining variables are evaluated for each method. Our results show that variable selection procedures rely on statistical assumptions that should be carefully checked. The Gaussian assumption and the number of explaining variables are the two key points. As soon as correlation exists, the regularization function Elastic-net provides better results than Lasso. LinSelect, a non-asymptotic model selection method, should be preferred to the eBIC criterion commonly used. Bolasso is a judicious strategy to limit the selection of non explaining variables.
The popular Bayesian meta-analysis expressed by Bayesian normal-normal hierarchical model (NNHM) synthesizes knowledge from several studies and is highly relevant in practice. Moreover, NNHM is the simplest Bayesian hierarchical model (BHM), which illustrates problems typical in more complex BHMs. Until now, it has been unclear to what extent the data determines the marginal posterior distributions of the parameters in NNHM. To address this issue we computed the second derivative of the Bhattacharyya coefficient with respect to the weighted likelihood, defined the total empirical determinacy (TED), the proportion of the empirical determinacy of location to TED (pEDL), and the proportion of the empirical determinacy of spread to TED (pEDS). We implemented this method in the R package \texttt{ed4bhm} and considered two case studies and one simulation study. We quantified TED, pEDL and pEDS under different modeling conditions such as model parametrization, the primary outcome, and the prior. This clarified to what extent the location and spread of the marginal posterior distributions of the parameters are determined by the data. Although these investigations focused on Bayesian NNHM, the method proposed is applicable more generally to complex BHMs.
The tensor Ising model is a discrete exponential family used for modeling binary data on networks with not just pairwise, but higher-order dependencies. In this exponential family, the sufficient statistic is a multi-linear form of degree $p\ge 2$, designed to capture $p$-fold interactions between the binary variables sitting on the nodes of a network. A particularly useful class of tensor Ising models are the tensor Curie-Weiss models, where one assumes that all $p$-tuples of nodes interact with the same intensity. Computing the maximum likelihood estimator (MLE) is computationally cumbersome in this model, due to the presence of an inexplicit normalizing constant in the likelihood, for which the standard alternative is to use the maximum pseudolikelihood estimator (MPLE). Both the MLE and the MPLE are consistent estimators of the natural parameter, provided the latter lies strictly above a certain threshold, which is slightly below $\log 2$, and approaches $\log 2$ as $p$ increases. In this paper, we compute the Bahadur efficiencies of the MLE and the MPLE above the threshold, and derive the optimal sample size (number of nodes) needed for either of these tests to achieve significance. We show that the optimal sample size for the MPLE and the MLE agree if either $p=2$ or the null parameter is greater than or equal to $\log 2$. On the other hand, if $p\ge 3$ and the null parameter lies strictly between the threshold and $\log 2$, then the two differ for sufficiently large values of the alternative. In particular, for every fixed alternative above the threshold, the Bahadur asymptotic relative efficiency of the MLE with respect to the MPLE goes to $\infty$ as the null parameter approaches the threshold. We also provide graphical presentations of the exact numerical values of the theoretical optimal sample sizes in different settings.
We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper analysis of the local convergence of EM and gradient EM, compared to previous works. Assuming a separation of $\Omega(\sqrt{\log K})$, we prove convergence of both methods to the global optima from an initialization region larger than those of previous works. Specifically, the initial guess of each component can be as far as (almost) half its distance to the nearest Gaussian. This is essentially the largest possible contraction region. Our second contribution are improved sample size requirements for accurate estimation by EM and gradient EM. In previous works, the required number of samples had a quadratic dependence on the maximal separation between the K components, and the resulting error estimate increased linearly with this maximal separation. In this manuscript we show that both quantities depend only logarithmically on the maximal separation.
Trust region methods rigorously enabled reinforcement learning (RL) agents to learn monotonically improving policies, leading to superior performance on a variety of tasks. Unfortunately, when it comes to multi-agent reinforcement learning (MARL), the property of monotonic improvement may not simply apply; this is because agents, even in cooperative games, could have conflicting directions of policy updates. As a result, achieving a guaranteed improvement on the joint policy where each agent acts individually remains an open challenge. In this paper, we extend the theory of trust region learning to MARL. Central to our findings are the multi-agent advantage decomposition lemma and the sequential policy update scheme. Based on these, we develop Heterogeneous-Agent Trust Region Policy Optimisation (HATPRO) and Heterogeneous-Agent Proximal Policy Optimisation (HAPPO) algorithms. Unlike many existing MARL algorithms, HATRPO/HAPPO do not need agents to share parameters, nor do they need any restrictive assumptions on decomposibility of the joint value function. Most importantly, we justify in theory the monotonic improvement property of HATRPO/HAPPO. We evaluate the proposed methods on a series of Multi-Agent MuJoCo and StarCraftII tasks. Results show that HATRPO and HAPPO significantly outperform strong baselines such as IPPO, MAPPO and MADDPG on all tested tasks, therefore establishing a new state of the art.
In this paper we consider the problem of quickly detecting changes in hidden Markov models (HMMs) in a Bayesian setting, as well as several structured generalisations including changes in statistically periodic processes, quickest detection of a Markov process across a sensor array, quickest detection of a moving target in a sensor network and quickest change detection (QCD) in multistream data. Our main result establishes an optimal Bayesian HMM QCD rule with a threshold structure. This framework and proof techniques allow us to elegantly establish optimal rules for the structured generalisations by showing that these problems are special cases of the Bayesian HMM QCD problem. The threshold structure enables us to develop bounds to characterise the performance of our optimal rule and provide an efficient method for computing the test statistic. Finally, we examine the performance of our rule in several simulation examples and propose a technique for calculating the optimal threshold.
Evaluation of predictive deep learning (DL) models beyond conventional performance metrics has become increasingly important for applications in sensitive environments like healthcare. Such models might have the capability to encode and analyse large sets of data but they often lack comprehensive interpretability methods, preventing clinical trust in predictive outcomes. Quantifying uncertainty of a prediction is one way to provide such interpretability and promote trust. However, relatively little attention has been paid to how to include such requirements into the training of the model. In this paper we: (i) quantify the data (aleatoric) and model (epistemic) uncertainty of a DL model for Cardiac Resynchronisation Therapy response prediction from cardiac magnetic resonance images, and (ii) propose and perform a preliminary investigation of an uncertainty-aware loss function that can be used to retrain an existing DL image-based classification model to encourage confidence in correct predictions and reduce confidence in incorrect predictions. Our initial results are promising, showing a significant increase in the (epistemic) confidence of true positive predictions, with some evidence of a reduction in false negative confidence.
A fundamental goal of scientific research is to learn about causal relationships. However, despite its critical role in the life and social sciences, causality has not had the same importance in Natural Language Processing (NLP), which has traditionally placed more emphasis on predictive tasks. This distinction is beginning to fade, with an emerging area of interdisciplinary research at the convergence of causal inference and language processing. Still, research on causality in NLP remains scattered across domains without unified definitions, benchmark datasets and clear articulations of the remaining challenges. In this survey, we consolidate research across academic areas and situate it in the broader NLP landscape. We introduce the statistical challenge of estimating causal effects, encompassing settings where text is used as an outcome, treatment, or as a means to address confounding. In addition, we explore potential uses of causal inference to improve the performance, robustness, fairness, and interpretability of NLP models. We thus provide a unified overview of causal inference for the computational linguistics community.
The recent proliferation of knowledge graphs (KGs) coupled with incomplete or partial information, in the form of missing relations (links) between entities, has fueled a lot of research on knowledge base completion (also known as relation prediction). Several recent works suggest that convolutional neural network (CNN) based models generate richer and more expressive feature embeddings and hence also perform well on relation prediction. However, we observe that these KG embeddings treat triples independently and thus fail to cover the complex and hidden information that is inherently implicit in the local neighborhood surrounding a triple. To this effect, our paper proposes a novel attention based feature embedding that captures both entity and relation features in any given entity's neighborhood. Additionally, we also encapsulate relation clusters and multihop relations in our model. Our empirical study offers insights into the efficacy of our attention based model and we show marked performance gains in comparison to state of the art methods on all datasets.
We report an evaluation of the effectiveness of the existing knowledge base embedding models for relation prediction and for relation extraction on a wide range of benchmarks. We also describe a new benchmark, which is much larger and complex than previous ones, which we introduce to help validate the effectiveness of both tasks. The results demonstrate that knowledge base embedding models are generally effective for relation prediction but unable to give improvements for the state-of-art neural relation extraction model with the existing strategies, while pointing limitations of existing methods.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191