Interference occurs when the treatment (or exposure) of a unit affects the outcome of another unit. In some settings, units may be grouped into clusters such that it is reasonable to assume that interference, if present, only occurs between individuals in the same cluster, i.e., there is clustered interference. Various causal estimands have been proposed to quantify treatment effects under clustered interference from observational data, but these estimands either entail treatment policies lacking real-world relevance or are based on parametric propensity score models. Here, we propose new causal estimands based on incremental changes to propensity scores which may be more relevant in many contexts and are not based on parametric models. Nonparametric sample splitting estimators of the new estimands are constructed, which allow for flexible data-adaptive estimation of nuisance functions and are consistent, asymptotically normal, and efficient, converging at the usual parametric rate. Simulations show the finite sample performance of the proposed estimators. The proposed methods are applied to evaluate the effect of water, sanitation, and hygiene facilities on diarrhea incidence among children in Senegal under clustered interference.
相關內容
Understanding and quantifying cause and effect is an important problem in many domains. The generally-agreed solution to this problem is to perform a randomised controlled trial. However, even when randomised controlled trials can be performed, they usually have relatively short duration's due to cost considerations. This makes learning long-term causal effects a very challenging task in practice, since the long-term outcome is only observed after a long delay. In this paper, we study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Previous work provided an estimation strategy to determine long-term causal effects from such data regimes. However, this strategy only works if one assumes there are no unobserved confounders in the observational data. In this paper, we specifically address the challenging case where unmeasured confounders are present in the observational data. Our long-term causal effect estimator is obtained by combining regression residuals with short-term experimental outcomes in a specific manner to create an instrumental variable, which is then used to quantify the long-term causal effect through instrumental variable regression. We prove this estimator is unbiased, and analytically study its variance. In the context of the front-door causal structure, this provides a new causal estimator, which may be of independent interest. Finally, we empirically test our approach on synthetic-data, as well as real-data from the International Stroke Trial.
A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB (Kris- tensen et al., 2016) framework in R for this purpose were illustrated recently Bacri et al. (2022). In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several ex- amples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach.
Estimating treatment effects plays a crucial role in causal inference, having many real-world applications like policy analysis and decision making. Nevertheless, estimating treatment effects in the longitudinal setting in the presence of hidden confounders remains an extremely challenging problem. Recently, there is a growing body of work attempting to obtain unbiased ITE estimates from time-dynamic observational data by ignoring the possible existence of hidden confounders. Additionally, many existing works handling hidden confounders are not applicable for continuous-time settings. In this paper, we extend the line of work focusing on deconfounding in the dynamic time setting in the presence of hidden confounders. We leverage recent advancements in neural differential equations to build a latent factor model using a stochastic controlled differential equation and Lipschitz constrained convolutional operation in order to continuously incorporate information about ongoing interventions and irregularly sampled observations. Experiments on both synthetic and real-world datasets highlight the promise of continuous time methods for estimating treatment effects in the presence of hidden confounders.
Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable than marginal ones, they may suffer from slow mixing in infinite mixtures, where some form of truncation, either deterministic or random, is required. In mixtures with random number of components, the exploration of parameter spaces of different dimensions can also be challenging. We tackle these issues by expressing the mixture components in the random order of appearance in an exchangeable sequence directed by the mixing distribution. We derive a sampler that is straightforward to implement for mixing distributions with tractable size-biased ordered weights, and that can be readily adapted to mixture models for which marginal samplers are not available. In infinite mixtures, no form of truncation is necessary. As for finite mixtures with random dimension, a simple updating of the number of components is obtained by a blocking argument, thus, easing challenges found in trans-dimensional moves via Metropolis-Hastings steps. Additionally, sampling occurs in the space of ordered partitions with blocks labelled in the least element order, which endows the sampler with good mixing properties. The performance of the proposed algorithm is evaluated in a simulation study.
In many bandit problems, the maximal reward achievable by a policy is often unknown in advance. We consider the problem of estimating the optimal policy value in the sublinear data regime before the optimal policy is even learnable. We refer to this as $V^*$ estimation. It was recently shown that fast $V^*$ estimation is possible but only in disjoint linear bandits with Gaussian covariates. Whether this is possible for more realistic context distributions has remained an open and important question for tasks such as model selection. In this paper, we first provide lower bounds showing that this general problem is hard. However, under stronger assumptions, we give an algorithm and analysis proving that $\widetilde{\mathcal{O}}(\sqrt{d})$ sublinear estimation of $V^*$ is indeed information-theoretically possible, where $d$ is the dimension. We then present a more practical, computationally efficient algorithm that estimates a problem-dependent upper bound on $V^*$ that holds for general distributions and is tight when the context distribution is Gaussian. We prove our algorithm requires only $\widetilde{\mathcal{O}}(\sqrt{d})$ samples to estimate the upper bound. We use this upper bound and the estimator to obtain novel and improved guarantees for several applications in bandit model selection and testing for treatment effects.
The study of almost surely discrete random probability measures is an active line of research in Bayesian nonparametrics. The idea of assuming interaction across the atoms of the random probability measure has recently spurred significant interest in the context of Bayesian mixture models. This allows the definition of priors that encourage well separated and interpretable clusters. In this work, we provide a unified framework for the construction and the Bayesian analysis of random probability measures with interacting atoms, encompassing both repulsive and attractive behaviors. Specifically we derive closed-form expressions for the posterior distribution, the marginal and predictive distributions, which were not previously available except for the case of measures with i.i.d. atoms. We show how these quantities are fundamental both for prior elicitation and to develop new posterior simulation algorithms for hierarchical mixture models. Our results are obtained without any assumption on the finite point process that governs the atoms of the random measure. Their proofs rely on new analytical tools borrowed from the theory of Palm calculus and that might be of independent interest. We specialize our treatment to the classes of Poisson, Gibbs, and Determinantal point processes, as well as to the case of shot-noise Cox processes.
Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework: the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We provide the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We demonstrate that neither of the identification models provides uniformly the most efficient estimation and give conditions under which some bounds are lower than others. We show when semiparametric estimating equation estimators based on influence functions attain the bounds, and study the robustness of the estimators to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Our results show that this choice implies a trade-off between efficiency and robustness to misspecification of the nuisance models.
The problems of selecting partial correlation and causality graphs for count data are considered. A parameter driven generalized linear model is used to describe the observed multivariate time series of counts. Partial correlation and causality graphs corresponding to this model explain the dependencies between each time series of the multivariate count data. In order to estimate these graphs with tunable sparsity, an appropriate likelihood function maximization is regularized with an l1-type constraint. A novel MCEM algorithm is proposed to iteratively solve this regularized MLE. Asymptotic convergence results are proved for the sequence generated by the proposed MCEM algorithm with l1-type regularization. The algorithm is first successfully tested on simulated data. Thereafter, it is applied to observed weekly dengue disease counts from each ward of Greater Mumbai city. The interdependence of various wards in the proliferation of the disease is characterized by the edges of the inferred partial correlation graph. On the other hand, the relative roles of various wards as sources and sinks of dengue spread is quantified by the number and weights of the directed edges originating from and incident upon each ward. From these estimated graphs, it is observed that some special wards act as epicentres of dengue spread even though their disease counts are relatively low.
Deep models, e.g., CNNs and Vision Transformers, have achieved impressive achievements in many vision tasks in the closed world. However, novel classes emerge from time to time in our ever-changing world, requiring a learning system to acquire new knowledge continually. For example, a robot needs to understand new instructions, and an opinion monitoring system should analyze emerging topics every day. Class-Incremental Learning (CIL) enables the learner to incorporate the knowledge of new classes incrementally and build a universal classifier among all seen classes. Correspondingly, when directly training the model with new class instances, a fatal problem occurs -- the model tends to catastrophically forget the characteristics of former ones, and its performance drastically degrades. There have been numerous efforts to tackle catastrophic forgetting in the machine learning community. In this paper, we survey comprehensively recent advances in deep class-incremental learning and summarize these methods from three aspects, i.e., data-centric, model-centric, and algorithm-centric. We also provide a rigorous and unified evaluation of 16 methods in benchmark image classification tasks to find out the characteristics of different algorithms empirically. Furthermore, we notice that the current comparison protocol ignores the influence of memory budget in model storage, which may result in unfair comparison and biased results. Hence, we advocate fair comparison by aligning the memory budget in evaluation, as well as several memory-agnostic performance measures. The source code to reproduce these evaluations is available at //github.com/zhoudw-zdw/CIL_Survey/
Image segmentation is still an open problem especially when intensities of the interested objects are overlapped due to the presence of intensity inhomogeneity (also known as bias field). To segment images with intensity inhomogeneities, a bias correction embedded level set model is proposed where Inhomogeneities are Estimated by Orthogonal Primary Functions (IEOPF). In the proposed model, the smoothly varying bias is estimated by a linear combination of a given set of orthogonal primary functions. An inhomogeneous intensity clustering energy is then defined and membership functions of the clusters described by the level set function are introduced to rewrite the energy as a data term of the proposed model. Similar to popular level set methods, a regularization term and an arc length term are also included to regularize and smooth the level set function, respectively. The proposed model is then extended to multichannel and multiphase patterns to segment colourful images and images with multiple objects, respectively. It has been extensively tested on both synthetic and real images that are widely used in the literature and public BrainWeb and IBSR datasets. Experimental results and comparison with state-of-the-art methods demonstrate that advantages of the proposed model in terms of bias correction and segmentation accuracy.
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191