We explore how observational and interventional causal discovery methods can be combined. A state-of-the-art observational causal discovery algorithm for time series capable of handling latent confounders and contemporaneous effects, called LPCMCI, is extended to profit from casual constraints found through randomized control trials. Numerical results show that, given perfect interventional constraints, the reconstructed structural causal models (SCMs) of the extended LPCMCI allow 84.6% of the time for the optimal prediction of the target variable. The implementation of interventional and observational causal discovery is modular, allowing causal constraints from other sources. The second part of this thesis investigates the question of regret minimizing control by simultaneously learning a causal model and planning actions through the causal model. The idea is that an agent to optimize a measured variable first learns the system's mechanics through observational causal discovery. The agent then intervenes on the most promising variable with randomized values allowing for the exploitation and generation of new interventional data. The agent then uses the interventional data to enhance the causal model further, allowing improved actions the next time. The extended LPCMCI can be favorable compared to the original LPCMCI algorithm. The numerical results show that detecting and using interventional constraints leads to reconstructed SCMs that allow 60.9% of the time for the optimal prediction of the target variable in contrast to the baseline of 53.6% when using the original LPCMCI algorithm. Furthermore, the induced average regret decreases from 1.2 when using the original LPCMCI algorithm to 1.0 when using the extended LPCMCI algorithm with interventional discovery.
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We analyze to what extent final users can infer information about the level of protection of their data when the data obfuscation mechanism is a priori unknown to them (the so-called ''black-box'' scenario). In particular, we delve into the investigation of two notions of local differential privacy (LDP), namely {\epsilon}-LDP and R\'enyi LDP. On one hand, we prove that, without any assumption on the underlying distributions, it is not possible to have an algorithm able to infer the level of data protection with provable guarantees; this result also holds for the central versions of the two notions of DP considered. On the other hand, we demonstrate that, under reasonable assumptions (namely, Lipschitzness of the involved densities on a closed interval), such guarantees exist and can be achieved by a simple histogram-based estimator. We validate our results experimentally and we note that, on a particularly well-behaved distribution (namely, the Laplace noise), our method gives even better results than expected, in the sense that in practice the number of samples needed to achieve the desired confidence is smaller than the theoretical bound, and the estimation of {\epsilon} is more precise than predicted.
We study the dynamics of matrix-valued time series with observed network structures by proposing a matrix network autoregression model with row and column networks of the subjects. We incorporate covariate information and a low rank intercept matrix. We allow incomplete observations in the matrices and the missing mechanism can be covariate dependent. To estimate the model, a two-step estimation procedure is proposed. The first step aims to estimate the network autoregression coefficients, and the second step aims to estimate the regression parameters, which are matrices themselves. Theoretically, we first separately establish the asymptotic properties of the autoregression coefficients and the error bounds of the regression parameters. Subsequently, a bias reduction procedure is proposed to reduce the asymptotic bias and the theoretical property of the debiased estimator is studied. Lastly, we illustrate the usefulness of the proposed method through a number of numerical studies and an analysis of a Yelp data set.
We provide sparse principal loading analysis which is a new concept that reduces dimensionality of cross sectional data and identifies the underlying covariance structure. Sparse principal loading analysis selects a subset of existing variables for dimensionality reduction while variables that have a small distorting effect on the covariance matrix are discarded. Therefore, we show how to detect these variables and provide methods to assess their magnitude of distortion. Sparse principal loading analysis is twofold and can also identify the underlying block diagonal covariance structure using sparse loadings. This is a new approach in this context and we provide a required criterion to evaluate if the found block-structure fits the sample. The method uses sparse loadings rather than eigenvectors to decompose the covariance matrix which can result in a large loss of information if the loadings of choice are too sparse. However, we show that this is no concern in our new concept because sparseness is controlled by the aforementioned evaluation criterion. Further, we show the advantages of sparse principal loading analysis both in the context of variable selection and covariance structure detection, and illustrate the performance of the method with simulations and on real datasets. Supplementary material for this article is available online.
BACKGROUND: In 1967, Frederick Lord posed a conundrum that has confused scientists for over 50-years. Subsequently named Lord's 'paradox', the puzzle centres on the observation that two common approach to analyses of 'change' between two time-points can produce radically different results. Approach 1 involves analysing the follow-up minus baseline (i.e., 'change score') and Approach 2 involves analysing the follow-up conditional on baseline. METHODS: At the heart of Lord's 'paradox' lies another puzzle concerning the use of 'change scores' in observational data. Using directed acyclic graphs and data simulations, we introduce, explore, and explain the 'paradox', consider the philosophy of change, and discuss the warnings and lessons of this 50-year puzzle. RESULTS: Understanding Lord's 'paradox' starts with recognising that a variable may change for three reasons: (A) 'endogenous change', which represents simple changes in scale, (B) 'random change', which represents change due to random processes, and (C) 'exogenous change', which represents all non-endogenous, non-random change. Unfortunately, in observational data, neither Approach 1 nor Approach 2 are able to reliably estimate the causes of 'exogenous change'. Approach 1 evaluates obscure estimands with little, if any, real-world interpretation. Approach 2 is susceptible to mediator-outcome confounding and cannot distinguish exogenous change from random change. Valid and precise estimates of a useful causal estimand instead require appropriate multivariate methods (such as g-methods) and more than two measures of the outcome. CONCLUSION: Lord's 'paradox' reiterates the dangers of analysing change scores in observational data and highlights the importance of considering causal questions within a causal framework.
For medical image segmentation, contrastive learning is the dominant practice to improve the quality of visual representations by contrasting semantically similar and dissimilar pairs of samples. This is enabled by the observation that without accessing ground truth label, negative examples with truly dissimilar anatomical features, if sampled, can significantly improve the performance. In reality, however, these samples may come from similar anatomical features and the models may struggle to distinguish the minority tail-class samples, making the tail classes more prone to misclassification, both of which typically lead to model collapse. In this paper, we propose ARCO, a semi-supervised contrastive learning (CL) framework with stratified group sampling theory in medical image segmentation. In particular, we first propose building ARCO through the concept of variance-reduced estimation, and show that certain variance-reduction techniques are particularly beneficial in medical image segmentation tasks with extremely limited labels. Furthermore, we theoretically prove these sampling techniques are universal in variance reduction. Finally, we experimentally validate our approaches on three benchmark datasets with different label settings, and our methods consistently outperform state-of-the-art semi- and fully-supervised methods. Additionally, we augment the CL frameworks with these sampling techniques and demonstrate significant gains over previous methods. We believe our work is an important step towards semi-supervised medical image segmentation by quantifying the limitation of current self-supervision objectives for accomplishing medical image analysis tasks.
Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption may no longer hold. For instance, in the context of social research, the outcome of a study unit will likely be affected by an intervention or treatment received by close neighbors. While inverse probability-of-treatment weighted (IPW) estimators have been developed for this setting, they are often highly inefficient. In this work, we assume that the network is a union of disjoint components and propose doubly robust (DR) estimators combining models for treatment and outcome that are consistent and asymptotically normal if either model is correctly specified. We present empirical results that illustrate the DR property and the efficiency gain of DR over IPW estimators when both the outcome and treatment models are correctly specified. Simulations are conducted for networks with equal and unequal component sizes and outcome data with and without a multilevel structure. We apply these methods in an illustrative analysis using the Add Health network, examining the impact of maternal college education on adolescent school performance, both direct and indirect.
Generating complex behaviors that satisfy the preferences of non-expert users is a crucial requirement on AI agents. Interactive reward learning from trajectory comparisons is one way to allow non-expert users to convey complex objectives by expressing preferences over short clips of agent behaviors. Even though this parametric method can encode complex tacit knowledge present in the underlying tasks, it implicitly assumes that the human is unable to provide richer feedback than binary preference labels, leading to intolerably high feedback complexity and poor user experience. While providing a detailed symbolic closed-form specification of the objectives might be tempting, it is not always feasible even for an expert user. However, in most cases, humans are aware of how the agent should change its behavior along meaningful axes to fulfill their underlying purpose, even if they are not able to fully specify task objectives symbolically. Using this as motivation, we introduce the notion of Relative Behavioral Attributes, which allows the users to tweak the agent behavior through symbolic concepts (e.g., increasing the softness or speed of agents' movement). We propose two practical methods that can learn to model any kind of behavioral attributes from ordered behavior clips. We demonstrate the effectiveness of our methods on four tasks with nine different behavioral attributes, showing that once the attributes are learned, end users can produce desirable agent behaviors relatively effortlessly, by providing feedback just around ten times. This is over an order of magnitude less than that required by the popular learning-from-human-preferences baselines. The supplementary video and source code are available at: //guansuns.github.io/pages/rba.
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first specify the maximal degree to which the distribution of unobserved potential outcomes may deviate from that of observed outcomes. We then derive sharp bounds on the average treatment effects under this assumption. Our framework encompasses the popular marginal sensitivity model as a special case, and we demonstrate how the proposed methodology can address a primary challenge of the marginal sensitivity model that it produces uninformative results when unobserved confounders substantially affect treatment and outcome. Specifically, we develop an alternative sensitivity model, called the distributional sensitivity model, under the assumption that heterogeneity of treatment effect due to unobserved variables is relatively small. Unlike the marginal sensitivity model, the distributional sensitivity model allows for potential lack of overlap and often produces informative bounds even when unobserved variables substantially affect both treatment and outcome. Finally, we show how to extend the distributional sensitivity model to difference-in-differences designs and settings with instrumental variables. Through simulation and empirical studies, we demonstrate the applicability of the proposed methodology.
Analyzing observational data from multiple sources can be useful for increasing statistical power to detect a treatment effect; however, practical constraints such as privacy considerations may restrict individual-level information sharing across data sets. This paper develops federated methods that only utilize summary-level information from heterogeneous data sets. Our federated methods provide doubly-robust point estimates of treatment effects as well as variance estimates. We derive the asymptotic distributions of our federated estimators, which are shown to be asymptotically equivalent to the corresponding estimators from the combined, individual-level data. We show that to achieve these properties, federated methods should be adjusted based on conditions such as whether models are correctly specified and stable across heterogeneous data sets.
This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.
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