In recent years, the development of technologies for causal inference with privacy preservation of distributed data has gained considerable attention. Many existing methods for distributed data focus on resolving the lack of subjects (samples) and can only reduce random errors in estimating treatment effects. In this study, we propose a data collaboration quasi-experiment (DC-QE) that resolves the lack of both subjects and covariates, reducing random errors and biases in the estimation. Our method involves constructing dimensionality-reduced intermediate representations from private data from local parties, sharing intermediate representations instead of private data for privacy preservation, estimating propensity scores from the shared intermediate representations, and finally, estimating the treatment effects from propensity scores. Through numerical experiments on both artificial and real-world data, we confirm that our method leads to better estimation results than individual analyses. While dimensionality reduction loses some information in the private data and causes performance degradation, we observe that sharing intermediate representations with many parties to resolve the lack of subjects and covariates sufficiently improves performance to overcome the degradation caused by dimensionality reduction. Although external validity is not necessarily guaranteed, our results suggest that DC-QE is a promising method. With the widespread use of our method, intermediate representations can be published as open data to help researchers find causalities and accumulate a knowledge base.
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Human participants play a central role in the development of modern artificial intelligence (AI) technology, in psychological science, and in user research. Recent advances in generative AI have attracted growing interest to the possibility of replacing human participants in these domains with AI surrogates. We survey several such "substitution proposals" to better understand the arguments for and against substituting human participants with modern generative AI. Our scoping review indicates that the recent wave of these proposals is motivated by goals such as reducing the costs of research and development work and increasing the diversity of collected data. However, these proposals ignore and ultimately conflict with foundational values of work with human participants: representation, inclusion, and understanding. This paper critically examines the principles and goals underlying human participation to help chart out paths for future work that truly centers and empowers participants.
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of uncovering interaction relations in such systems using observable dynamics is called relational inference. In this study, we propose a Diffusion model for Relational Inference (DiffRI), inspired by a self-supervised method for probabilistic time series imputation. DiffRI learns to infer the probability of the presence of connections between components through conditional diffusion modeling. Experiments on both simulated and quasi-real datasets show that DiffRI is highly competent compared with other state-of-the-art models in discovering ground truth interactions in an unsupervised manner. Our code will be made public soon.
Analysis of geospatial data has traditionally been model-based, with a mean model, customarily specified as a linear regression on the covariates, and a covariance model, encoding the spatial dependence. We relax the strong assumption of linearity and propose embedding neural networks directly within the traditional geostatistical models to accommodate non-linear mean functions while retaining all other advantages including use of Gaussian Processes to explicitly model the spatial covariance, enabling inference on the covariate effect through the mean and on the spatial dependence through the covariance, and offering predictions at new locations via kriging. We propose NN-GLS, a new neural network estimation algorithm for the non-linear mean in GP models that explicitly accounts for the spatial covariance through generalized least squares (GLS), the same loss used in the linear case. We show that NN-GLS admits a representation as a special type of graph neural network (GNN). This connection facilitates use of standard neural network computational techniques for irregular geospatial data, enabling novel and scalable mini-batching, backpropagation, and kriging schemes. Theoretically, we show that NN-GLS will be consistent for irregularly observed spatially correlated data processes. To our knowledge this is the first asymptotic consistency result for any neural network algorithm for spatial data. We demonstrate the methodology through simulated and real datasets.
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.
It is a challenge to manage infinite- or high-dimensional data in situations where storage, transmission, or computation resources are constrained. In the simplest scenario when the data consists of a noisy infinite-dimensional signal, we introduce the notion of local \emph{effective dimension} (i.e., pertinent to the underlying signal), formulate and study the problem of its recovery on the basis of noisy data. This problem can be associated to the problems of adaptive quantization, (lossy) data compression, oracle signal estimation. We apply a Bayesian approach and study frequentists properties of the resulting posterior, a purely frequentist version of the results is also proposed. We derive certain upper and lower bounds results about identifying the local effective dimension which show that only the so called \emph{one-sided inference} on the local effective dimension can be ensured whereas the \emph{two-sided inference}, on the other hand, is in general impossible. We establish the \emph{minimal} conditions under which two-sided inference can be made. Finally, connection to the problem of smoothness estimation for some traditional smoothness scales (Sobolev scales) is considered.
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.
We study the problem of auditing classifiers with the notion of statistical subgroup fairness. Kearns et al. (2018) has shown that the problem of auditing combinatorial subgroups fairness is as hard as agnostic learning. Essentially all work on remedying statistical measures of discrimination against subgroups assumes access to an oracle for this problem, despite the fact that no efficient algorithms are known for it. If we assume the data distribution is Gaussian, or even merely log-concave, then a recent line of work has discovered efficient agnostic learning algorithms for halfspaces. Unfortunately, the boosting-style reductions given by Kearns et al. required the agnostic learning algorithm to succeed on reweighted distributions that may not be log-concave, even if the original data distribution was. In this work, we give positive and negative results on auditing for the Gaussian distribution: On the positive side, we an alternative approach to leverage these advances in agnostic learning and thereby obtain the first polynomial-time approximation scheme (PTAS) for auditing nontrivial combinatorial subgroup fairness: we show how to audit statistical notions of fairness over homogeneous halfspace subgroups when the features are Gaussian. On the negative side, we find that under cryptographic assumptions, no polynomial-time algorithm can guarantee any nontrivial auditing, even under Gaussian feature distributions, for general halfspace subgroups.
While methods for measuring and correcting differential performance in risk prediction models have proliferated in recent years, most existing techniques can only be used to assess fairness across relatively large subgroups. The purpose of algorithmic fairness efforts is often to redress discrimination against groups that are both marginalized and small, so this sample size limitation often prevents existing techniques from accomplishing their main aim. We take a three-pronged approach to address the problem of quantifying fairness with small subgroups. First, we propose new estimands built on the "counterfactual fairness" framework that leverage information across groups. Second, we estimate these quantities using a larger volume of data than existing techniques. Finally, we propose a novel data borrowing approach to incorporate "external data" that lacks outcomes and predictions but contains covariate and group membership information. This less stringent requirement on the external data allows for more possibilities for external data sources. We demonstrate practical application of our estimators to a risk prediction model used by a major Midwestern health system during the COVID-19 pandemic.
Typical pipelines for model geometry generation in computational biomedicine stem from images, which are usually considered to be at rest, despite the object being in mechanical equilibrium under several forces. We refer to the stress-free geometry computation as the reference configuration problem, and in this work we extend such a formulation to the theory of fully nonlinear poroelastic media. The main steps are (i) writing the equations in terms of the reference porosity and (ii) defining a time dependent problem whose steady state solution is the reference porosity. This problem can be computationally challenging as it can require several hundreds of iterations to converge, so we propose the use of Anderson acceleration to speed up this procedure. Our evidence shows that this strategy can reduce the number of iterations up to 80\%. In addition, we note that a primal formulation of the nonlinear mass conservation equations is not consistent due to the presence of second order derivatives of the displacement, which we alleviate through adequate mixed formulations. All claims are validated through numerical simulations in both idealized and realistic scenarios.
In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.
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