We consider learning a sparse pairwise Markov Random Field (MRF) with continuous-valued variables from i.i.d samples. We adapt the algorithm of Vuffray et al. (2019) [39] to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise MRFs with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of the optimization criterion employed in Vuffray et al. (2019) [39] can be interpreted as local maximum likelihood estimation (MLE). As part of our analysis, we introduce a robust variation of sparse linear regression à la Lasso, which may be of interest in its own right.

Inferring causal individual treatment effect (ITE) from observational data is a challenging problem whose difficulty is exacerbated by the presence of treatment assignment bias. In this work, we propose a new way to estimate the ITE using the domain generalization framework of invariant risk minimization (IRM). IRM uses data from multiple domains, learns predictors that do not exploit spurious domain-dependent factors, and generalizes better to unseen domains. We propose an IRM-based ITE estimator aimed at tackling treatment assignment bias when there is little support overlap between the control group and the treatment group. We accomplish this by creating diversity: given a single dataset, we split the data into multiple domains artificially. These diverse domains are then exploited by IRM to more effectively generalize regression-based models to data regions that lack support overlap. We show gains over classical regression approaches to ITE estimation in settings when support mismatch is more pronounced.

Abstract-We consider the cooperative data exchange problem, in which nodes are fully connected with each other. Each node initially only has a subset of the K packets making up a file and wants to recover the whole file. Node i can make a broadcast transmission, which incurs cost wi and is received by all other nodes. The goal is to minimize the total cost of transmissions that all nodes have to send, which is also called weighted cost. Following the same idea of our previous work [1] which provided a method based on dBasis construction to solve cooperative data exchange problem without weighted cost, we present a modified method to solve cooperative data exchange problem with weighted cost. We present a polynomial-time deterministic algorithm to compute the minimum weighted cost and determine the rate vector and the packets that should be used to generate each transmission. By leveraging the connection to Maximum Distance Separable codes, the coefficients of linear combinations of the optimal coding scheme can be efficiently generated. Our algorithm has significantly lower complexity than the state of the art. In particular, we prove that the minimum weighted cost function is a convex function of the total number of transmissions for integer rate cases.

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Compressing the output of ε-locally differentially private (LDP) randomizers naively leads to suboptimal utility. In this work, we demonstrate the benefits of using schemes that jointly compress and privatize the data using shared randomness. In particular, we investigate a family of schemes based on Minimal Random Coding (Havasi et al., 2019) and prove that they offer optimal privacy-accuracy-communication tradeoffs. Our theoretical and empirical findings show that our approach can compress PrivUnit 2 (Bhowmick et al., 2018) and Subset Selection (Ye and Barg, 2018), the best known LDP algorithms for mean and frequency estimation, to the order of ε bits of communication while preserving their privacy and accuracy guarantees.

Treatment effect estimation from observational data is a fundamental problem in causal inference. There are two very different schools of thought that have tackled this problem. On the one hand, the Pearlian framework commonly assumes structural knowledge (provided by an expert) in the form of Directed Acyclic Graphs (DAGs) and provides graphical criteria such as the back-door criterion to identify the valid adjustment sets. On the other hand, the potential outcomes (PO) framework commonly assumes that all the observed features satisfy ignorability (i.e., no hidden confounding), which in general is untestable. In this work, we take steps to bridge these two frameworks. We show that even if we know only one parent of the treatment variable (provided by an expert), then quite remarkably it suffices to test a broad class of (but not all) back-door criteria. Importantly, we also cover the non-trivial case where the entire set of observed features is not ignorable (generalizing the PO framework) without requiring all the parents of the treatment variable to be observed. Our key technical idea involves a more general result -Given a synthetic sub-sampling (or environment) variable that is a function of the parent variable, we show that an invariance test involving this sub-sampling variable is equivalent to testing a broad class of back-door criteria. We demonstrate our approach on synthetic data as well as real causal effect estimation benchmarks.

Inferring causal individual treatment effect (ITE) from observational data is a challenging problem whose difficulty is exacerbated by the presence of treatment assignment bias. In this work, we propose a new way to estimate the ITE using the domain generalization framework of invariant risk minimization (IRM). IRM uses data from multiple domains, learns predictors that do not exploit spurious domain-dependent factors, and generalizes better to unseen domains. We propose an IRM-based ITE estimator aimed at tackling treatment assignment bias when there is little support overlap between the control group and the treatment group. We accomplish this by creating diversity: given a single dataset, we split the data into multiple domains artificially. These diverse domains are then exploited by IRM to more effectively generalize regression-based models to data regions that lack support overlap. We show gains over classical regression approaches to ITE estimation in settings when support mismatch is more pronounced.

Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting fewer samples). However, as shown in this work, in some cases, the performance of minority group can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive groups. We show that such an unwanted behavior can be avoided if we can construct features satisfying the sufficiency criterion, so that the mean prediction and the associated uncertainty are calibrated across all the groups. Further, to mitigate the disparity in the performance across groups, we introduce two approaches based on this calibration criterion: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for mean and uncertainty prediction. The effectiveness of these approaches are demonstrated on synthetic as well as real-world datasets.