Nested Nonparametric Instrumental Variable Regression

• URL: http://arxiv.org/abs/2112.14249v4
• Date: Fri, 30 May 2025 16:07:09 GMT
• Title: Nested Nonparametric Instrumental Variable Regression
• Authors: Isaac Meza, Rahul Singh,
• Abstract summary: Several causal parameters in short panel data models are functionals of a nested nonparametric instrumental variable regression (nested NPIV)<n>Recent examples include mediated, time varying, and long term treatment effects identified using proxy variables.<n>We provide explicit mean square rates for nested NPIV and efficient inference for recently identified causal parameters.
• Score: 2.2984209387877628
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Several causal parameters in short panel data models are functionals of a nested nonparametric instrumental variable regression (nested NPIV). Recent examples include mediated, time varying, and long term treatment effects identified using proxy variables. In econometrics, examples arise in triangular simultaneous equations and hedonic price systems. However, it appears that explicit mean square convergence rates for nested NPIV are unknown, preventing inference on some of these parameters with generic machine learning. A major challenge is compounding ill posedness due to the nested inverse problems. To limit how ill posedness compounds, we introduce two techniques: relative well posedness, and multiple robustness to ill posedness. With these techniques, we provide explicit mean square rates for nested NPIV and efficient inference for recently identified causal parameters. Our nonasymptotic analysis accommodates neural networks, random forests, and reproducing kernel Hilbert spaces. It extends to causal functions, e.g. heterogeneous long term treatment effects.

Related papers

• Geometric Neural Operators via Lie Group-Constrained Latent Dynamics [14.152015935335358]
  We show that our method effectively lowers the relative prediction error by 30-50% at the cost of 2.26% of parameter increase.<n>The results show that our approach provides a scalable solution for improving long-term prediction fidelity.
  arXiv  Detail & Related papers  (2026-02-18T06:17:47Z)
• Nonparametric Instrumental Variable Regression with Observed Covariates [32.91951875577007]
  We study the problem of nonparametric instrumental variable regression with observed covariables, which we refer to as NPIV-O.<n> observed covariables induce a partial identity structure, which renders previous NPIV analyses inapplicable.<n>For the second challenge, we introduce a novel Fourier measure of partial smoothing.<n>We prove upper $L2$-learning rates for KIV-O and the first $L2$-minimax lower learning rates for NPIV-O.
  arXiv  Detail & Related papers  (2025-11-24T18:42:49Z)
• Stochastic Parameter Decomposition [0.0]
  A key step in reverse engineering neural networks is to decompose them into simpler parts that can be studied in relative isolation.<n>The current main method in this framework, Attribution-based.<n>Decomposition (APD), is impractical on account of its computational cost.<n>We introduce textitStochastic.<n>Decomposition (SPD), a method that is more scalable and robust.
  arXiv  Detail & Related papers  (2025-06-25T19:26:31Z)
• Linear causal disentanglement via higher-order cumulants [0.0]
  We study the identifiability of linear causal disentanglement, assuming access to data under multiple contexts. We show that one perfect intervention on each latent variable is sufficient and in the worst case necessary to recover parameters under perfect interventions.
  arXiv  Detail & Related papers  (2024-07-05T15:53:16Z)
• PAVI: Plate-Amortized Variational Inference [55.975832957404556]
  Inference is challenging for large population studies where millions of measurements are performed over a cohort of hundreds of subjects. This large cardinality renders off-the-shelf Variational Inference (VI) computationally impractical. In this work, we design structured VI families that efficiently tackle large population studies.
  arXiv  Detail & Related papers  (2023-08-30T13:22:20Z)
• A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions [2.76240219662896]
  We introduce a new general representation framework that leverages recent results on em decompositions of multi parameter persistent homology. We establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.
  arXiv  Detail & Related papers  (2023-06-19T21:28:53Z)
• Nonparametric Identifiability of Causal Representations from Unknown Interventions [63.1354734978244]
  We study causal representation learning, the task of inferring latent causal variables and their causal relations from mixtures of the variables. Our goal is to identify both the ground truth latents and their causal graph up to a set of ambiguities which we show to be irresolvable from interventional data.
  arXiv  Detail & Related papers  (2023-06-01T10:51:58Z)
• Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding [5.854757988966379]
  We study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Our long-term causal effect estimator is obtained by combining regression residuals with short-term experimental outcomes.
  arXiv  Detail & Related papers  (2023-02-21T12:22:47Z)
• Posterior Collapse and Latent Variable Non-identifiability [54.842098835445]
  We propose a class of latent-identifiable variational autoencoders, deep generative models which enforce identifiability without sacrificing flexibility. Across synthetic and real datasets, latent-identifiable variational autoencoders outperform existing methods in mitigating posterior collapse and providing meaningful representations of the data.
  arXiv  Detail & Related papers  (2023-01-02T06:16:56Z)
• Inference on Time Series Nonparametric Conditional Moment Restrictions Using General Sieves [4.065100518793487]
  This paper considers general nonlinear sieve quasi-likelihood ratio (GN-QLR) based on expectation inferences of time series data. While the normality of the estimated functionals depends on some unknown Riesz representer of the functional space, we show that the optimally weighted GN-QLR statistic is Chi-square distributed.
  arXiv  Detail & Related papers  (2022-12-31T01:44:17Z)
• Instance-Dependent Generalization Bounds via Optimal Transport [51.71650746285469]
  Existing generalization bounds fail to explain crucial factors that drive the generalization of modern neural networks. We derive instance-dependent generalization bounds that depend on the local Lipschitz regularity of the learned prediction function in the data space. We empirically analyze our generalization bounds for neural networks, showing that the bound values are meaningful and capture the effect of popular regularization methods during training.
  arXiv  Detail & Related papers  (2022-11-02T16:39:42Z)
• Partial Identification of Treatment Effects with Implicit Generative Models [20.711877803169134]
  We propose a new method for partial identification of average treatment effects(ATEs) in general causal graphs using implicit generative models. We prove that our algorithm converges to tight bounds on ATE in linear structural causal models.
  arXiv  Detail & Related papers  (2022-10-14T22:18:00Z)
• Data-Driven Influence Functions for Optimization-Based Causal Inference [105.5385525290466]
  We study a constructive algorithm that approximates Gateaux derivatives for statistical functionals by finite differencing. We study the case where probability distributions are not known a priori but need to be estimated from data.
  arXiv  Detail & Related papers  (2022-08-29T16:16:22Z)
• Inference on Strongly Identified Functionals of Weakly Identified Functions [71.42652863687117]
  We study a novel condition for the functional to be strongly identified even when the nuisance function is not. We propose penalized minimax estimators for both the primary and debiasing nuisance functions.
  arXiv  Detail & Related papers  (2022-08-17T13:38:31Z)
• Robust and Agnostic Learning of Conditional Distributional Treatment Effects [62.44901952244514]
  The conditional average treatment effect (CATE) is the best point prediction of individual causal effects. In aggregate analyses, this is usually addressed by measuring distributional treatment effect (DTE) We provide a new robust and model-agnostic methodology for learning the conditional DTE (CDTE) for a wide class of problems.
  arXiv  Detail & Related papers  (2022-05-23T17:40:31Z)
• Equivariance Discovery by Learned Parameter-Sharing [153.41877129746223]
  We study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme.
  arXiv  Detail & Related papers  (2022-04-07T17:59:19Z)
• E-detectors: a nonparametric framework for sequential change detection [86.15115654324488]
  We develop a fundamentally new and general framework for sequential change detection. Our procedures come with clean, nonasymptotic bounds on the average run length. We show how to design their mixtures in order to achieve both statistical and computational efficiency.
  arXiv  Detail & Related papers  (2022-03-07T17:25:02Z)
• The SKIM-FA Kernel: High-Dimensional Variable Selection and Nonlinear Interaction Discovery in Linear Time [26.11563787525079]
  We show how a kernel trick can reduce computation with suitable Bayesian models to O(# covariates) time for both variable selection and estimation. Our approach outperforms existing methods used for large, high-dimensional datasets.
  arXiv  Detail & Related papers  (2021-06-23T13:53:36Z)
• Multiply Robust Causal Mediation Analysis with Continuous Treatments [12.196869756333797]
  We propose an estimator suitable for settings with continuous treatments inspired by the influence function-based estimator of Tchetgen Tchetgen and Shpitser (2012) Our proposed approach employs cross-fitting, relaxing the smoothness requirements on the nuisance functions and allowing them to be estimated at slower rates than the target parameter.
  arXiv  Detail & Related papers  (2021-05-19T16:58:57Z)
• Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach [84.29777236590674]
  We study the estimation of causal parameters when not all confounders are observed and instead negative controls are available. Recent work has shown how these can enable identification and efficient estimation via two so-called bridge functions.
  arXiv  Detail & Related papers  (2021-03-25T17:59:19Z)
• Efficient Causal Inference from Combined Observational and Interventional Data through Causal Reductions [68.6505592770171]
  Unobserved confounding is one of the main challenges when estimating causal effects. We propose a novel causal reduction method that replaces an arbitrary number of possibly high-dimensional latent confounders. We propose a learning algorithm to estimate the parameterized reduced model jointly from observational and interventional data.
  arXiv  Detail & Related papers  (2021-03-08T14:29:07Z)
• Preventing Posterior Collapse Induced by Oversmoothing in Gaussian VAE [7.845959449872641]
  We propose AR-ELBO, which controls the smoothness of the model by adapting the variance parameter. In addition, we extend VAE with alternative parameterizations on the variance parameter to deal with non-uniform or conditional data variance. The proposed VAE extensions trained with AR-ELBO show improved Fr'echet inception distance (FID) on images generated from the MNIST and CelebA datasets.
  arXiv  Detail & Related papers  (2021-02-17T10:00:49Z)
• NP-PROV: Neural Processes with Position-Relevant-Only Variances [113.20013269514327]
  We present a new member named Neural Processes with Position-Relevant-Only Variances (NP-PROV) NP-PROV hypothesizes that a target point close to a context point has small uncertainty, regardless of the function value at that position. Our evaluation on synthetic and real-world datasets reveals that NP-PROV can achieve state-of-the-art likelihood while retaining a bounded variance.
  arXiv  Detail & Related papers  (2020-06-15T06:11:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.