Hierarchical Gaussian Process Models for Regression Discontinuity/Kink under Sharp and Fuzzy Designs

• URL: http://arxiv.org/abs/2110.00921v1
• Date: Sun, 3 Oct 2021 04:23:56 GMT
• Title: Hierarchical Gaussian Process Models for Regression Discontinuity/Kink under Sharp and Fuzzy Designs
• Authors: Ximing Wu
• Abstract summary: We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) These estimators are extended to hierarchical GP models with an intermediate Bayesian neural network layer. Monte Carlo simulations show that our estimators perform similarly and often better than competing estimators in terms of precision, coverage and interval length.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We propose nonparametric Bayesian estimators for causal inference exploiting Regression Discontinuity/Kink (RD/RK) under sharp and fuzzy designs. Our estimators are based on Gaussian Process (GP) regression and classification. The GP methods are powerful probabilistic modeling approaches that are advantageous in terms of derivative estimation and uncertainty qualification, facilitating RK estimation and inference of RD/RK models. These estimators are extended to hierarchical GP models with an intermediate Bayesian neural network layer and can be characterized as hybrid deep learning models. Monte Carlo simulations show that our estimators perform similarly and often better than competing estimators in terms of precision, coverage and interval length. The hierarchical GP models improve upon one-layer GP models substantially. An empirical application of the proposed estimators is provided.

Related papers

• Conformal Approach To Gaussian Process Surrogate Evaluation With Coverage Guarantees [47.22930583160043]
  We propose a method for building adaptive cross-conformal prediction intervals. The resulting conformal prediction intervals exhibit a level of adaptivity akin to Bayesian credibility sets. The potential applicability of the method is demonstrated in the context of surrogate modeling of an expensive-to-evaluate simulator of the clogging phenomenon in steam generators of nuclear reactors.
  arXiv  Detail & Related papers  (2024-01-15T14:45:18Z)
• Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms [88.74308282658133]
  Reization (RP) Policy Gradient Methods (PGMs) have been widely adopted for continuous control tasks in robotics and computer graphics. Recent studies have revealed that, when applied to long-term reinforcement learning problems, model-based RP PGMs may experience chaotic and non-smooth optimization landscapes. We propose a spectral normalization method to mitigate the exploding variance issue caused by long model unrolls.
  arXiv  Detail & Related papers  (2023-10-30T18:43:21Z)
• Consensus-Adaptive RANSAC [104.87576373187426]
  We propose a new RANSAC framework that learns to explore the parameter space by considering the residuals seen so far via a novel attention layer. The attention mechanism operates on a batch of point-to-model residuals, and updates a per-point estimation state to take into account the consensus found through a lightweight one-step transformer.
  arXiv  Detail & Related papers  (2023-07-26T08:25:46Z)
• Volatility Based Kernels and Moving Average Means for Accurate Forecasting with Gaussian Processes [36.712632126776285]
  We show how to re-cast a class of volatility models as a hierarchical Gaussian process (GP) model with specialized covariance functions. Within this framework, we take inspiration from well studied domains to introduce a new class of models, Volt and Magpie, that significantly outperform baselines in stock and wind speed forecasting.
  arXiv  Detail & Related papers  (2022-07-13T23:02:54Z)
• Training Discrete Deep Generative Models via Gapped Straight-Through Estimator [72.71398034617607]
  We propose a Gapped Straight-Through ( GST) estimator to reduce the variance without incurring resampling overhead. This estimator is inspired by the essential properties of Straight-Through Gumbel-Softmax. Experiments demonstrate that the proposed GST estimator enjoys better performance compared to strong baselines on two discrete deep generative modeling tasks.
  arXiv  Detail & Related papers  (2022-06-15T01:46:05Z)
• Low-variance estimation in the Plackett-Luce model via quasi-Monte Carlo sampling [58.14878401145309]
  We develop a novel approach to producing more sample-efficient estimators of expectations in the PL model. We illustrate our findings both theoretically and empirically using real-world recommendation data from Amazon Music and the Yahoo learning-to-rank challenge.
  arXiv  Detail & Related papers  (2022-05-12T11:15:47Z)
• Approximate Bayesian inference from noisy likelihoods with Gaussian process emulated MCMC [0.24275655667345403]
  We model the log-likelihood function using a Gaussian process (GP) The main methodological innovation is to apply this model to emulate the progression that an exact Metropolis-Hastings (MH) sampler would take. The resulting approximate sampler is conceptually simple and sample-efficient.
  arXiv  Detail & Related papers  (2021-04-08T17:38:02Z)
• On MCMC for variationally sparse Gaussian processes: A pseudo-marginal approach [0.76146285961466]
  Gaussian processes (GPs) are frequently used in machine learning and statistics to construct powerful models. We propose a pseudo-marginal (PM) scheme that offers exact inference as well as computational gains through doubly estimators for the likelihood and large datasets.
  arXiv  Detail & Related papers  (2021-03-04T20:48:29Z)
• SUMO: Unbiased Estimation of Log Marginal Probability for Latent Variable Models [80.22609163316459]
  We introduce an unbiased estimator of the log marginal likelihood and its gradients for latent variable models based on randomized truncation of infinite series. We show that models trained using our estimator give better test-set likelihoods than a standard importance-sampling based approach for the same average computational cost.
  arXiv  Detail & Related papers  (2020-04-01T11:49:30Z)
• Robust Gaussian Process Regression with a Bias Model [0.6850683267295248]
  Most existing approaches replace an outlier-prone Gaussian likelihood with a non-Gaussian likelihood induced from a heavy tail distribution. The proposed approach models an outlier as a noisy and biased observation of an unknown regression function. Conditioned on the bias estimates, the robust GP regression can be reduced to a standard GP regression problem.
  arXiv  Detail & Related papers  (2020-01-14T06:21:51Z)

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.