Bayesian Nonlinear Regression using Sums of Simple Functions

• URL: http://arxiv.org/abs/2312.01881v1
• Date: Mon, 4 Dec 2023 13:24:46 GMT
• Title: Bayesian Nonlinear Regression using Sums of Simple Functions
• Abstract summary: This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. In simulations, we show that our approach produces accurate point and density forecasts.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: This paper proposes a new Bayesian machine learning model that can be applied to large datasets arising in macroeconomics. Our framework sums over many simple two-component location mixtures. The transition between components is determined by a logistic function that depends on a single threshold variable and two hyperparameters. Each of these individual models only accounts for a minor portion of the variation in the endogenous variables. But many of them are capable of capturing arbitrary nonlinear conditional mean relations. Conjugate priors enable fast and efficient inference. In simulations, we show that our approach produces accurate point and density forecasts. In a real-data exercise, we forecast US macroeconomic aggregates and consider the nonlinear effects of financial shocks in a large-scale nonlinear VAR.

Related papers

• Scalable Learning of Multivariate Distributions via Coresets [48.02318786960811]
  We develop a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency.<n>Our approach yields substantial data reduction via importance sampling.<n>Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability.
  arXiv  Detail & Related papers  (2026-03-20T09:28:43Z)
• Variational Hierarchical Mixtures for Probabilistic Learning of Inverse Dynamics [20.953728061894044]
  Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. We consider a probabilistic hierarchical modeling paradigm that combines the benefits of both worlds to deliver computationally efficient representations with inherent complexity regularization. We derive two efficient variational inference techniques to learn these representations and highlight the advantages of hierarchical infinite local regression models.
  arXiv  Detail & Related papers  (2022-11-02T13:54:07Z)
• FeDXL: Provable Federated Learning for Deep X-Risk Optimization [105.17383135458897]
  We tackle a novel federated learning (FL) problem for optimizing a family of X-risks, to which no existing algorithms are applicable. The challenges for designing an FL algorithm for X-risks lie in the non-decomability of the objective over multiple machines and the interdependency between different machines.
  arXiv  Detail & Related papers  (2022-10-26T00:23:36Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Easy Differentially Private Linear Regression [16.325734286930764]
  We study an algorithm which uses the exponential mechanism to select a model with high Tukey depth from a collection of non-private regression models. We find that this algorithm obtains strong empirical performance in the data-rich setting.
  arXiv  Detail & Related papers  (2022-08-15T17:42:27Z)
• Variational Inference for Bayesian Bridge Regression [0.0]
  We study the implementation of Automatic Differentiation Variational inference (ADVI) for Bayesian inference on regression models with bridge penalization. The bridge approach uses $ell_alpha$ norm, with $alpha in (0, +infty)$ to define a penalization on large values of the regression coefficients. We illustrate the approach on non-parametric regression models with B-splines, although the method works seamlessly for other choices of basis functions.
  arXiv  Detail & Related papers  (2022-05-19T12:29:09Z)
• Bias-variance decomposition of overparameterized regression with random linear features [0.0]
  "Over parameterized models" avoid overfitting even when the number of fit parameters is large enough to perfectly fit the training data. We show how each transition arises due to small nonzero eigenvalues in the Hessian matrix. We compare and contrast the phase diagram of the random linear features model to the random nonlinear features model and ordinary regression.
  arXiv  Detail & Related papers  (2022-03-10T16:09:21Z)
• Multivariate Probabilistic Regression with Natural Gradient Boosting [63.58097881421937]
  We propose a Natural Gradient Boosting (NGBoost) approach based on nonparametrically modeling the conditional parameters of the multivariate predictive distribution. Our method is robust, works out-of-the-box without extensive tuning, is modular with respect to the assumed target distribution, and performs competitively in comparison to existing approaches.
  arXiv  Detail & Related papers  (2021-06-07T17:44:49Z)
• Flexible Model Aggregation for Quantile Regression [92.63075261170302]
  Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions. We investigate methods for aggregating any number of conditional quantile models. All of the models we consider in this paper can be fit using modern deep learning toolkits.
  arXiv  Detail & Related papers  (2021-02-26T23:21:16Z)
• A Hypergradient Approach to Robust Regression without Correspondence [85.49775273716503]
  We consider a variant of regression problem, where the correspondence between input and output data is not available. Most existing methods are only applicable when the sample size is small. We propose a new computational framework -- ROBOT -- for the shuffled regression problem.
  arXiv  Detail & Related papers  (2020-11-30T21:47:38Z)
• Piecewise Linear Regression via a Difference of Convex Functions [50.89452535187813]
  We present a new piecewise linear regression methodology that utilizes fitting a difference of convex functions (DC functions) to the data. We empirically validate the method, showing it to be practically implementable, and to have comparable performance to existing regression/classification methods on real-world datasets.
  arXiv  Detail & Related papers  (2020-07-05T18:58:47Z)
• Flexible Bayesian Nonlinear Model Configuration [10.865434331546126]
  Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. We introduce a flexible approach for the construction and selection of highly flexible nonlinear parametric regression models. A genetically modified mode jumping chain Monte Carlo algorithm is adopted to perform Bayesian inference.
  arXiv  Detail & Related papers  (2020-03-05T21:20:55Z)

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.