Inference with Mondrian Random Forests

• URL: http://arxiv.org/abs/2310.09702v2
• Date: Tue, 27 Aug 2024 11:12:12 GMT
• Title: Inference with Mondrian Random Forests
• Authors: Matias D. Cattaneo, Jason M. Klusowski, William G. Underwood,
• Abstract summary: We give precise bias and variance characterizations, along with a Berry-Esseen-type central limit theorem, for the Mondrian random forest regression estimator. We present valid statistical inference methods for the unknown regression function. Efficient and implementable algorithms are devised for both batch and online learning settings.
• Score: 6.97762648094816
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Random forests are popular methods for regression and classification analysis, and many different variants have been proposed in recent years. One interesting example is the Mondrian random forest, in which the underlying constituent trees are constructed via a Mondrian process. We give precise bias and variance characterizations, along with a Berry-Esseen-type central limit theorem, for the Mondrian random forest regression estimator. By combining these results with a carefully crafted debiasing approach and an accurate variance estimator, we present valid statistical inference methods for the unknown regression function. These methods come with explicitly characterized error bounds in terms of the sample size, tree complexity parameter, and number of trees in the forest, and include coverage error rates for feasible confidence interval estimators. Our novel debiasing procedure for the Mondrian random forest also allows it to achieve the minimax-optimal point estimation convergence rate in mean squared error for multivariate $\beta$-H\"older regression functions, for all $\beta > 0$, provided that the underlying tuning parameters are chosen appropriately. Efficient and implementable algorithms are devised for both batch and online learning settings, and we carefully study the computational complexity of different Mondrian random forest implementations. Finally, simulations with synthetic data validate our theory and methodology, demonstrating their excellent finite-sample properties.

Related papers

• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• Relaxed Quantile Regression: Prediction Intervals for Asymmetric Noise [51.87307904567702]
  Quantile regression is a leading approach for obtaining such intervals via the empirical estimation of quantiles in the distribution of outputs. We propose Relaxed Quantile Regression (RQR), a direct alternative to quantile regression based interval construction that removes this arbitrary constraint. We demonstrate that this added flexibility results in intervals with an improvement in desirable qualities.
  arXiv  Detail & Related papers  (2024-06-05T13:36:38Z)
• Adaptive Split Balancing for Optimal Random Forest [8.916614661563893]
  We propose a new random forest algorithm that constructs the trees using a novel adaptive split-balancing method. Our method achieves optimality in simple, smooth scenarios while adaptively learning the tree structure from the data.
  arXiv  Detail & Related papers  (2024-02-17T09:10:40Z)
• Distributional Adaptive Soft Regression Trees [0.0]
  This article proposes a new type of a distributional regression tree using a multivariate soft split rule. One great advantage of the soft split is that smooth high-dimensional functions can be estimated with only one tree. We show by means of extensive simulation studies that the algorithm has excellent properties and outperforms various benchmark methods.
  arXiv  Detail & Related papers  (2022-10-19T08:59:02Z)
• On Variance Estimation of Random Forests [0.0]
  This paper develops an unbiased variance estimator based on incomplete U-statistics. We show that our estimators enjoy lower bias and more accurate confidence interval coverage without additional computational costs.
  arXiv  Detail & Related papers  (2022-02-18T03:35:47Z)
• Minimax Rates for High-Dimensional Random Tessellation Forests [0.0]
  Mondrian forests is the first class of random forests for which minimax rates were obtained in arbitrary dimension. We show that a large class of random forests with general split directions also achieve minimax optimal convergence rates in arbitrary dimension.
  arXiv  Detail & Related papers  (2021-09-22T06:47:38Z)
• Near-optimal inference in adaptive linear regression [60.08422051718195]
  Even simple methods like least squares can exhibit non-normal behavior when data is collected in an adaptive manner. We propose a family of online debiasing estimators to correct these distributional anomalies in at least squares estimation. We demonstrate the usefulness of our theory via applications to multi-armed bandit, autoregressive time series estimation, and active learning with exploration.
  arXiv  Detail & Related papers  (2021-07-05T21:05:11Z)
• 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)
• Probabilistic Gradient Boosting Machines for Large-Scale Probabilistic Regression [51.770998056563094]
  Probabilistic Gradient Boosting Machines (PGBM) is a method to create probabilistic predictions with a single ensemble of decision trees. We empirically demonstrate the advantages of PGBM compared to existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-03T08:32:13Z)
• Achieving Reliable Causal Inference with Data-Mined Variables: A Random Forest Approach to the Measurement Error Problem [1.5749416770494704]
  A common empirical strategy involves the application of predictive modeling techniques to'mine' variables of interest from available data. Recent work highlights that, because the predictions from machine learning models are inevitably imperfect, econometric analyses based on the predicted variables are likely to suffer from bias due to measurement error. We propose a novel approach to mitigate these biases, leveraging the ensemble learning technique known as the random forest.
  arXiv  Detail & Related papers  (2020-12-19T21:48:23Z)
• Censored Quantile Regression Forest [81.9098291337097]
  We develop a new estimating equation that adapts to censoring and leads to quantile score whenever the data do not exhibit censoring. The proposed procedure named it censored quantile regression forest, allows us to estimate quantiles of time-to-event without any parametric modeling assumption.
  arXiv  Detail & Related papers  (2020-01-08T23:20:23Z)

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.