We present Natural Gradient Boosting (NGBoost), an algorithm for generic probabilistic prediction via gradient boosting. Typical regression models return a point estimate, conditional on covariates, but probabilistic regression models output a full probability distribution over the outcome space, conditional on the covariates. This allows for predictive uncertainty estimation -- crucial in applications like healthcare and weather forecasting. NGBoost generalizes gradient boosting to probabilistic regression by treating the parameters of the conditional distribution as targets for a multiparameter boosting algorithm. Furthermore, we show how the Natural Gradient is required to correct the training dynamics of our multiparameter boosting approach. NGBoost can be used with any base learner, any family of distributions with continuous parameters, and any scoring rule. NGBoost matches or exceeds the performance of existing methods for probabilistic prediction while offering additional benefits in flexibility, scalability, and usability. An open-source implementation is available at github.com/stanfordmlgroup/ngboost.
The University of California, San Diego（加州大学圣地亚哥分校）
Natural gradient has been recently introduced to the field of boosting to enable the generic probabilistic predication capability. Natural gradient boosting shows promising performance improvements on small datasets due to better training dynamics, but it suffers from slow training speed overhead especially for large datasets. We present a replication study of NGBoost(Duan et al., 2019) training that carefully examines the impacts of key hyper-parameters under the circumstance of best-first decision tree learning. We find that with the regularization of leaf number clipping, the performance of…
STOR-i Centre for Doctoral Training（STOR-i博士培训中心）；Lancaster University（兰卡斯特大学）；Stanford University（斯坦福大学）
Many single-target regression problems require estimates of uncertainty along with the point predictions. Probabilistic regression algorithms are well-suited for these tasks. However, the options are much more limited when the prediction target is multivariate and a joint measure of uncertainty is required. For example, in predicting a 2D velocity vector a joint uncertainty would quantify the probability of any vector in the plane, which would be more expressive than two separate uncertainties on the x- and y- components. To enable joint probabilistic regression, we propose a Natural Gradient …
Stanford University（斯坦福大学）；Open Climate Fix（开放气候修复）；National Center for Atmospheric Research（美国国家大气研究中心）
Advancing probabilistic solar forecasting methods is essential to supporting the integration of solar energy into the electricity grid. In this work, we develop a variety of state-of-the-art probabilistic models for forecasting solar irradiance. We investigate the use of post-hoc calibration techniques for ensuring well-calibrated probabilistic predictions. We train and evaluate the models using public data from seven stations in the SURFRAD network, and demonstrate that the best model, NGBoost, achieves higher performance at an intra-hourly resolution than the best benchmark solar irradiance …
Gradient Boosting Machines (GBM) are hugely popular for solving tabular data problems. However, practitioners are not only interested in point predictions, but also in probabilistic predictions in order to quantify the uncertainty of the predictions. Creating such probabilistic predictions is difficult with existing GBM-based solutions: they either require training multiple models or they become too computationally expensive to be useful for large-scale settings. We propose Probabilistic Gradient Boosting Machines (PGBM), a method to create probabilistic predictions with a single ensemble of d…
Solar energy is a clean and renewable energy. Photovoltaic (PV) power is an important way to utilize solar energy. Accurate PV power forecast is crucial to the large-scale application of PV power and the stability of electricity grid. This paper proposes a novel method for short-term photovoltaic power forecast using deep convolutional long short-term memory (ConvLSTM) network and kernel density estimation (KDE). In the proposed method, ConvLSTM is used to forecast the future photovoltaic power and KDE is used for estimating the joint probabilistic density function and giving the probabilistic…
University of Bristol（布里斯托尔大学）；University of Manchester（曼彻斯特大学）
In this paper, we derive a novel probabilistic model of boosting as a Product of Experts. We re-derive the boosting algorithm as a greedy incremental model selection procedure which ensures that addition of new experts to the ensemble does not decrease the likelihood of the data. These learning rules lead to a generic boosting algorithm - POE- Boost which turns out to be similar to the AdaBoost algorithm under certain assumptions on the expert probabilities. The paper then extends the POEBoost algorithm to POEBoost.CS which handles hypothesis that produce probabilistic predictions. This new al…
We present a theory of boosting probabilistic classifiers. We place ourselves in the situation of a user who only provides a stopping parameter and a probabilistic weak learner/classifier and compare three types of boosting algorithms: probabilistic Adaboost, decision tree, and tree of trees of ... of trees, which we call matryoshka. "Nested tree," "embedded tree" and "recursive tree" are also appropriate names for this algorithm, which is one of our contributions. Our other contribution is the theoretical analysis of the algorithms, in which we give training error bounds. This analysis sugges…
We present a unified probabilistic gradient boosting framework for regression tasks that models and predicts the entire conditional distribution of a univariate response variable as a function of covariates. Our likelihood-based approach allows us to either model all conditional moments of a parametric distribution, or to approximate the conditional cumulative distribution function via Normalizing Flows. As underlying computational backbones, our framework is based on XGBoost and LightGBM. Modelling and predicting the entire conditional distribution greatly enhances existing tree-based gradien…
Institute of Combustion and Power Plant Technology, University of Stuttgart（斯图加特大学燃烧与发电厂技术研究所）
PV power forecasting models are predominantly based on machine learning algorithms which do not provide any insight into or explanation about their predictions (black boxes). Therefore, their direct implementation in environments where transparency is required, and the trust associated with their predictions may be questioned. To this end, we propose a two stage probabilistic forecasting framework able to generate highly accurate, reliable, and sharp forecasts yet offering full transparency on both the point forecasts and the prediction intervals (PIs). In the first stage, we exploit natural g…
Unlike previous studies on mixture distributions, a bagging and boosting based convexly combined mixture probabilistic model has been suggested. This model is a result of iteratively searching for obtaining the optimum probabilistic model that provides the maximum p value.
Yandex；HSE University（高等经济大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
For many practical, high-risk applications, it is essential to quantify uncertainty in a model's predictions to avoid costly mistakes. While predictive uncertainty is widely studied for neural networks, the topic seems to be under-explored for models based on gradient boosting. However, gradient boosting often achieves state-of-the-art results on tabular data. This work examines a probabilistic ensemble-based framework for deriving uncertainty estimates in the predictions of gradient boosting classification and regression models. We conducted experiments on a range of synthetic and real datase…
Multivariate Forecasting of Bitcoin Volatility with Gradient Boosting: Deterministic, Probabilistic, and Feature Importance Perspectives
Faculty of Electrical Engineering, Czestochowa University of Technology（电子工程学院，捷斯托霍瓦技术大学）；Faculty of Computer Science and Artificial Intelligence, Czestochowa University of Technology（计算机科学与人工智能学院，捷斯托霍瓦技术大学）
In this study, we utilize Gaussian processes, probabilistic neural network, natural gradient boosting, and quantile regression augmented gradient boosting to model lead times of laser manufacturing processes. We introduce probabilistic modelling in the domain and compare the models in terms of different abilities. While providing a comparison between the models in real-life data, our work has many use cases and substantial business value. Our results indicate that all of the models beat the company estimation benchmark that uses domain experience and have good calibration with the empirical fr…
University of Patras（帕特雷大学）；Roma Tre University（罗马第三大学）；National Technical University of Athens（雅典国立技术大学）
Machine and statistical learning algorithms can be reliably automated and applied at scale. Therefore, they can constitute a considerable asset for designing practical forecasting systems, such as those related to urban water demand. Quantile regression algorithms are statistical and machine learning algorithms that can provide probabilistic forecasts in a straightforward way, and have not been applied so far for urban water demand forecasting. In this work, we aim to fill this gap by automating and extensively comparing several quantile-regression-based practical systems for probabilistic one…
Gradient Boosting (GB) is a popular methodology used to solve prediction problems by minimizing a differentiable loss function, $L$. GB performs very well on tabular machine learning (ML) problems; however, as a pure ML solver it lacks the ability to fit models with probabilistic but correlated multi-dimensional outputs, for example, multiple correlated Bernoulli outputs. GB also does not form intermediate abstract data embeddings, one property of Deep Learning that gives greater flexibility and performance on other types of problems. This paper presents a simple adjustment to GB motivated in …
University of Technology, Sydney（悉尼科技大学）；University of Canberra（堪培拉大学）；International University, HCMC（胡志明市国际大学）
This article applies Machine Learning techniques to solve Intrusion Detection problems within computer networks. Due to complex and dynamic nature of computer networks and hacking techniques, detecting malicious activities remains a challenging task for security experts, that is, currently available defense systems suffer from low detection capability and high number of false alarms. To overcome such performance limitations, we propose a novel Machine Learning algorithm, namely Boosted Subspace Probabilistic Neural Network (BSPNN), which integrates an adaptive boosting technique and a semi par…
Budapest University of Technology and Economics（布达佩斯技术与经济大学）
Energy price forecasting is a relevant yet hard task in the field of multi-step time series forecasting. In this paper we compare a well-known and established method, ARMA with exogenous variables with a relatively new technique Gradient Boosting Regression. The method was tested on data from Global Energy Forecasting Competition 2014 with a year long rolling window forecast. The results from the experiment reveal that a multi-model approach is significantly better performing in terms of error metrics. Gradient Boosting can deal with seasonality and auto-correlation out-of-the box and achieve …
Uniform convergence of the smooth calibration error and its relationship with functional gradient
The University of Osaka / RIKEN AIP, Japan（大阪大学 / RIKEN AIP，日本）；CFAR and IHPC, Agency for Science, Technology and Research (A*STAR), Singapore（CFAR 和 IHPC，新加坡科技研究局（A*STAR））；College of Computing and Data Science, Nanyang Technological University, Singapore（南洋理工大学计算机与数据科学学院，新加坡）
Lucerne University of Applied Sciences and Arts（卢塞恩应用科学与艺术大学）
Latent Gaussian models and boosting are widely used techniques in statistics and machine learning. Tree-boosting shows excellent prediction accuracy on many data sets, but potential drawbacks are that it assumes conditional independence of samples, produces discontinuous predictions for, e.g., spatial data, and it can have difficulty with high-cardinality categorical variables. Latent Gaussian models, such as Gaussian process and grouped random effects models, are flexible prior models which explicitly model dependence among samples and which allow for efficient learning of predictor functions…
Microsoft Research NYC（微软研究院纽约中心）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Institute for Advanced Study（高等研究院）
We give the first statistical-query lower bounds for agnostically learning any non-polynomial activation with respect to Gaussian marginals (e.g., ReLU, sigmoid, sign). For the specific problem of ReLU regression (equivalently, agnostically learning a ReLU), we show that any statistical-query algorithm with tolerance $n^{-(1/ε)^b}$ must use at least $2^{n^c} ε$ queries for some constant $b, c > 0$, where $n$ is the dimension and $ε$ is the accuracy parameter. Our results rule out general (as opposed to correlational) SQ learning algorithms, which is unusual for real-valued learning problems. O…
Current implementations of Gradient Boosting Machines are mostly designed for single-target regression tasks and commonly assume independence between responses when used in multivariate settings. As such, these models are not well suited if non-negligible dependencies exist between targets. To overcome this limitation, we present an extension of XGBoostLSS that models multiple targets and their dependencies in a probabilistic regression setting. Empirical results show that our approach outperforms existing GBMs with respect to runtime and compares well in terms of accuracy.
University College London（伦敦大学学院）；University of Warwick（华威大学）；University of Oxford（牛津大学）
Predictive modelling and supervised learning are central to modern data science. With predictions from an ever-expanding number of supervised black-box strategies - e.g., kernel methods, random forests, deep learning aka neural networks - being employed as a basis for decision making processes, it is crucial to understand the statistical uncertainty associated with these predictions. As a general means to approach the issue, we present an overarching framework for black-box prediction strategies that not only predict the target but also their own predictions' uncertainty. Moreover, the framewo…
Probabilistic indirect models for undrained shear strength: addressing significant data missing and variability with advanced imputation and machine learning techniques
