Predicting future states or actions of a given system remains a fundamental, yet unsolved challenge of intelligence, especially in the scope of complex and non-deterministic scenarios, such as modeling behavior of humans. Existing approaches provide results under strong assumptions concerning unimodality of future states, or, at best, assuming specific probability distributions that often poorly fit to real-life conditions. In this work we introduce a robust and flexible probabilistic framework that allows to model future predictions with virtually no constrains regarding the modality or underlying probability distribution. To achieve this goal, we leverage a hypernetwork architecture and train a continuous normalizing flow model. The resulting method dubbed RegFlow achieves state-of-the-art results on several benchmark datasets, outperforming competing approaches by a significant margin.
Efficient Regression-Based Training of Normalizing Flows for Boltzmann Generators
Mila – Québec AI Institute（魁北克AI研究所）；Université de Montréal（蒙特利尔大学）；Massachusetts Institute of Technology（麻省理工学院）；University of Oxford（牛津大学）；AITHYRA；HEC Montréal（蒙特利尔HEC）
DistPred: A Distribution-Free Probabilistic Inference Method for Regression and Forecasting
School of Information Science and Engineering, Shandong University（山东大学信息科学与工程学院）；School of Control Science and Engineering, Shandong University（山东大学控制科学与工程学院）；School of Qilu Transportation, Shandong University（山东大学齐鲁交通学院）
University of Kaiserslautern（凯泽斯劳滕大学）；German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））
Time series forecasting is one of the challenging problems for humankind. Traditional forecasting methods using mean regression models have severe shortcomings in reflecting real-world fluctuations. While new probabilistic methods rush to rescue, they fight with technical difficulties like quantile crossing or selecting a prior distribution. To meld the different strengths of these fields while avoiding their weaknesses as well as to push the boundary of the state-of-the-art, we introduce ForGAN - one step ahead probabilistic forecasting with generative adversarial networks. ForGAN utilizes th…
TabResFlow: A Normalizing Spline Flow Model for Probabilistic Univariate Tabular Regression
Information Systems and Machine Learning Lab (ISMLL), University of Hildesheim（信息系统与机器学习实验室（ISMLL）、希尔德斯海姆大学）；VWFS Data Analytics Research Center（VWFS数据分析研究中心）
TU Darmstadt（达姆施塔特工业大学）；Nanjing University of Aeronautics and Astronautics（南京航空航天大学）；Aalto University（阿尔托大学）；Centre for Cognitive Science TU Darmstadt（达姆施塔特工业大学认知科学中心）；Hessian Center for AI (hessian.AI)（黑森人工智能中心（hessian.AI））
Inspired by recent advances in the field of expert-based approximations of Gaussian processes (GPs), we present an expert-based approach to large-scale multi-output regression using single-output GP experts. Employing a deeply structured mixture of single-output GPs encoded via a probabilistic circuit allows us to capture correlations between multiple output dimensions accurately. By recursively partitioning the covariate space and the output space, posterior inference in our model reduces to inference on single-output GP experts, which only need to be conditioned on a small subset of the obse…
While deep learning-based classification is generally tackled using standardized approaches, a wide variety of techniques are employed for regression. In computer vision, one particularly popular such technique is that of confidence-based regression, which entails predicting a confidence value for each input-target pair (x,y). While this approach has demonstrated impressive results, it requires important task-dependent design choices, and the predicted confidences lack a natural probabilistic meaning. We address these issues by proposing a general and conceptually simple regression method with…
Royal Holloway, University of London（伦敦大学皇家霍洛威学院）；Massachusetts Institute of Technology（麻省理工学院）
Gaussian Processes (GPs) are widely used tools in statistics, machine learning, robotics, computer vision, and scientific computation. However, despite their popularity, they can be difficult to apply; all but the simplest classification or regression applications require specification and inference over complex covariance functions that do not admit simple analytical posteriors. This paper shows how to embed Gaussian processes in any higher-order probabilistic programming language, using an idiom based on memoization, and demonstrates its utility by implementing and extending classic and stat…
Improved probabilistic regression using diffusion models
Ludwig-Maximilians-Universität München（慕尼黑莱布尼茨大学）；Munich Center for Machine Learning (MCML)（慕尼黑机器学习中心）；University of Tromsø（特罗姆斯大学）；DLR-German Aerospace Center（德国航空航天中心）
Oilfield development related decisions are made using reservoir simulation-based optimization study in which different production scenarios and well controls are compared. Such simulations are computationally expensive and so surrogate models are used to accelerate studies. Deep learning has been used in past to generate surrogates, but such models often fail to quantify prediction uncertainty and are not interpretable. In this work, beta-VAE based regression is proposed to generate simulation surrogates for use in optimization workflow. beta-VAE enables interpretable, factorized representatio…
Quantile Regression, Variational Autoencoders, and Diffusion Models for Uncertainty Quantification: A Spatial Analysis of Sub-seasonal Wind Speed Prediction
University of California, Santa Barbara（加州大学圣巴巴拉分校）
Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed simultaneously. To this end, we propose to leverage the spatial structure of a typical oracle by constructing a statistical surrogate for the underlying logistic regression step. We investigate several non-parametric surrogates, including Binomial Gaussian Processes (B-GP), Polyno…
University of Cambridge（剑桥大学）；Universidad Autónoma de Madrid（马德里自治大学）；Harvard University（哈佛大学）
Deep Gaussian processes (DGPs) are multi-layer hierarchical generalisations of Gaussian processes (GPs) and are formally equivalent to neural networks with multiple, infinitely wide hidden layers. DGPs are nonparametric probabilistic models and as such are arguably more flexible, have a greater capacity to generalise, and provide better calibrated uncertainty estimates than alternative deep models. This paper develops a new approximate Bayesian learning scheme that enables DGPs to be applied to a range of medium to large scale regression problems for the first time. The new method uses an appr…
Gaussian Process (GP) regression is a flexible non-parametric approach to approximate complex models. In many cases, these models correspond to processes with bounded physical properties. Standard GP regression typically results in a proxy model which is unbounded for all temporal or spacial points, and thus leaves the possibility of taking on infeasible values. We propose an approach to enforce the physical constraints in a probabilistic way under the GP regression framework. In addition, this new approach reduces the variance in the resulting GP model.
Center for Computing Research（计算研究中心）；Sandia National Laboratories（桑迪亚国家实验室）；Electrical Models and Simulation（电气模型与仿真部门）；Quantitative Modeling and Analysis（定量建模与分析部门）
Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of training parameters. We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based minimization of a maximum likelihood loss. The resulting architecture provides spatial representations of both noiseless and noisy data as Gaussian mixtures with closed form expressions for variance which provides an estimator of local error. The training process yields remarkably sharp par…
Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Real-time state estimation and forecasting is critical for efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for probabilistic forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data, whereas in PhI-GPR, we compute the prior statistics by solving sto…
Infinite-dimensional spherical-radial decomposition for probabilistic functions, with application to constrained optimal control and Gaussian process regression
Courant Institute School of Mathematics, Computing and Data Science（Courant学院数学、计算与数据科学系）
University of Cambridge（剑桥大学）；University of Oxford（牛津大学）；Northeastern University（东北大学）
Existing methods for structure discovery in time series data construct interpretable, compositional kernels for Gaussian process regression models. While the learned Gaussian process model provides posterior mean and variance estimates, typically the structure is learned via a greedy optimization procedure. This restricts the space of possible solutions and leads to over-confident uncertainty estimates. We introduce a fully Bayesian approach, inferring a full posterior over structures, which more reliably captures the uncertainty of the model.
With increasing concerns of climate change, renewable resources such as photovoltaic (PV) have gained popularity as a means of energy generation. The smooth integration of such resources in power system operations is enabled by accurate forecasting mechanisms that address their inherent intermittency and variability. This paper proposes a probabilistic framework to predict short-term PV output taking into account the uncertainty of weather. To this end, we make use of datasets that comprise of power output and meteorological data such as irradiance, temperature, zenith, and azimuth. First, we …
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…
Forschungszentrum Jülich GmbH（于利希研究中心）；RWTH Aachen University（亚琛工业大学）；University of Cologne（科隆大学）；JARA-ENERGY（于利希-亚琛研究联盟能源部）
Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price in…
Direct quantile regression involves estimating a given quantile of a response variable as a function of input variables. We present a new framework for direct quantile regression where a Gaussian process model is learned, minimising the expected tilted loss function. The integration required in learning is not analytically tractable so to speed up the learning we employ the Expectation Propagation algorithm. We describe how this work relates to other quantile regression methods and apply the method on both synthetic and real data sets. The method is shown to be competitive with state of the ar…
University of Bristol（布里斯托大学）；University of Tartu（塔尔图大学）
The task of calibration is to retrospectively adjust the outputs from a machine learning model to provide better probability estimates on the target variable. While calibration has been investigated thoroughly in classification, it has not yet been well-established for regression tasks. This paper considers the problem of calibrating a probabilistic regression model to improve the estimated probability densities over the real-valued targets. We propose to calibrate a regression model through the cumulative probability density, which can be derived from calibrating a multi-class classifier. We …
Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted forests) trained on different coarsenings of the target value. By combining such classifiers and averaging the resulting densities, we are able to compute precise conditional densities with minimal assumptions on the shape or form of the density. We combine this approach with a structured cross-entropy loss function which serves to regularize and smooth the re…
Parametric quantile regressions are a useful tool for creating probabilistic energy forecasts. Nonetheless, since classical quantile regressions are trained using a non-differentiable cost function, their creation using complex data mining techniques (e.g., artificial neural networks) may be complicated. This article presents a method that uses a new nearest neighbors quantile filter to obtain quantile regressions independently of the utilized data mining technique and without the non-differentiable cost function. Thereafter, a validation of the presented method using the dataset of the Global…
Regression problems assume every instance is annotated (labeled) with a real value, a form of annotation we call \emph{strong guidance}. In order for these annotations to be accurate, they must be the result of a precise experiment or measurement. However, in some cases additional \emph{weak guidance} might be given by imprecise measurements, a domain expert or even crowd sourcing. Current formulations of regression are unable to use both types of guidance. We propose a regression framework that can also incorporate weak guidance based on relative orderings, bounds, neighboring and similarity …
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…
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）；Harvard Medical School（哈佛医学院）
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 multiparame…
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…
Multilabel classification is an important problem in a wide range of domains such as text categorization and music annotation. In this paper, we present a probabilistic model, Multilabel Logistic Regression with Hidden variables (MLRH), which extends the standard logistic regression by introducing hidden variables. Hidden variables make it possible to go beyond the conventional multiclass logistic regression by relaxing the one-hot-encoding constraint. We define a new joint distribution of labels and hidden variables which enables us to obtain one classifier for multilabel classification. Our …
Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Beijing Normal University（北京师范大学）
Uncertainty is the only certainty there is. Modeling data uncertainty is essential for regression, especially in unconstrained settings. Traditionally the direct regression formulation is considered and the uncertainty is modeled by modifying the output space to a certain family of probabilistic distributions. On the other hand, classification based regression and ranking based solutions are more popular in practice while the direct regression methods suffer from the limited performance. How to model the uncertainty within the present-day technologies for regression remains an open issue. In t…
A fully nonparametric approach for making probabilistic predictions in multi-response regression problems is introduced. Random forests are used as marginal models for each response variable and, as novel contribution of the present work, the dependence between the multiple response variables is modeled by a generative neural network. This combined modeling approach of random forests, corresponding empirical marginal residual distributions and a generative neural network is referred to as RafterNet. Multiple datasets serve as examples to demonstrate the flexibility of the approach and its impa…
UiT The Arctic University of Norway（挪威北极大学）；Kongsberg Satellite Services（康斯伯格卫星服务公司）；NORCE Norwegian Research Centre（挪威NORCE研究中心）
This paper presents a novel probabilistic forecasting method called ensemble conformalized quantile regression (EnCQR). EnCQR constructs distribution-free and approximately marginally valid prediction intervals (PIs), which are suitable for nonstationary and heteroscedastic time series data. EnCQR can be applied on top of a generic forecasting model, including deep learning architectures. EnCQR exploits a bootstrap ensemble estimator, which enables the use of conformal predictors for time series by removing the requirement of data exchangeability. The ensemble learners are implemented as gener…
Algorithmic fairness involves expressing notions such as equity, or reasonable treatment, as quantifiable measures that a machine learning algorithm can optimise. Most work in the literature to date has focused on classification problems where the prediction is categorical, such as accepting or rejecting a loan application. This is in part because classification fairness measures are easily computed by comparing the rates of outcomes, leading to behaviours such as ensuring that the same fraction of eligible men are selected as eligible women. But such measures are computationally difficult to …
Visual tracking is fundamentally the problem of regressing the state of the target in each video frame. While significant progress has been achieved, trackers are still prone to failures and inaccuracies. It is therefore crucial to represent the uncertainty in the target estimation. Although current prominent paradigms rely on estimating a state-dependent confidence score, this value lacks a clear probabilistic interpretation, complicating its use. In this work, we therefore propose a probabilistic regression formulation and apply it to tracking. Our network predicts the conditional probabilit…
