In recent years, impressive progress has been made in the design of implicit probabilistic models via Generative Adversarial Networks (GAN) and its extension, the Conditional GAN (CGAN). Excellent solutions have been demonstrated mostly in image processing applications which involve large, continuous output spaces. There is almost no application of these powerful tools to problems having small dimensional output spaces. Regression problems involving the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$, with $m$ small (e.g., $m=1$ or just a few) is one good case in point. The standard approach to solve regression problems is to probabilistically model the output $y$ as the sum of a mean function $m(x)$ and a noise term $z$; it is also usual to take the noise to be a Gaussian. These are done for convenience sake so that the likelihood of observed data is expressible in closed form. In the real world, on the other hand, stochasticity of the output is usually caused by missing or noisy input variables. Such a real world situation is best represented using an implicit model in which an extra noise vector, $z$ is included with $x$ as input. CGAN is naturally suited to design such implicit models. This paper makes the first step in this direction and compares the existing regression methods with CGAN.
We notice however, that the existing methods like mixture density networks (MDN) and XGBoost do quite well compared to CGAN in terms of likelihood and mean absolute error, respectively. Both these methods are comparatively easier to train than CGANs. CGANs need more innovation to have a comparable modeling and ease-of-training with respect to the existing regression solvers. In summary, for modeling uncertainty MDNs are better while XGBoost is better for the cases where accurate prediction is more important.
SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；University of Neuchâtel（纳沙泰尔大学）
Adversarial Regression is a proposition to perform high dimensional non-linear regression with uncertainty estimation. We used Conditional Generative Adversarial Network to obtain an estimate of the full predictive distribution for a new observation. Generative Adversarial Networks (GAN) are implicit generative models which produce samples from a distribution approximating the distribution of the data. The conditional version of it (CGAN) takes the following expression: $\min\limits_G \max\limits_D V(D, G) = \mathbb{E}_{x\sim p_{r}(x)} [log(D(x, y))] + \mathbb{E}_{z\sim p_{z}(z)} [log (1-D(G(z…
University of Guelph（圭尔夫大学）；Vector Institute（向量研究所）；Facebook AI Research（Facebook人工智能研究）
Conditional Generative Adversarial Networks (cGANs) are finding increasingly widespread use in many application domains. Despite outstanding progress, quantitative evaluation of such models often involves multiple distinct metrics to assess different desirable properties, such as image quality, conditional consistency, and intra-conditioning diversity. In this setting, model benchmarking becomes a challenge, as each metric may indicate a different "best" model. In this paper, we propose the Frechet Joint Distance (FJD), which is defined as the Frechet distance between joint distributions of im…
Conditional generative adversarial networks (cGAN) have led to large improvements in the task of conditional image generation, which lies at the heart of computer vision. The major focus so far has been on performance improvement, while there has been little effort in making cGAN more robust to noise. The regression (of the generator) might lead to arbitrarily large errors in the output, which makes cGAN unreliable for real-world applications. In this work, we introduce a novel conditional GAN model, called RoCGAN, which leverages structure in the target space of the model to address the issue…
The neural linear model is a simple adaptive Bayesian linear regression method that has recently been used in a number of problems ranging from Bayesian optimization to reinforcement learning. Despite its apparent successes in these settings, to the best of our knowledge there has been no systematic exploration of its capabilities on simple regression tasks. In this work we characterize these on the UCI datasets, a popular benchmark for Bayesian regression models, as well as on the recently introduced UCI "gap" datasets, which are better tests of out-of-distribution uncertainty. We demonstrate…
UiT The Arctic University of Norway（挪威北极大学）；KSAT Kongsberg Satellite Services（康斯伯格卫星服务公司）；NORCE Norwegian Research Centre（挪威NORCE研究中心）；Norwegian University of Life Sciences（挪威生命科学大学）；Sokoine University of Agriculture（索科因农业大学）
This study derives regression models for above-ground biomass (AGB) estimation in miombo woodlands of Tanzania that utilise the high availability and low cost of Sentinel-1 data. The limited forest canopy penetration of C-band SAR sensors along with the sparseness of available ground truth restrict their usefulness in traditional AGB regression models. Therefore, we propose to use AGB predictions based on airborne laser scanning (ALS) data as a surrogate response variable for SAR data. This dramatically increases the available training data and opens for flexible regression models that capture…
Conventional predictive Artificial Neural Networks (ANNs) commonly employ deterministic weight matrices; therefore, their prediction is a point estimate. Such a deterministic nature in ANNs causes the limitations of using ANNs for medical diagnosis, law problems, and portfolio management, in which discovering not only the prediction but also the uncertainty of the prediction is essentially required. To address such a problem, we propose a predictive probabilistic neural network model, which corresponds to a different manner of using the generator in conditional Generative Adversarial Network (…
AutoML serves as the bridge between varying levels of expertise when designing machine learning systems and expedites the data science process. A wide range of techniques is taken to address this, however there does not exist an objective comparison of these techniques. We present a benchmark of current open source AutoML solutions using open source datasets. We test auto-sklearn, TPOT, auto_ml, and H2O's AutoML solution against a compiled set of regression and classification datasets sourced from OpenML and find that auto-sklearn performs the best across classification datasets and TPOT perfo…
Generative Nowcasting of Marine Fog Visibility in the Grand Banks area and Sable Island in Canada
Southern Illinois University Edwardsville（南伊利诺伊大学爱德华兹维尔分校）；University of Notre Dame（圣母大学）；NOAA（美国国家海洋和大气管理局）；University of North Florida（北佛罗里达大学）；University of North Dakota（北达科他大学）；Ontario Tech University（安大略理工大学）
Imperial College London（帝国理工学院）；The Alan Turing Institute（阿兰·图灵研究所）
In chemical process engineering, surrogate models of complex systems are often necessary for tasks of domain exploration, sensitivity analysis of the design parameters, and optimization. A suite of computational fluid dynamics (CFD) simulations geared toward chemical process equipment modeling has been developed and validated with experimental results from the literature. Various regression-based active learning strategies are explored with these CFD simulators in-the-loop under the constraints of a limited function evaluation budget. Specifically, five different sampling strategies and five r…
Generative Adversarial Networks (GANs) are well-known tools for data generation and semi-supervised classification. GANs, with less labeled data, outperform Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) in classification across various tasks, this shows promise for developing GANs capable of trespassing into the domain of semi-supervised regression. However, developing GANs for regression introduce two major challenges: (1) inherent instability in the GAN formulation and (2) performing regression and achieving stability simultaneously. This paper introduces techniques th…
University of Electronic Science and Technology of China（电子科技大学）；Macau University of Science and Technology（澳门科技大学）
Nonlinear sparse data regression and generation have been a long-term challenge, to cite the flow field reconstruction as a typical example. The huge computational cost of computational fluid dynamics (CFD) makes it much expensive for large scale CFD data producing, which is the reason why we need some cheaper ways to do this, of which the traditional reduced order models (ROMs) were promising but they couldn't generate a large number of full domain flow field data (FFD) to realize high-precision flow field reconstructions. Motivated by the problems of existing approaches and inspired by the s…
University of Minnesota（明尼苏达大学）；Virginia Tech（弗吉尼亚理工大学）；Criteo AI Lab（Criteo人工智能实验室）；LinkedIn Corporation（领英公司）
This paper addresses the classic problem of regression, which involves the inductive learning of a map, $y=f(x,z)$, $z$ denoting noise, $f:\mathbb{R}^n\times \mathbb{R}^k \rightarrow \mathbb{R}^m$. Recently, Conditional GAN (CGAN) has been applied for regression and has shown to be advantageous over the other standard approaches like Gaussian Process Regression, given its ability to implicitly model complex noise forms. However, the current CGAN implementation for regression uses the classical generator-discriminator architecture with the minimax optimization approach, which is notorious for b…
University of Chicago（芝加哥大学）；University of Toronto（多伦多大学）；Vector Institute（矢量研究所）
While uncertainty estimation is a well-studied topic in deep learning, most such work focuses on marginal uncertainty estimates, i.e. the predictive mean and variance at individual input locations. But it is often more useful to estimate predictive correlations between the function values at different input locations. In this paper, we consider the problem of benchmarking how accurately Bayesian models can estimate predictive correlations. We first consider a downstream task which depends on posterior predictive correlations: transductive active learning (TAL). We find that TAL makes better us…
Berkeley Education Alliance for Research in Singapore（新加坡伯克利教育研究联盟）；University of California, Berkeley（加州大学伯克利分校）；National University of Singapore（新加坡国立大学）
Building energy performance benchmarking has been adopted widely in the USA and Canada through the Energy Star Portfolio Manager platform. Building operations and energy management professionals have long used a simple 1-100 score to understand how their building compares to its peers. This single number is easy to use, but is created by inaccurate linear regression (MLR) models. This paper proposes a methodology that enhances the existing Energy Star calculation method by increasing accuracy and providing additional model output processing to help explain why a building is achieving a certain…
We consider the use of automated supervised learning systems for data tables that not only contain numeric/categorical columns, but one or more text fields as well. Here we assemble 18 multimodal data tables that each contain some text fields and stem from a real business application. Our publicly-available benchmark enables researchers to comprehensively evaluate their own methods for supervised learning with numeric, categorical, and text features. To ensure that any single modeling strategy which performs well over all 18 datasets will serve as a practical foundation for multimodal text/tab…
Growing competitiveness and increasing availability of data is generating tremendous interest in data-driven analytics across industries. In the retail sector, stores need targeted guidance to improve both the efficiency and effectiveness of individual stores based on their specific locations, demographics, and environment. We propose an effective data-driven framework for internal benchmarking that can lead to targeted guidance for individual stores. In particular, we propose an objective method for segmenting stores using a model-based clustering technique that accounts for similarity in sto…
University of Freiburg（弗莱堡大学）；University of British Columbia（不列颠哥伦比亚大学）
The optimization of algorithm (hyper-)parameters is crucial for achieving peak performance across a wide range of domains, ranging from deep neural networks to solvers for hard combinatorial problems. The resulting algorithm configuration (AC) problem has attracted much attention from the machine learning community. However, the proper evaluation of new AC procedures is hindered by two key hurdles. First, AC benchmarks are hard to set up. Second and even more significantly, they are computationally expensive: a single run of an AC procedure involves many costly runs of the target algorithm who…
Linear-LLM-SCM: Benchmarking LLMs for Coefficient Elicitation in Linear-Gaussian Causal Models
Data Science and its Applications, German Research Centre for Artificial Intelligence (DFKI)（德国人工智能研究中心数据科学与应用部门）；Dept. of Computer Science, University of Kaiserslautern–Landau (RPTU)（科隆-兰道大学计算机科学系）；Digital Health - Machine Learning Research Group, Hasso Plattner Institute for Digital Engineering（哈索·普朗纳研究所数字工程学院数字健康-机器学习研究组）；Institute of Informatics, University of Munich (LMU)（慕尼黑大学信息学院）；Hasso Plattner Institute for Digital Health at Mount Sinai, Icahn School of Medicine at Mount Sinai（西奈山医学院哈索·普朗纳研究所数字健康中心）；Munich Center for Machine Learning (MCML), Germany（慕尼黑机器学习中心）
We propose a framework for the assessment of uncertainty quantification in deep regression. The framework is based on regression problems where the regression function is a linear combination of nonlinear functions. Basically, any level of complexity can be realized through the choice of the nonlinear functions and the dimensionality of their domain. Results of an uncertainty quantification for deep regression are compared against those obtained by a statistical reference method. The reference method utilizes knowledge of the underlying nonlinear functions and is based on a Bayesian linear reg…
Singapore University of Technology and Design（新加坡科技设计大学）；Building and Construction Authority Academy（建设局学院）
Air conditioning (AC) accounts for a critical portion of the global energy consumption. To improve its energy performance, it is important to fairly benchmark its energy performance and provide the evaluation feedback to users. However, this task has not been well tackled in the residential sector. In this paper, we propose a data-driven approach to fairly benchmark the AC energy performance of residential rooms. First, regression model is built for each benchmarked room so that its power consumption can be predicted given different weather conditions and AC settings. Then, all the rooms are c…
In this paper we provide a broad benchmarking of recent genetic programming approaches to symbolic regression in the context of state of the art machine learning approaches. We use a set of nearly 100 regression benchmark problems culled from open source repositories across the web. We conduct a rigorous benchmarking of four recent symbolic regression approaches as well as nine machine learning approaches from scikit-learn. The results suggest that symbolic regression performs strongly compared to state-of-the-art gradient boosting algorithms, although in terms of running times is among the sl…
Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression
Department of Statistics, Federal University of São Carlos (UFSCar)（圣卡洛斯联邦大学统计系）；Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK（格勒诺布尔阿尔卑斯大学、法国国家信息与自动化研究所、法国国家科学研究中心、格勒诺布尔国立理工学院、让·库尔坦数学实验室）
Due to the growing adoption of deep neural networks in many fields of science and engineering, modeling and estimating their uncertainties has become of primary importance. Despite the growing literature about uncertainty quantification in deep learning, the quality of the uncertainty estimates remains an open question. In this work, we assess for the first time the performance of several approximation methods for Bayesian neural networks on regression tasks by evaluating the quality of the confidence regions with several coverage metrics. The selected algorithms are also compared in terms of …
Monash University（莫纳什大学）；University of East Anglia（东英吉利大学）；University of California Riverside（加州大学河滨分校）
Time series research has gathered lots of interests in the last decade, especially for Time Series Classification (TSC) and Time Series Forecasting (TSF). Research in TSC has greatly benefited from the University of California Riverside and University of East Anglia (UCR/UEA) Time Series Archives. On the other hand, the advancement in Time Series Forecasting relies on time series forecasting competitions such as the Makridakis competitions, NN3 and NN5 Neural Network competitions, and a few Kaggle competitions. Each year, thousands of papers proposing new algorithms for TSC and TSF have utiliz…
Time series classification problems have drawn increasing attention in the machine learning and statistical community. Closely related is the field of functional data analysis (FDA): it refers to the range of problems that deal with the analysis of data that is continuously indexed over some domain. While often employing different methods, both fields strive to answer similar questions, a common example being classification or regression problems with functional covariates. We study methods from functional data analysis, such as functional generalized additive models, as well as functionality …
This paper proposes a data and Machine Learning-based forecasting solution for the Telecommunications network-rollout planning problem. Milestone completion-time estimation is crucial to network-rollout planning; accurate estimates enable better crew utilisation and optimised cost of materials and logistics. Using historical data of milestone completion times, a model needs to incorporate domain knowledge, handle noise and yet be interpretable to project managers. This paper proposes partition-based regression models that incorporate data-driven statistical models within each partition, as a s…
University of Pennsylvania（宾夕法尼亚大学）；Ursinus College（乌尔辛纳斯学院）
Modern biomedical data mining requires feature selection methods that can (1) be applied to large scale feature spaces (e.g. `omics' data), (2) function in noisy problems, (3) detect complex patterns of association (e.g. gene-gene interactions), (4) be flexibly adapted to various problem domains and data types (e.g. genetic variants, gene expression, and clinical data) and (5) are computationally tractable. To that end, this work examines a set of filter-style feature selection algorithms inspired by the `Relief' algorithm, i.e. Relief-Based algorithms (RBAs). We implement and expand these RBA…
University of Maryland（马里兰大学）；University of Washington（华盛顿大学）；Imperial College（帝国理工学院）
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system identification across scientific domains, but there remains a gap in the literature for large-scale methodological comparisons that are evaluated on a variety of dynamical systems. In this work, we systematically benchmark sparse regression variants by utilizing the dysts standardized database of chaotic systems. In particular, we demonstrate how this open-so…
