An essential problem in automated machine learning (AutoML) is that of model selection. A unique challenge in the sequential setting is the fact that the optimal model itself may vary over time, depending on the distribution of features and labels available up to each point in time. In this paper, we propose a novel Bayesian optimization (BO) algorithm to tackle the challenge of model selection in this setting. This is accomplished by treating the performance at each time step as its own black-box function. In order to solve the resulting multiple black-box function optimization problem jointly and efficiently, we exploit potential correlations among black-box functions using deep kernel learning (DKL). To the best of our knowledge, we are the first to formulate the problem of stepwise model selection (SMS) for sequence prediction, and to design and demonstrate an efficient joint-learning algorithm for this purpose. Using multiple real-world datasets, we verify that our proposed method outperforms both standard BO and multi-objective BO algorithms on a variety of sequence prediction tasks.
Nagoya Institute of Technology（名古屋工业大学）；RIKEN（理化学研究所）
Conditional selective inference (SI) has been actively studied as a new statistical inference framework for data-driven hypotheses. The basic idea of conditional SI is to make inferences conditional on the selection event characterized by a set of linear and/or quadratic inequalities. Conditional SI has been mainly studied in the context of feature selection such as stepwise feature selection (SFS). The main limitation of the existing conditional SI methods is the loss of power due to over-conditioning, which is required for computational tractability. In this study, we develop a more powerful…
University of Louisiana at Lafayette（路易斯安那大学拉法叶分校）
In this era of big data, feature selection techniques, which have long been proven to simplify the model, makes the model more comprehensible, speed up the process of learning, have become more and more important. Among many developed methods, forward and stepwise feature selection regression remained widely used due to their simplicity and efficiency. However, they all involving rescanning all the un-selected features again and again. Moreover, many times, the backward steps in stepwise deem unnecessary, as we will illustrate in our example. These remarks motivate us to introduce a novel algo…
Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance parameter goes to zero, RMP exhibits a surprising connection to Stepwise Regression. Further, we derive novel guarantees for Stepwise Regression algorithms, which also shed light on RMP. Our guarantees for Forward Regression improve on deterministic and probabilistic results for Orthogonal Matching Pursuit with noise. Our analysis of Backward Regression on dete…
I consider unsupervised extensions of the fast stepwise linear regression algorithm \cite{efroymson1960multiple}. These extensions allow one to efficiently identify highly-representative feature variable subsets within a given set of jointly distributed variables. This in turn allows for the efficient dimensional reduction of large data sets via the removal of redundant features. Fast search is effected here through the avoidance of repeat computations across trial fits, allowing for a full representative-importance ranking of a set of feature variables to be carried out in $O(n^2 m)$ time, wh…
We consider the two-group classification problem and propose a kernel classifier based on the optimal scoring framework. Unlike previous approaches, we provide theoretical guarantees on the expected risk consistency of the method. We also allow for feature selection by imposing structured sparsity using weighted kernels. We propose fully-automated methods for selection of all tuning parameters, and in particular adapt kernel shrinkage ideas for ridge parameter selection. Numerical studies demonstrate the superior classification performance of the proposed approach compared to existing nonparam…
Harvard University（哈佛大学）；University of Michigan（密歇根大学）
Motivated by the need for efficient and personalized learning in mobile health, we investigate the problem of online kernel selection for Gaussian Process regression in the multi-task setting. We propose a novel generative process on the kernel composition for this purpose. Our method demonstrates that trajectories of kernel evolutions can be transferred between users to improve learning and that the kernels themselves are meaningful for an mHealth prediction goal.
National University of Singapore（新加坡国立大学）；Shenzhen University（深圳大学）
This paper presents a variational Bayesian kernel selection (VBKS) algorithm for sparse Gaussian process regression (SGPR) models. In contrast to existing GP kernel selection algorithms that aim to select only one kernel with the highest model evidence, our proposed VBKS algorithm considers the kernel as a random variable and learns its belief from data such that the uncertainty of the kernel can be interpreted and exploited to avoid overconfident GP predictions. To achieve this, we represent the probabilistic kernel as an additional variational variable in a variational inference (VI) framewo…
BOOST: A Data-Driven Framework for the Automated Joint Selection of Kernel and Acquisition Functions in Bayesian Optimization
Department of Chemical and Biomolecular Engineering, Korea Advanced Institute of Science and Technology（化学与生物分子工程系，韩国科学技术院）；Department of AX, Korea Advanced Institute of Science and Technology（AX系，韩国科学技术院）；Saudi Aramco-KAIST CO2 Management Center（沙特阿美-KAIST二氧化碳管理中心）
Center of Cognitive Interactive Technology (CITEC)（认知交互技术中心（CITEC））；Bielefeld University（比勒费尔德大学）
Prototype-based methods are of the particular interest for domain specialists and practitioners as they summarize a dataset by a small set of representatives. Therefore, in a classification setting, interpretability of the prototypes is as significant as the prediction accuracy of the algorithm. Nevertheless, the state-of-the-art methods make inefficient trade-offs between these concerns by sacrificing one in favor of the other, especially if the given data has a kernel-based representation. In this paper, we propose a novel interpretable multiple-kernel prototype learning (IMKPL) to construct…
University College London（伦敦大学学院）；Kyoto University（京都大学）；RIKEN AIP（理化学研究所先进智能项目中心）；MPI for Intelligent Systems, Tübingen（图宾根马克斯·普朗克智能系统研究所）；Osaka University（大阪大学）；Nagoya University（名古屋大学）
Refining one's hypotheses in the light of data is a common scientific practice; however, the dependency on the data introduces selection bias and can lead to specious statistical analysis. An approach for addressing this is via conditioning on the selection procedure to account for how we have used the data to generate our hypotheses, and prevent information to be used again after selection. Many selective inference (a.k.a. post-selection inference) algorithms typically take this approach but will "over-condition" for sake of tractability. While this practice yields well calibrated statistic t…
Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descents
Center for Intelligent Decision-Making and Machine Learning, School of Management, Xi’an Jiaotong University, Xi’an, China（智能决策与机器学习中心，管理学院，西安交通大学，西安，中国）；Department of Mathematics, The University of Hong Kong, Hongkong, China（数学系，香港大学，香港，中国）
We propose a method for feature selection that employs kernel-based measures of independence to find a subset of covariates that is maximally predictive of the response. Building on past work in kernel dimension reduction, we show how to perform feature selection via a constrained optimization problem involving the trace of the conditional covariance operator. We prove various consistency results for this procedure, and also demonstrate that our method compares favorably with other state-of-the-art algorithms on a variety of synthetic and real data sets.
We study the construction of the theoretical foundation of model comparison for ergodic stochastic differential equation (SDE) models and an extension of the applicable scope of the conventional Bayesian information criterion. Different from previous studies, we suppose that the candidate models are possibly misspecified models, and we consider both Wiener and a pure-jump Lévy noise driven SDE. Based on the asymptotic behavior of the marginal quasi-log likelihood, the Schwarz type statistics and stepwise model selection procedure are proposed. We also prove the model selection consistency of t…
To support the 2019 U.S. Supreme Court case "Flowers v. Mississippi", APM Reports collated historical court records to assess whether the State exhibited a racial bias in striking potential jurors. This analysis used backward stepwise logistic regression to conclude that race was a significant factor, however this method for selecting relevant features is only a heuristic, and additionally cannot consider interactions between features. We apply Optimal Feature Selection to identify the globally-optimal subset of features and affirm that there is significant evidence of racial bias in the strik…
Institut Charles Delaunay, Universite de Technologie de Troyes（特鲁瓦理工大学夏尔·德洛纳研究所）；Biomedicine Research Institute of Buenos Aires - Max Planck Partner Institute（布宜诺斯艾利斯生物医学研究所-马克斯·普朗克伙伴研究所）；Universidad Tecnologica Nacional Buenos Aires（布宜诺斯艾利斯国立理工大学）
The transcriptomics of cancer tumors are characterized with tens of thousands of gene expression features. Patient prognosis or tumor stage can be assessed by machine learning techniques like supervised classification tasks given a gene expression profile. Feature selection is a useful approach to select the key genes which helps to classify tumors. In this work we propose a feature selection method based on Multiple Kernel Learning that results in a reduced subset of genes and a custom kernel that improves the classification performance when used in support vector classification. During the f…
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian …
A recent paradigm for decoding behavioral variables or stimuli from neuron ensembles relies on joint models for electrode spike trains and their waveforms, which, in principle, is more efficient than decoding from electrode spike trains alone or from sorted neuron spike trains. In this paper, we decode the velocity of arm reaches of a rhesus macaque monkey to show that including waveform features indiscriminately in a joint decoding model can contribute more noise and bias than useful information about the kinematics, and thus degrade decoding performance. We also show that selecting which wav…
In this paper, we improve the regret bound for online kernel selection under bandit feedback. Previous algorithm enjoys a $O((\Vert f\Vert^2_{\mathcal{H}_i}+1)K^{\frac{1}{3}}T^{\frac{2}{3}})$ expected bound for Lipschitz loss functions. We prove two types of regret bounds improving the previous bound. For smooth loss functions, we propose an algorithm with a $O(U^{\frac{2}{3}}K^{-\frac{1}{3}}(\sum^K_{i=1}L_T(f^\ast_i))^{\frac{2}{3}})$ expected bound where $L_T(f^\ast_i)$ is the cumulative losses of optimal hypothesis in $\mathbb{H}_{i}=\{f\in\mathcal{H}_i:\Vert f\Vert_{\mathcal{H}_i}\leq U\}$.…
This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a variable-wise variance and yields selection of better, more robust regressors. Experimental results show superior performance on both simulated and real data sets compared to Leave-One-Out Cross-Validation (LOOCV), kernel-based Information Complexity (ICOMP), and maximum log of marginal likelihood in Gaussian Process Regression (GPR).
Gaussian processes are powerful, yet analytically tractable models for supervised learning. A Gaussian process is characterized by a mean function and a covariance function (kernel), which are determined by a model selection criterion. The functions to be compared do not just differ in their parametrization but in their fundamental structure. It is often not clear which function structure to choose, for instance to decide between a squared exponential and a rational quadratic kernel. Based on the principle of approximation set coding, we develop a framework for model selection to rank kernels …
Universite de Technologie de Troyes（特鲁瓦技术大学）；Instituto de Investigacion en Biomedicina de Buenos Aires (IBioBA)—CONICET Partner Institute of the Max Planck Society（布宜诺斯艾利斯生物医学研究所（IBioBA）—马克斯·普朗克学会合作研究所）
Molecular data from tumor profiles is high dimensional. Tumor profiles can be characterized by tens of thousands of gene expression features. Due to the size of the gene expression feature set machine learning methods are exposed to noisy variables and complexity. Tumor types present heterogeneity and can be subdivided in tumor subtypes. In many cases tumor data does not include tumor subtype labeling thus unsupervised learning methods are necessary for tumor subtype discovery. This work aims to learn meaningful and low dimensional representations of tumor samples and find tumor subtype cluste…
The t-distributed stochastic neighbor embedding (t- SNE) is a method for interpreting high dimensional (HD) data by mapping each point to a low dimensional (LD) space (usually two-dimensional). It seeks to retain the structure of the data. An important component of the t-SNE algorithm is the initialization procedure, which begins with the random initialization of an LD vector. Points in this initial vector are then updated to minimize the loss function (the KL divergence) iteratively using gradient descent. This leads comparable points to attract one another while pushing dissimilar points apa…
Improved identification accuracy in equation learning via comprehensive $\boldsymbol{R^2}$-elimination and Bayesian model selection
University of Augsburg（奥格斯堡大学）；African Institute for Mathematical Sciences (AIMS)（非洲数学科学研究所（AIMS））；Medical Research Council Unit The Gambia（冈比亚医学研究理事会单位）；London School of Hygiene & Tropical Medicine（伦敦卫生与热带医学院）
Growth mixture models are an important tool for detecting group structure in repeated measures data. Unlike traditional clustering methods, they explicitly model the repeat measurements on observations, and the statistical framework they are based on allows for model selection methods to be used to select the number of clusters. However, the basic growth mixture model makes the assumption that all of the measurements in the data have grouping information/separate the clusters. In other clustering contexts, it has been shown that including non-clustering variables in clustering procedures can l…
Stepwise Fine and Gray: Subject-Specific Variable Selection Shows When Hemodynamic Data Improves Prognostication of Comatose Post-Cardiac Arrest Patients
Heinz College of Information Systems and Public Policy Carnegie Mellon University（卡内基梅隆大学海因兹信息系统与公共政策学院）；Department of Emergency Medicine University of Pittsburgh（匹兹堡大学急诊医学系）
提出一种逐步动态竞争风险模型，通过扩展Fine and Gray模型并引入神经网络，自动确定何时利用时变血流动力学数据，从而改善心脏骤停后昏迷患者的预后预测。
RIKEN（理化学研究所）；Nagoya Institute of Technology（名古屋工业大学）；Nagoya University（名古屋大学）；Tokyo Institute of Technology（东京工业大学）
In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the estimator using a few variables by l1-type penalized estimation. We see that the proposed method can be applied to various kernel nonparametric estimation such as kernel ridge regression, kernel-based density and density-ratio estimation. We prove that the proposed method has the property of the variable selection consistency when the power series kernel is …
Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high computational complexity. Thus, the objective of this letter is to propose an fast and efficient method to select the bandwidth parameter of the Gaussian kernel in the kernel based classification methods. The proposed method is developed based on the operators in the reproducing kernel Hilbert space and it is evaluated on Support vector machines and PerTurbo…
Toyota Technological Institute at Chicago（芝加哥丰田技术研究院）
We study the problem of column selection in large-scale kernel canonical correlation analysis (KCCA) using the Nyström approximation, where one approximates two positive semi-definite kernel matrices using "landmark" points from the training set. When building low-rank kernel approximations in KCCA, previous work mostly samples the landmarks uniformly at random from the training set. We propose novel strategies for sampling the landmarks non-uniformly based on a version of statistical leverage scores recently developed for kernel ridge regression. We study the approximation accuracy of the pro…
Geneva School of Business Administration, HES-SO（日内瓦工商管理学院，HES-SO）；University of Geneva（日内瓦大学）
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the first kernel-based variable selection method applicable to large datasets. It sidesteps the typical poor scaling properties of kernel methods by mapping the inputs into a relatively low-dimensional space of random features. The algorithm discovers the variables relevant for the regression task together with learning the prediction model through learning the app…
Shanghai University of Finance and Economics（上海财经大学）；City University of Hong Kong（香港城市大学）；Nanjing Audit University（南京审计大学）
Variable selection is central to high-dimensional data analysis, and various algorithms have been developed. Ideally, a variable selection algorithm shall be flexible, scalable, and with theoretical guarantee, yet most existing algorithms cannot attain these properties at the same time. In this article, a three-step variable selection algorithm is developed, involving kernel-based estimation of the regression function and its gradient functions as well as a hard thresholding. Its key advantage is that it assumes no explicit model assumption, admits general predictor effects, allows for scalabl…
CITEC cluster of excellence（CITEC卓越集群）；Bielefeld University（比勒费尔德大学）
Multiple kernel learning (MKL) algorithms combine different base kernels to obtain a more efficient representation in the feature space. Focusing on discriminative tasks, MKL has been used successfully for feature selection and finding the significant modalities of the data. In such applications, each base kernel represents one dimension of the data or is derived from one specific descriptor. Therefore, MKL finds an optimal weighting scheme for the given kernels to increase the classification accuracy. Nevertheless, the majority of the works in this area focus on only binary classification pro…
TorchKM: A GPU-Oriented Library for Kernel Learning and Model Selection
University of Iowa（爱荷华大学）；University of Minnesota（明尼苏达大学）；Individual Researcher（独立研究者）；AIScientists, Inc. (MorphMind)（AIScientists公司（MorphMind））；Department of Statistics and Actuarial Science, University of Iowa（爱荷华大学统计与精算科学系）
Seoul National University（首尔国立大学）；Korea University（高丽大学）
Variable selection is essential in high-dimensional data analysis. Although various variable selection methods have been developed, most rely on the linear model assumption. This article proposes a nonparametric variable selection method for the large-margin classifier defined by reproducing the kernel Hilbert space (RKHS). we propose a gradient-based representation of the large-margin classifier and then regularize the gradient functions by the group-lasso penalty to obtain sparse gradients that naturally lead to the variable selection. The groupwise-majorization-decent algorithm (GMD, Yang a…
NEC Corporation（日本电气公司）；RIKEN AIP（理化学研究所先进智能项目中心）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）；University of Tübingen（蒂宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；The Institute of Statistical Mathematics（统计数理研究所）
We propose a novel approach to model selection for simulator-based statistical models. The proposed approach defines a mixture of candidate models, and then iteratively updates the weight coefficients for those models as well as the parameters in each model simultaneously; this is done by recursively applying Bayes' rule, using the recently proposed kernel recursive ABC algorithm. The practical advantage of the method is that it can be used even when a modeler lacks appropriate prior knowledge about the parameters in each model. We demonstrate the effectiveness of the proposed approach with a …
Automated tuning of compute kernels is a popular area of research, mainly focused on finding optimal kernel parameters for a problem with fixed input sizes. This approach is good for deploying machine learning models, where the network topology is constant, but machine learning research often involves changing network topologies and hyperparameters. Traditional kernel auto-tuning has limited impact in this case; a more general selection of kernels is required for libraries to accelerate machine learning research. In this paper we present initial results using machine learning to select kernels…
Support Vector Data Description (SVDD) provides a useful approach to construct a description of multivariate data for single-class classification and outlier detection with various practical applications. Gaussian kernel used in SVDD formulation allows flexible data description defined by observations designated as support vectors. The data boundary of such description is non-spherical and conforms to the geometric features of the data. By varying the Gaussian kernel bandwidth parameter, the SVDD-generated boundary can be made either smoother (more spherical) or tighter/jagged. The former case…
Support vector data description (SVDD) is a popular technique for detecting anomalies. The SVDD classifier partitions the whole space into an inlier region, which consists of the region near the training data, and an outlier region, which consists of points away from the training data. The computation of the SVDD classifier requires a kernel function, and the Gaussian kernel is a common choice for the kernel function. The Gaussian kernel has a bandwidth parameter, whose value is important for good results. A small bandwidth leads to overfitting, and the resulting SVDD classifier overestimates …
Tokyo University of Agriculture and Technology（东京农工大学）；October Sky Co., Ltd.（October Sky株式会社）；University of Tsukuba（筑波大学）
We study the mixed-integer optimization (MIO) approach to feature subset selection in nonlinear kernel support vector machines (SVMs) for binary classification. First proposed for linear regression in the 1970s, this approach has recently moved into the spotlight with advances in optimization algorithms and computer hardware. The goal of this paper is to establish an MIO approach for selecting the best subset of features for kernel SVM classification. To measure the performance of subset selection, we use the kernel-target alignment, which is the distance between the centroids of two response …
Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally efficient?". First, we show that a Biweight kernel is optimal in the sense of minimizing an asymptotic mean squared error of a resulting MLR parameter. This result is derived from our refined analysis of an asymptotic statistical behavior of MLR. Secondly, we provide a kernel class for which iteratively reweighted least-squares algorithm (IRLS) is guaranteed to…
Indian Institute of Technology, Madras（印度理工学院马德拉斯分校）
Face Recognition (FR) has been the interest to several researchers over the past few decades due to its passive nature of biometric authentication. Despite high accuracy achieved by face recognition algorithms under controlled conditions, achieving the same performance for face images obtained in surveillance scenarios, is a major hurdle. Some attempts have been made to super-resolve the low-resolution face images and improve the contrast, without considerable degree of success. The proposed technique in this paper tries to cope with the very low resolution and low contrast face images obtaine…
INRIA（法国国家信息与自动化研究所）；Laboratoire d’Informatique de l’Ecole Normale Supérieure（巴黎高等师范学院计算机实验室）；CNRS（法国国家科学研究中心）；ENS（巴黎高等师范学院）
We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that characterize non-linear interactions between the original variables. To select efficiently from these many kernels, we use the natural hierarchical structure of the problem to extend the multiple kernel learning framework to kernels that can be embedded in a directed acyclic graph; we show that it is then possible to perform kernel selection through a graph-adapted sp…
Variational Autoencoder Kernel Interpretation and Selection for Classification
University of Madeira（马德拉大学）；Interactive Technologies Institute（交互技术研究所）；Institute for Technological Development and Innovation in Communications, Universidad de Las Palmas de Gran Canaria（拉斯帕尔马斯大学通信技术发展与创新研究所）
Australian National University（澳大利亚国立大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Tokyo（东京大学）
Kernel maximum moment restriction (KMMR) recently emerges as a popular framework for instrumental variable (IV) based conditional moment restriction (CMR) models with important applications in conditional moment (CM) testing and parameter estimation for IV regression and proximal causal learning. The effectiveness of this framework, however, depends critically on the choice of a reproducing kernel Hilbert space (RKHS) chosen as a space of instruments. In this work, we presents a systematic way to select the instrument space for parameter estimation based on a principle of the least identifiabl…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；University of Colorado Boulder（科罗拉多大学博尔德分校）
Scalable kernel methods, including kernel ridge regression, often rely on low-rank matrix approximations using the Nystrom method, which involves selecting landmark points from large data sets. The existing approaches to selecting landmarks are typically computationally demanding as they require manipulating and performing computations with large matrices in the input or feature space. In this paper, our contribution is twofold. The first contribution is to propose a novel landmark selection method that promotes diversity using an efficient two-step approach. Our landmark selection technique f…
