Combining the mutual information criterion with a forward feature selection strategy offers a good trade-off between optimality of the selected feature subset and computation time. However, it requires to set the parameter(s) of the mutual information estimator and to determine when to halt the forward procedure. These two choices are difficult to make because, as the dimensionality of the subset increases, the estimation of the mutual information becomes less and less reliable. This paper proposes to use resampling methods, a K-fold cross-validation and the permutation test, to address both issues. The resampling methods bring information about the variance of the estimator, information which can then be used to automatically set the parameter and to calculate a threshold to stop the forward procedure. The procedure is illustrated on a synthetic dataset as well as on real-world examples.
Enhancing Credit Default Prediction Using Boruta Feature Selection and DBSCAN Algorithm with Different Resampling Techniques
Department of Statistics, Western Michigan University（统计系，西部密歇根大学）；Department of Biostatistics and Data Science, Celia Scott Weatherhead School of Public Health and Tropical Medicine, Tulane University（生物统计学与数据科学系，Celia Scott Weatherhead公共卫生与热带医学学院，路易斯安那大学塔金斯分校）；School of Mathematical and Statistical Science, College of Sciences, University of Texas Rio Grande Valley（数学与统计科学学院，德克萨斯里奥格兰德谷大学）；Department of Economics, Western Michigan University（经济学系，西部密歇根大学）；Department of Economics, University of Ottawa（经济学系，渥太华大学）
Swinburne University of Technology（斯威本科技大学）；Deakin University（迪肯大学）；Harvard Medical School（哈佛医学院）
Biomedical data are widely accepted in developing prediction models for identifying a specific tumor, drug discovery and classification of human cancers. However, previous studies usually focused on different classifiers, and overlook the class imbalance problem in real-world biomedical datasets. There are a lack of studies on evaluation of data pre-processing techniques, such as resampling and feature selection, on imbalanced biomedical data learning. The relationship between data pre-processing techniques and the data distributions has never been analysed in previous studies. This article ma…
We study active feature selection, a novel feature selection setting in which unlabeled data is available, but the budget for labels is limited, and the examples to label can be actively selected by the algorithm. We focus on feature selection using the classical mutual information criterion, which selects the $k$ features with the largest mutual information with the label. In the active feature selection setting, the goal is to use significantly fewer labels than the data set size and still find $k$ features whose mutual information with the label based on the \emph{entire} data set is large.…
University of Coimbra（科英布拉大学）；Institute of Systems and Robotics（系统与机器人研究所）
This paper presents a novel feature selection method based on the conditional mutual information (CMI). The proposed High Order Conditional Mutual Information Maximization (HOCMIM) incorporates high order dependencies into the feature selection procedure and has a straightforward interpretation due to its bottom-up derivation. The HOCMIM is derived from the CMI's chain expansion and expressed as a maximization optimization problem. The maximization problem is solved using a greedy search procedure, which speeds up the entire feature selection process. The experiments are run on a set of benchm…
Università degli Studi di Bologna（博洛尼亚大学）；Politecnico di Milano（米兰理工大学）
Mutual information has been successfully adopted in filter feature-selection methods to assess both the relevancy of a subset of features in predicting the target variable and the redundancy with respect to other variables. However, existing algorithms are mostly heuristic and do not offer any guarantee on the proposed solution. In this paper, we provide novel theoretical results showing that conditional mutual information naturally arises when bounding the ideal regression/classification errors achieved by different subsets of features. Leveraging on these insights, we propose a novel stoppin…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Markov blanket feature selection, while theoretically optimal, is generally challenging to implement. This is due to the shortcomings of existing approaches to conditional independence (CI) testing, which tend to struggle either with the curse of dimensionality or computational complexity. We propose a novel two-step approach which facilitates Markov blanket feature selection in high dimensions. First, neural networks are used to map features to low-dimensional representations. In the second step, CI testing is performed by applying the $k$-NN conditional mutual information estimator to the le…
Mutual information and sensitivity analysis for feature selection in customer targeting: a comparative study
Universidad Nacional de Tres de Febrero（阿根廷 Tres de Febrero 国立大学）；Instituto Universitário de Lisboa (ISCTE-IUL)（里斯本大学学院）；ISTAR-IUL（ISTAR-IUL 研究所）；ALGORITMI Research Centre（ALGORITMI 研究中心）；University of Minho（米尼奥大学）；Dataxplore；Boldt Gaming
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等理工学院）；EPF Lausanne（洛桑联邦理工学院）
Feature selection problems arise in a variety of applications, such as microarray analysis, clinical prediction, text categorization, image classification and face recognition, multi-label learning, and classification of internet traffic. Among the various classes of methods, forward feature selection methods based on mutual information have become very popular and are widely used in practice. However, comparative evaluations of these methods have been limited by being based on specific datasets and classifiers. In this paper, we develop a theoretical framework that allows evaluating the metho…
This paper introduces a new property of estimators of the strength of statistical association, which helps characterize how well an estimator will perform in scenarios where dependencies between continuous and discrete random variables need to be rank ordered. The new property, termed the estimator response curve, is easily computable and provides a marginal distribution agnostic way to assess an estimator's performance. It overcomes notable drawbacks of current metrics of assessment, including statistical power, bias, and consistency. We utilize the estimator response curve to test various me…
Feature selection is a preprocessing step which plays a crucial role in the domain of machine learning and data mining. Feature selection methods have been shown to be effctive in removing redundant and irrelevant features, improving the learning algorithm's prediction performance. Among the various methods of feature selection based on redundancy, the fast correlation-based filter (FCBF) is one of the most effective. In this paper, we proposed a novel extension of FCBF, called RFCBF, which combines resampling technique to improve classification accuracy. We performed comprehensive experiments…
This study introduces a framework for the forecasting, reconstruction and feature engineering of multivariate processes along with its renewable energy applications. We integrate derivative-free optimization with an ensemble of sequence-to-sequence networks and design a new resampling technique called additive resampling, which, along with Bootstrap aggregating (bagging) resampling, are applied to initialize the ensemble structure. Moreover, we explore the proposed framework performance on three renewable energy sources---wind, solar and ocean wave---and conduct several short- to long-term for…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Institute for Information Transmission Problems（信息传输问题研究所）
One possible approach to tackle the class imbalance in classification tasks is to resample a training dataset, i.e., to drop some of its elements or to synthesize new ones. There exist several widely-used resampling methods. Recent research showed that the choice of resampling method significantly affects the quality of classification, which raises resampling selection problem. Exhaustive search for optimal resampling is time-consuming and hence it is of limited use. In this paper, we describe an alternative approach to the resampling selection. We follow the meta-learning concept to build res…
Sparse and geometry-aware generalisation of the mutual information for joint discriminative clustering and feature selection
Université Côte d’Azur（蔚蓝海岸大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Maasai Team（马赛团队）；CHU de Québec Research Centre（魁北克大学中心医院研究中心）；Laval University（拉瓦尔大学）
Faculty of Computing, Universiti Teknologi Malaysia（马来西亚理工大学计算机学院）
Crypto-ransomware is characterized by its irreversible effect even after the detection and removal. As such, the early detection is crucial to protect user data and files of being held to ransom. Several solutions have proposed utilizing the data extracted during the initial phases of the attacks before the encryption takes place. However, the lack of enough data at the early phases of the attack along with high dimensional features space renders the model prone to overfitting which decreases its detection accuracy. To this end, this paper proposed a novel redundancy coefficient gradual up-wei…
Feature selection, which searches for the most representative features in observed data, is critical for health data analysis. Unlike feature extraction, such as PCA and autoencoder based methods, feature selection preserves interpretability, meaning that the selected features provide direct information about certain health conditions (i.e., the label). Thus, feature selection allows domain experts, such as clinicians, to understand the predictions made by machine learning based systems, as well as improve their own diagnostic skills. Mutual information is often used as a basis for feature sel…
Distance-based mutual congestion feature selection with genetic algorithm for high-dimensional medical datasets
Modern College of Business and Science（现代商业与科学学院）；Emory University（埃默里大学）；Sari Branch, Islamic Azad University（伊斯兰阿扎德大学萨里分校）；Universiti Teknologi Malaysia（马来西亚理工大学）
Mutual Information (MI) based feature selection makes use of MI to evaluate each feature and eventually shortlists a relevant feature subset, in order to address issues associated with high-dimensional datasets. Despite the effectiveness of MI in feature selection, we notice that many state-of-the-art algorithms disregard the so-called unique relevance (UR) of features, and arrive at a suboptimal selected feature subset which contains a non-negligible number of redundant features. We point out that the heart of the problem is that all these MIBFS algorithms follow the criterion of Maximize Rel…
Northeastern University（东北大学）；Graz University of Technology（格拉茨技术大学）；Silicon Austria Labs（硅谷奥地利实验室）
Feature ranking and selection is a widely used approach in various applications of supervised dimensionality reduction in discriminative machine learning. Nevertheless there exists significant evidence on feature ranking and selection algorithms based on any criterion leading to potentially sub-optimal solutions for class separability. In that regard, we introduce emerging information theoretic feature transformation protocols as an end-to-end neural network training approach. We present a dimensionality reduction network (MMINet) training procedure based on the stochastic estimate of the mutu…
Feature selection plays a vital role in promoting the classifier's performance. However, current methods ineffectively distinguish the complex interaction in the selected features. To further remove these hidden negative interactions, we propose a GA-like dynamic probability (GADP) method with mutual information which has a two-layer structure. The first layer applies the mutual information method to obtain a primary feature subset. The GA-like dynamic probability algorithm, as the second layer, mines more supportive features based on the former candidate features. Essentially, the GA-like met…
An Orthogonal Least Squares (OLS) based feature selection method is proposed for both binomial and multinomial classification. The novel Squared Orthogonal Correlation Coefficient (SOCC) is defined based on Error Reduction Ratio (ERR) in OLS and used as the feature ranking criterion. The equivalence between the canonical correlation coefficient, Fisher's criterion, and the sum of the SOCCs is revealed, which unveils the statistical implication of ERR in OLS for the first time. It is also shown that the OLS based feature selection method has speed advantages when applied for greedy search. The …
With the abundance of machine learning methods available and the temptation of using them all in an ensemble method, having a model-agnostic method of feature selection is incredibly alluring. Principal component analysis was developed in 1901 and has been a strong contender in this role since, but in the end is an unsupervised method. It offers no guarantee that the features that are selected have good predictive power because it does not know what is being predicted. To this end, Peng et al. developed the minimum redundancy-maximum relevance (mRMR) method in 2005. It uses the mutual informat…
University of Minnesota Twin Cities（明尼苏达大学双城分校）；Splunk（Splunk公司）
In the context of supervised parametric models, we introduce the concept of e-values. An e-value is a scalar quantity that represents the proximity of the sampling distribution of parameter estimates in a model trained on a subset of features to that of the model trained on all features (i.e. the full model). Under general conditions, a rank ordering of e-values separates models that contain all essential features from those that do not. The e-values are applicable to a wide range of parametric models. We use data depths and a fast resampling-based algorithm to implement a feature selection pr…
Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）；Humboldt-Universität zu Berlin（柏林洪堡大学）
The identification of relevant features, i.e., the driving variables that determine a process or the properties of a system, is an essential part of the analysis of data sets with a large number of variables. A mathematical rigorous approach to quantifying the relevance of these features is mutual information. Mutual information determines the relevance of features in terms of their joint mutual dependence to the property of interest. However, mutual information requires as input probability distributions, which cannot be reliably estimated from continuous distributions such as physical quanti…
Stability of a Generalized Debiased Lasso with Applications to Resampling-Based Variable Selection
Department of Statistics, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校统计系）；Department of Electrical and Computer Engineering, the Grainger College of Engineering（格拉inger工程学院电子与计算机工程系）
Mutual information for the selection of relevant variables in spectrometric nonlinear modelling
INRIA-Rocquencourt（法国国家信息与自动化研究所罗夸恩库尔特中心）；Helsinki University of Technology（赫尔辛基理工大学）；Université catholique de Louvain（天主教鲁汶大学）；Université Paris I Panthéon Sorbonne（巴黎第一大学先贤祠-索邦大学）
Princeton University（普林斯顿大学）；University of California, Berkeley（加州大学伯克利分校）；Creative Computing Institute, University of the Arts London（伦敦艺术大学创意计算学院）
Large-scale social networks are thought to contribute to polarization by amplifying people's biases. However, the complexity of these technologies makes it difficult to identify the mechanisms responsible and to evaluate mitigation strategies. Here we show under controlled laboratory conditions that information transmission through social networks amplifies motivational biases on a simple perceptual decision-making task. Participants in a large behavioral experiment showed increased rates of biased decision-making when part of a social network relative to asocial participants, across 40 indepe…
The estimation of mutual information (MI) or conditional mutual information (CMI) from a set of samples is a long-standing problem. A recent line of work in this area has leveraged the approximation power of artificial neural networks and has shown improvements over conventional methods. One important challenge in this new approach is the need to obtain, given the original dataset, a different set where the samples are distributed according to a specific product density function. This is particularly challenging when estimating CMI. In this paper, we introduce a new technique, based on k neare…
Virginia State University（弗吉尼亚州立大学）；Henan Normal University（河南师范大学）
Due to the advantage of achieving a better performance under weak regularization, elastic net has attracted wide attention in statistics, machine learning, bioinformatics, and other fields. In particular, a variation of the elastic net, adaptive elastic net (AEN), integrates the adaptive grouping effect. In this paper, we aim to develop a new algorithm: Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI) that further improves AEN by incorporating conditional mutual information into the gene selection process. We apply this new algorithm to screen significant genes for two kinds …
Shenzhen International Graduate School, Tsinghua University（清华大学深圳国际研究生院）；Ping An Technology (Shenzhen) Co., Ltd.（平安科技（深圳）有限公司）；The Chinese University of Hong Kong（香港中文大学）
One-shot voice conversion (VC) with only a single target speaker's speech for reference has become a hot research topic. Existing works generally disentangle timbre, while information about pitch, rhythm and content is still mixed together. To perform one-shot VC effectively with further disentangling these speech components, we employ random resampling for pitch and content encoder and use the variational contrastive log-ratio upper bound of mutual information and gradient reversal layer based adversarial mutual information learning to ensure the different parts of the latent space containing…
University of Texas at Dallas（德克萨斯大学达拉斯分校）；Indian Institute of Technology Bombay（印度理工学院孟买分校）；University of Washington（华盛顿大学）
With the rapid growth of data, it is becoming increasingly difficult to train or improve deep learning models with the right subset of data. We show that this problem can be effectively solved at an additional labeling cost by targeted data subset selection(TSS) where a subset of unlabeled data points similar to an auxiliary set are added to the training data. We do so by using a rich class of Submodular Mutual Information (SMI) functions and demonstrate its effectiveness for image classification on CIFAR-10 and MNIST datasets. Lastly, we compare the performance of SMI functions for TSS with o…
Laboratoire des Images et des Signaux (LIS) – CNRS UMR 5083（图像与信号实验室（LIS）——法国国家科学研究中心 UMR 5083）；INPG（格勒诺布尔国立理工学院）；UJF（约瑟夫·傅里叶大学（格勒诺布尔第一大学））；Sharif University of Technology（谢里夫理工大学）；Université Catholique de Louvain (UCL)（鲁汶天主教大学（UCL））；Laboratoire Systémes Complexes (LSC) – CNRS FRE 2494（复杂系统实验室（LSC）——法国国家科学研究中心 FRE 2494）
Blind source separation (BSS) techniques have revealed to be promising approaches for, among other, biomedical signal processing applications. Specifically, for the noninvasive extraction of fetal cardiac signals from maternal abdominal recordings, where conventional filtering schemes have failed to extract the complete fetal ECG components. From previous studies, it is now believed that a carefully selected array of electrodes well-placed over the abdomen of a pregnant woman contains the required `information' for BSS, to extract the complete fetal components. Based on this idea, in previous …
