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. We explain and experimentally study the choices that we make in the algorithm, and show that they lead to a successful algorithm, compared to other more naive approaches. Our design draws on insights which relate the problem of active feature selection to the study of pure-exploration multi-armed bandits settings. While we focus here on mutual information, our general methodology can be adapted to other feature-quality measures as well. The code is available at the following url: https://github.com/ShacharSchnapp/ActiveFeatureSelection.
Kyushu Institute of Technology（九州工业大学）；The Institute of Statistical Mathematics（统计数理研究所）；RIKEN AIP（理化学研究所革新智能统合研究中心）
Active learning is a framework for supervised learning to improve the predictive performance by adaptively annotating a small number of samples. To realize efficient active learning, both an acquisition function that determines the next datum and a stopping criterion that determines when to stop learning should be considered. In this study, we propose a stopping criterion based on error stability, which guarantees that the change in generalization error upon adding a new sample is bounded by the annotation cost and can be applied to any Bayesian active learning. We demonstrate that the propose…
Kyushu Institute of Technology（九州工业大学）；The Institute of Statistical Mathematics（统计数学研究所）；RIKEN AIP（理化学研究所人工智能研究中心）
Active learning is a framework in which the learning machine can select the samples to be used for training. This technique is promising, particularly when the cost of data acquisition and labeling is high. In active learning, determining the timing at which learning should be stopped is a critical issue. In this study, we propose a criterion for automatically stopping active learning. The proposed stopping criterion is based on the difference in the expected generalization errors and hypothesis testing. We derive a novel upper bound for the difference in expected generalization errors before …
The Maximum Mutual Information (MMI) criterion is different from the Least Error Rate (LER) criterion. It can reduce failing to report small probability events. This paper introduces the Channels Matching (CM) algorithm for the MMI classifications of unseen instances. It also introduces some semantic information methods, which base the CM algorithm. In the CM algorithm, label learning is to let the semantic channel match the Shannon channel (Matching I) whereas classifying is to let the Shannon channel match the semantic channel (Matching II). We can achieve the MMI classifications by repeatin…
Université catholique de Louvain（鲁汶天主教大学）；INRIA Rocquencourt（法国国家信息与自动化研究所罗克库尔分部）
The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the performances of prediction or classification methods, and interpreting the application. In a nonlinear context, the mutual information is widely used as relevance criterion for features and sets of features. Nevertheless, it suffers from at least three major limitations: mutual information estimators depend on smoothing parameters, there is no theoretically jus…
Center for Perceptual Systems（感知系统中心）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
The ultimate goal of optimization is to find the minimizer of a target function.However, typical criteria for active optimization often ignore the uncertainty about the minimizer. We propose a novel criterion for global optimization and an associated sequential active learning strategy using Gaussian processes.Our criterion is the reduction of uncertainty in the posterior distribution of the function minimizer. It can also flexibly incorporate multiple global minimizers. We implement a tractable approximation of the criterion and demonstrate that it obtains the global minimizer accurately comp…
Labeling each instance in a large dataset is extremely labor- and time- consuming . One way to alleviate this problem is active learning, which aims to which discover the most valuable instances for labeling to construct a powerful classifier. Considering both informativeness and representativeness provides a promising way to design a practical active learning. However, most existing active learning methods select instances favoring either informativeness or representativeness. Meanwhile, many are designed based on the binary class, so that they may present suboptimal solutions on the datasets…
Learning from label proportions (LLP) is a weakly supervised setting for classification in which unlabeled training instances are grouped into bags, and each bag is annotated with the proportion of each class occurring in that bag. Prior work on LLP has yet to establish a consistent learning procedure, nor does there exist a theoretically justified, general purpose training criterion. In this work we address these two issues by posing LLP in terms of mutual contamination models (MCMs), which have recently been applied successfully to study various other weak supervision settings. In the proces…
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 …
Modern deep learning has achieved great success in various fields. However, it requires the labeling of huge amounts of data, which is expensive and labor-intensive. Active learning (AL), which identifies the most informative samples to be labeled, is becoming increasingly important to maximize the efficiency of the training process. The existing AL methods mostly use only a single final fixed model for acquiring the samples to be labeled. This strategy may not be good enough in that the structural uncertainty of a model for given training data is not considered to acquire the samples. In this…
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…
Université catholique de Louvain（鲁汶大学）；INRIA（法国国家信息与自动化研究所）
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 i…
State-of-the-art machine learning models require access to significant amount of annotated data in order to achieve the desired level of performance. While unlabelled data can be largely available and even abundant, annotation process can be quite expensive and limiting. Under the assumption that some samples are more important for a given task than others, active learning targets the problem of identifying the most informative samples that one should acquire annotations for. Instead of the conventional reliance on model uncertainty as a proxy to leverage new unknown labels, in this work we pr…
IBM T.J. Watson Research（IBM T.J. 沃森研究中心）；Limagrain Europe（利马格兰欧洲）
Whole genome prediction of complex phenotypic traits using high-density genotyping arrays has attracted a great deal of attention, as it is relevant to the fields of plant and animal breeding and genetic epidemiology. As the number of genotypes is generally much bigger than the number of samples, predictive models suffer from the curse-of-dimensionality. The curse-of-dimensionality problem not only affects the computational efficiency of a particular genomic selection method, but can also lead to poor performance, mainly due to correlation among markers. In this work we proposed the first tran…
Bell Laboratories, Nokia（诺基亚贝尔实验室）；Courant Institute of Mathematical Sciences, New York University（纽约大学库朗数学科学研究所）
The remarkable performance of deep neural networks depends on the availability of massive labeled data. To alleviate the load of data annotation, active deep learning aims to select a minimal set of training points to be labelled which yields maximal model accuracy. Most existing approaches implement either an `exploration'-type selection criterion, which aims at exploring the joint distribution of data and labels, or a `refinement'-type criterion which aims at localizing the detected decision boundaries. We propose a versatile and efficient criterion that automatically switches from explorati…
Active learning aims to train a classifier as fast as possible with as few labels as possible. The core element in virtually any active learning strategy is the criterion that measures the usefulness of the unlabeled data based on which new points to be labeled are picked. We propose a novel approach which we refer to as maximizing variance for active learning or MVAL for short. MVAL measures the value of unlabeled instances by evaluating the rate of change of output variables caused by changes in the next sample to be queried and its potential labelling. In a sense, this criterion measures ho…
University of Corsica（科西嘉大学）；Hospital of Castelluccio（卡斯泰卢乔医院）；Galatasaray University（加拉塔萨雷大学）；University HouaryBoumédiène（胡阿里·布迈丁大学）
Numerous methods exist and were developed for global radiation forecasting. The two most popular types are the numerical weather predictions (NWP) and the predictions using stochastic approaches. We propose to compute a parameter noted constructed in part from the mutual information which is a quantity that measures the mutual dependence of two variables. Both of these are calculated with the objective to establish the more relevant method between NWP and stochastic models concerning the current problem.
Explicit Mutual Information Maximization for Self-Supervised Learning
School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University（上海交通大学电子信息与电气工程学院）；Advanced Computing and Storage Laboratory, Huawei Technologies Co., Ltd.（华为技术有限公司先进计算与存储实验室）
Harbin Engineering University（哈尔滨工程大学）；Anhui University（安徽大学）；Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；University of York（约克大学）
A novel sparse array (SA) structure is proposed based on the maximum inter-element spacing (IES) constraint (MISC) criterion. Compared with the traditional MISC array, the proposed SA configurations, termed as improved MISC (IMISC) has significantly increased uniform degrees of freedom (uDOF) and reduced mutual coupling. In particular, the IMISC arrays are composed of six uniform linear arrays (ULAs), which can be determined by an IES set. The IES set is constrained by two parameters, namely the maximum IES and the number of sensors. The uDOF of the IMISC arrays is derived and the weight funct…
A Mutual Information Lower Bound for Multimodal Regression Active Learning
Graduate Group on Applied Mathematics & Computational Science（应用数学与计算科学研究生组）；Department of Computer and Information Science（计算机与信息科学系）；University of Pennsylvania（宾夕法尼亚大学）；Department of Mechanical Engineering and Applied Mechanics（机械工程与应用力学系）
We introduce a new unsupervised pretraining objective for reinforcement learning. During the unsupervised reward-free pretraining phase, the agent maximizes mutual information between tasks and states induced by the policy. Our key contribution is a novel lower bound of this intractable quantity. We show that by reinterpreting and combining variational successor features~\citep{Hansen2020Fast} with nonparametric entropy maximization~\citep{liu2021behavior}, the intractable mutual information can be efficiently optimized. The proposed method Active Pretraining with Successor Feature (APS) explo…
We consider the problem of learning structures and parameters of Continuous-time Bayesian Networks (CTBNs) from time-course data under minimal experimental resources. In practice, the cost of generating experimental data poses a bottleneck, especially in the natural and social sciences. A popular approach to overcome this is Bayesian optimal experimental design (BOED). However, BOED becomes infeasible in high-dimensional settings, as it involves integration over all possible experimental outcomes. We propose a novel criterion for experimental design based on a variational approximation of the …
This paper addresses the problem of active learning of a multi-output Gaussian process (MOGP) model representing multiple types of coexisting correlated environmental phenomena. In contrast to existing works, our active learning problem involves selecting not just the most informative sampling locations to be observed but also the types of measurements at each selected location for minimizing the predictive uncertainty (i.e., posterior joint entropy) of a target phenomenon of interest given a sampling budget. Unfortunately, such an entropy criterion scales poorly in the numbers of candidate sa…
Institute for AI Industry Research, Tsinghua University（清华大学智能产业研究院）
Vertical Federated Learning (VFL) is widely utilized in real-world applications to enable collaborative learning while protecting data privacy and safety. However, previous works show that parties without labels (passive parties) in VFL can infer the sensitive label information owned by the party with labels (active party) or execute backdoor attacks to VFL. Meanwhile, active party can also infer sensitive feature information from passive party. All these pose new privacy and security challenges to VFL systems. We propose a new general defense method which limits the mutual information between…
Multi-label learning draws great interests in many real world applications. It is a highly costly task to assign many labels by the oracle for one instance. Meanwhile, it is also hard to build a good model without diagnosing discriminative labels. Can we reduce the label costs and improve the ability to train a good model for multi-label learning simultaneously? Active learning addresses the less training samples problem by querying the most valuable samples to achieve a better performance with little costs. In multi-label active learning, some researches have been done for querying the releva…
We introduce Information Condensing Active Learning (ICAL), a batch mode model agnostic Active Learning (AL) method targeted at Deep Bayesian Active Learning that focuses on acquiring labels for points which have as much information as possible about the still unacquired points. ICAL uses the Hilbert Schmidt Independence Criterion (HSIC) to measure the strength of the dependency between a candidate batch of points and the unlabeled set. We develop key optimizations that allow us to scale our method to large unlabeled sets. We show significant improvements in terms of model accuracy and negativ…
Bayesian neural networks have successfully designed and optimized a robust neural network model in many application problems, including uncertainty quantification. However, with its recent success, information-theoretic understanding about the Bayesian neural network is still at an early stage. Mutual information is an example of an uncertainty measure in a Bayesian neural network to quantify epistemic uncertainty. Still, no analytic formula is known to describe it, one of the fundamental information measures to understand the Bayesian deep learning framework. In this paper, we derive the anal…
École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院 (EPFL)）
We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting. Considering both Ising and Gaussian models, we provide algorithm-independent lower bounds for high-probability recovery within the class of degree-bounded graphs. Our main results are minimax lower bounds for the active setting that match the best known lower bounds for the passive setting, which in turn are known to be tig…
Semantic Variational Bayes Based on Semantic Information G Theory for Solving Latent Variables
Intelligence Engineering and Mathematics Institute, Liaoning Technical University（辽宁工程技术大学智能工程与数学研究所）；School of Computer Engineering and Applied Mathematics, Changsha University（长沙大学计算机工程与应用数学学院）
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 …
The abundance of training data is not guaranteed in various supervised learning applications. One of these situations is the post-earthquake regional damage assessment of buildings. Querying the damage label of each building requires a thorough inspection by experts, and thus, is an expensive task. A practical approach is to sample the most informative buildings in a sequential learning scheme. Active learning methods recommend the most informative cases that are able to maximally reduce the generalization error. The information theoretic measure of mutual information (MI) is one of the most e…
Online multiple kernel learning (OMKL) has provided an attractive performance in nonlinear function learning tasks. Leveraging a random feature approximation, the major drawback of OMKL, known as the curse of dimensionality, has been recently alleviated. In this paper, we introduce a new research problem, termed (stream-based) active multiple kernel learning (AMKL), in which a learner is allowed to label selected data from an oracle according to a selection criterion. This is necessary in many real-world applications as acquiring true labels is costly or time-consuming. We prove that AMKL achi…
In this paper, we suggest a framework to make use of mutual information as a regularization criterion to train Auto-Encoders (AEs). In the proposed framework, AEs are regularized by minimization of the mutual information between input and encoding variables of AEs during the training phase. In order to estimate the entropy of the encoding variables and the mutual information, we propose a non-parametric method. We also give an information theoretic view of Variational AEs (VAEs), which suggests that VAEs can be considered as parametric methods that estimate entropy. Experimental results show t…
Department of Computational Neuroscience, University Medical Center Hamburg-Eppendorf, Hamburg University（汉堡大学附属埃彭多夫医学中心计算神经科学系，汉堡大学）
The use of mutual information as a similarity measure in agglomerative hierarchical clustering (AHC) raises an important issue: some correction needs to be applied for the dimensionality of variables. In this work, we formulate the decision of merging dependent multivariate normal variables in an AHC procedure as a Bayesian model comparison. We found that the Bayesian formulation naturally shrinks the empirical covariance matrix towards a matrix set a priori (e.g., the identity), provides an automated stopping rule, and corrects for dimensionality using a term that scales up the measure as a f…
We introduce Polytopic Matrix Factorization (PMF) as a novel data decomposition approach. In this new framework, we model input data as unknown linear transformations of some latent vectors drawn from a polytope. In this sense, the article considers a semi-structured data model, in which the input matrix is modeled as the product of a full column rank matrix and a matrix containing samples from a polytope as its column vectors. The choice of polytope reflects the presumed features of the latent components and their mutual relationships. As the factorization criterion, we propose the determinan…
This work addresses testing the independence of two continuous and finite-dimensional random variables from the design of a data-driven partition. The empirical log-likelihood statistic is adopted to approximate the sufficient statistics of an oracle test against independence (that knows the two hypotheses). It is shown that approximating the sufficient statistics of the oracle test offers a learning criterion for designing a data-driven partition that connects with the problem of mutual information estimation. Applying these ideas in the context of a data-dependent tree-structured partition (…
Recently proposed methods in data subset selection, that is active learning and active sampling, use Fisher information, Hessians, similarity matrices based on gradients, and gradient lengths to estimate how informative data is for a model's training. Are these different approaches connected, and if so, how? We revisit the fundamentals of Bayesian optimal experiment design and show that these recently proposed methods can be understood as approximations to information-theoretic quantities: among them, the mutual information between predictions and model parameters, known as expected informatio…
We are assisting at a growing interest in the development of learning architectures with application to digital communication systems. Herein, we consider the detection/decoding problem. We aim at developing an optimal neural architecture for such a task. The definition of the optimal criterion is a fundamental step. We propose to use the mutual information (MI) of the channel input-output signal pair, which yields to the minimization of the a-posteriori information of the transmitted codeword given the communication channel output observation. The computation of the a-posteriori information i…
EECS University of Michigan（密歇根大学EECS学院）；CSE University of Maine（缅因大学计算机科学与工程学院）
Most approaches to deep neural network compression via pruning either evaluate a filter's importance using its weights or optimize an alternative objective function with sparsity constraints. While these methods offer a useful way to approximate contributions from similar filters, they often either ignore the dependency between layers or solve a more difficult optimization objective than standard cross-entropy. Our method, Mutual Information-based Neuron Trimming (MINT), approaches deep compression via pruning by enforcing sparsity based on the strength of the relationship between filters of a…
