Adaptive algorithms based on kernel structures have been a topic of significant research over the past few years. The main advantage is that they form a family of universal approximators, offering an elegant solution to problems with nonlinearities. Nevertheless these methods deal with kernel expansions, creating a growing structure also known as dictionary, whose size depends on the number of new inputs. In this paper we derive the set-membership kernel-based normalized least-mean square (SM-NKLMS) algorithm, which is capable of limiting the size of the dictionary created in stationary environments. We also derive as an extension the set-membership kernelized affine projection (SM-KAP) algorithm. Finally several experiments are presented to compare the proposed SM-NKLMS and SM-KAP algorithms to the existing methods.
In this paper we study the adaptive learnability of decision trees of depth at most $d$ from membership queries. This has many applications in automated scientific discovery such as drugs development and software update problem. Feldman solves the problem in a randomized polynomial time algorithm that asks $\tilde O(2^{2d})\log n$ queries and Kushilevitz-Mansour in a deterministic polynomial time algorithm that asks $ 2^{18d+o(d)}\log n$ queries. We improve the query complexity of both algorithms. We give a randomized polynomial time algorithm that asks $\tilde O(2^{2d}) + 2^{d}\log n$ queries…
Centre for Telecommunications Studies (CETUC), PUC-Rio（里约热内卢天主教大学电信研究中心（CETUC））；University of York（约克大学）
In the last decade, a considerable research effort has been devoted to developing adaptive algorithms based on kernel functions. One of the main features of these algorithms is that they form a family of universal approximation techniques, solving problems with nonlinearities elegantly. In this paper, we present data-selective adaptive kernel normalized least-mean square (KNLMS) algorithms that can increase their learning rate and reduce their computational complexity. In fact, these methods deal with kernel expansions, creating a growing structure also known as the dictionary, whose size depe…
Google AI Princeton（谷歌AI普林斯顿）；Princeton University（普林斯顿大学）；UC Berkeley（加州大学伯克利分校）
In the framework of online convex optimization, most iterative algorithms require the computation of projections onto convex sets, which can be computationally expensive. To tackle this problem HK12 proposed the study of projection-free methods that replace projections with less expensive computations. The most common approach is based on the Frank-Wolfe method, that uses linear optimization computation in lieu of projections. Recent work by GK22 gave sublinear adaptive regret guarantees with projection free algorithms based on the Frank Wolfe approach. In this work we give projection-free alg…
Princeton University（普林斯顿大学）；Meta AI；University of Wisconsin（威斯康星大学）
Given a trained model and a data sample, membership-inference (MI) attacks predict whether the sample was in the model's training set. A common countermeasure against MI attacks is to utilize differential privacy (DP) during model training to mask the presence of individual examples. While this use of DP is a principled approach to limit the efficacy of MI attacks, there is a gap between the bounds provided by DP and the empirical performance of MI attacks. In this paper, we derive bounds for the \textit{advantage} of an adversary mounting a MI attack, and demonstrate tightness for the widely-…
In traditional ELM and its improved versions suffer from the problems of outliers or noises due to overfitting and imbalance due to distribution. We propose a novel hybrid adaptive fuzzy ELM(HA-FELM), which introduces a fuzzy membership function to the traditional ELM method to deal with the above problems. We define the fuzzy membership function not only basing on the distance between each sample and the center of the class but also the density among samples which based on the quantum harmonic oscillator model. The proposed fuzzy membership function overcomes the shortcoming of the traditiona…
School of Electronics and Information Technology, Sun Yat-Sen University（中山大学电子与信息工程学院）
Reproducing Kernel Hilbert Space (RKHS) is the common mathematical platform for various kernel methods in machine learning. The purpose of kernel learning is to learn an appropriate RKHS according to different machine learning scenarios and training samples. Because RKHS is uniquely generated by the kernel function, kernel learning can be regarded as kernel function learning. This paper proposes a Domain Adaptive Learning method based on Sample-Dependent and Learnable Kernels (SDLK-DAL). The first contribution of our work is to propose a sample-dependent and learnable Positive Definite Quadrat…
University of Cambridge（剑桥大学）；MPI for Intelligent Systems（马克斯·普朗克智能系统研究所）
We propose Adaptive Deep Kernel Fitting with Implicit Function Theorem (ADKF-IFT), a novel framework for learning deep kernel Gaussian processes (GPs) by interpolating between meta-learning and conventional deep kernel learning. Our approach employs a bilevel optimization objective where we meta-learn generally useful feature representations across tasks, in the sense that task-specific GP models estimated on top of such features achieve the lowest possible predictive loss on average. We solve the resulting nested optimization problem using the implicit function theorem (IFT). We show that our…
Multiple kernel methods based on k-means aims to integrate a group of kernels to improve the performance of kernel k-means clustering. However, we observe that most existing multiple kernel k-means methods exploit the nonlinear relationship within kernels, whereas the local manifold structure among multiple kernel space is not sufficiently considered. In this paper, we adopt the manifold adaptive kernel, instead of the original kernel, to integrate the local manifold structure of kernels. Thus, the induced multiple manifold adaptive kernels not only reflect the nonlinear relationship but also …
In this work, we propose two low-complexity set-membership normalized least-mean-square (LCSM-NLMS1 and LCSM-NLMS2) algorithms to exploit the sparsity of an unknown system. For this purpose, in the LCSM-NLMS1 algorithm, we employ a function called the discard function to the adaptive coefficients in order to neglect the coefficients close to zero in the update process. Moreover, in the LCSM-NLMS2 algorithm, to decrease the overall number of computations needed even further, we substitute small coefficients with zero. Numerical results present similar performance of these algorithms when compar…
Robust Non-adaptive Group Testing under Errors in Group Membership Specifications
IITB-Monash Research Academy（IITB-墨尔本研究学院）；Department of Mathematics, IIT Bombay（数学系，IIT 巴纳拉西）；Department of Electrical and Computer Systems Engineering, Monash University（电气与计算机系统工程系，墨尔本大学）；Department of Computer Science and Engineering, IIT Bombay（计算机科学与工程系，IIT 巴纳拉西）
We propose cKAM, cyclical Kernel Adaptive Metropolis, which incorporates a cyclical stepsize scheme to allow control for exploration and sampling. We show that on a crafted bimodal distribution, existing Adaptive Metropolis type algorithms would fail to converge to the true posterior distribution. We point out that this is because adaptive samplers estimates the local/global covariance structure using past history of the chain, which will lead to adaptive algorithms be trapped in a local mode. We demonstrate that cKAM encourages exploration of the posterior distribution and allows the sampler …
Tokyo University of Agriculture and Technology（东京农工大学）；Università Politecnica delle Marche（马尔凯理工大学）
The present paper proposes generalized Gaussian kernel adaptive filtering, where the kernel parameters are adaptive and data-driven. The Gaussian kernel is parametrized by a center vector and a symmetric positive definite (SPD) precision matrix, which is regarded as a generalization of the scalar width parameter. These parameters are adaptively updated on the basis of a proposed least-square-type rule to minimize the estimation error. The main contribution of this paper is to establish update rules for precision matrices on the SPD manifold in order to keep their symmetric positive-definitenes…
This paper discusses a special kind of a simple yet possibly powerful algorithm, called single-kernel Gradraker (SKG), which is an adaptive learning method predicting unknown nodal values in a network using known nodal values and the network structure. We aim to find out how to configure the special kind of the model in applying the algorithm. To be more specific, we focus on SKG with a Gaussian kernel and specify how to find a suitable variance for the kernel. To do so, we introduce two variables with which we are able to set up requirements on the variance of the Gaussian kernel to achieve (…
Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel operator that can be combined with a differentiable kernel algorithm during inference. While previous work within this framework has focused on learning a single kernel for large datasets, we learn a kernel family for a variety of few-shot regression tasks. Compared to single deep kernel learning, our algorithm enables the identification of the appropriate k…
KU Leuven（鲁汶大学）；Shanghai Jiao Tong University（上海交通大学）；Nanjing University of Science and Technology（南京理工大学）；Hong Kong Polytechnic University（香港理工大学）；Tsinghua University（清华大学）
In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise scheme. Learning this data-adaptive matrix in a formulation-free strategy enlarges the margin between classes and thus improves the model flexibility. The introduced two constraints are imposed either exactly (on small data sets) or approximately (on large data sets) in our model, which provides a controllable trade-off between model flexibility and complex…
We introduce a balloon estimator in a generalized expectation-maximization method for estimating all parameters of a Gaussian mixture model given one data sample per mixture component. Instead of limiting explicitly the model size, this regularization strategy yields low-complexity sparse models where the number of effective mixture components reduces with an increase of a smoothing probability parameter $\mathbf{P>0}$. This semi-parametric method bridges from non-parametric adaptive kernel density estimation (KDE) to parametric ordinary least-squares when $\mathbf{P=1}$. Experiments show that…
Iqra University（伊克拉大学）；The University of Western Australia（西澳大学）
In this paper, we propose a novel adaptive kernel for the radial basis function (RBF) neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels using the gradient descent method thereby alleviating the need for predetermined weights. The proposed method is shown to outperform the manual fusion of the kernels on three major problems of estimation namely nonlinear system identification, pattern classification and function ap…
Recent technology and equipment advancements provide with us opportunities to better analyze Alzheimer's disease (AD), where we could collect and employ the data from different image and genetic modalities that may potentially enhance the predictive performance. To perform better clustering in AD analysis, in this paper we propose a novel model to leverage data from all different modalities/views, which can learn the weights of each view adaptively. Different from previous vanilla Non-negative Matrix Factorization which assumes data is linearly separable, we propose a simple yet efficient meth…
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Institute of Software, Chinese Academy of Sciences（中国科学院软件研究所）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
Existing multi-view learning methods based on kernel function either require the user to select and tune a single predefined kernel or have to compute and store many Gram matrices to perform multiple kernel learning. Apart from the huge consumption of manpower, computation and memory resources, most of these models seek point estimation of their parameters, and are prone to overfitting to small training data. This paper presents an adaptive kernel nonlinear max-margin multi-view learning model under the Bayesian framework. Specifically, we regularize the posterior of an efficient multi-view la…
Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；COPPE（COPPE（巴西里约热内卢联邦大学工程研究生院））
Adaptive filters are applied in several electronic and communication devices like smartphones, advanced headphones, DSP chips, smart antenna, and teleconference systems. Also, they have application in many areas such as system identification, channel equalization, noise reduction, echo cancellation, interference cancellation, signal prediction, and stock market. Therefore, reducing the energy consumption of the adaptive filtering algorithms has great importance, particularly in green technologies and in devices using battery. In this thesis, data-selective adaptive filters, in particular the s…
Adaptive kernel predictors from feature-learning infinite limits of neural networks
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保罗森工程与应用科学学校）；Center for Brain Sciences（脑科学中心）；Kempner Institute（凯普纳研究所）
