We prove that, under low noise assumptions, the support vector machine with $N\ll m$ random features (RFSVM) can achieve the learning rate faster than $O(1/\sqrt{m})$ on a training set with $m$ samples when an optimized feature map is used. Our work extends the previous fast rate analysis of random features method from least square loss to 0-1 loss. We also show that the reweighted feature selection method, which approximates the optimized feature map, helps improve the performance of RFSVM in experiments on a synthetic data set.
One-class support vector machine (OC-SVM) for a long time has been one of the most effective anomaly detection methods and extensively adopted in both research as well as industrial applications. The biggest issue for OC-SVM is yet the capability to operate with large and high-dimensional datasets due to optimization complexity. Those problems might be mitigated via dimensionality reduction techniques such as manifold learning or autoencoder. However, previous work often treats representation learning and anomaly prediction separately. In this paper, we propose autoencoder based one-class supp…
Toyota Technological Institute at Chicago（芝加哥丰田理工学院）；Ben-Gurion University（本-古里安大学）
We analyze a family of supervised learning algorithms based on sample compression schemes that are stable, in the sense that removing points from the training set which were not selected for the compression set does not alter the resulting classifier. We use this technique to derive a variety of novel or improved data-dependent generalization bounds for several learning algorithms. In particular, we prove a new margin bound for SVM, removing a log factor. The new bound is provably optimal. This resolves a long-standing open question about the PAC margin bounds achievable by SVM.
We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised approach is based on sampling features from support vectors. We prove that the margin in the feature space is preserved to within $ε$-relative error of the margin in the full feature space in the worst-case. In the unsupervised setting, we also provide worst-case guarantees of the radius of the minimum enclosing ball, thereby ensuring comparable generalization as i…
Emotion recognition has become a major problem in computer vision in recent years that made a lot of effort by researchers to overcome the difficulties in this task. In the field of affective computing, emotion recognition has a wide range of applications, such as healthcare, robotics, human-computer interaction. Due to its practical importance for other tasks, many techniques and approaches have been investigated for different problems and various data sources. Nevertheless, comprehensive fusion of the audio-visual and language modalities to get the benefits from them is still a problem to so…
Computing Institute University of Campinas（坎皮纳斯大学计算研究所）；Facultad de Ciencias y Filosofía Universidad Peruana Cayetano Heredia（秘鲁卡耶塔诺埃雷迪亚大学科学与哲学学院）
SVM with an RBF kernel is usually one of the best classification algorithms for most data sets, but it is important to tune the two hyperparameters $C$ and $γ$ to the data itself. In general, the selection of the hyperparameters is a non-convex optimization problem and thus many algorithms have been proposed to solve it, among them: grid search, random search, Bayesian optimization, simulated annealing, particle swarm optimization, Nelder Mead, and others. There have also been proposals to decouple the selection of $γ$ and $C$. We empirically compare 18 of these proposed search algorithms (wit…
This article proposes a performance analysis of kernel least squares support vector machines (LS-SVMs) based on a random matrix approach, in the regime where both the dimension of data $p$ and their number $n$ grow large at the same rate. Under a two-class Gaussian mixture model for the input data, we prove that the LS-SVM decision function is asymptotically normal with means and covariances shown to depend explicitly on the derivatives of the kernel function. This provides improved understanding along with new insights into the internal workings of SVM-type methods for large datasets.
Based on the BioBricks standard, restriction synthesis is a novel catabolic iterative DNA synthesis method that utilizes endonucleases to synthesize a query sequence from a reference sequence. In this work, the reference sequence is built from shorter subsequences by classifying them as applicable or inapplicable for the synthesis method using three different machine learning methods: Support Vector Machines (SVMs), random forest, and Convolution Neural Networks (CNNs). Before applying these methods to the data, a series of feature selection, curation, and reduction steps are applied to create…
National Taiwan University（国立台湾大学）；Academia Sinica（中央研究院）
Machine learning algorithms, such as Support Vector Machine (SVM) and Deep Neural Network (DNN), have gained a lot of interests recently. When training a machine learning algorithm, randomly shuffle all the training data can improve the testing accuracy and boost the convergence rate. Nevertheless, realizing training data random shuffling in a real system is not a straightforward process due to the slow random accesses in hard disk drive (HDD). To avoid frequent random disk access, the effect of random shuffling is often limited in existing approaches. With the emerging non-volatile memory-bas…
School of Microelectornics and Communication Engineering, Chongqing University（重庆大学微电子与通信工程学院）
Deep learning is a kind of feature learning method with strong nonliear feature transformation and becomes more and more important in many fields of artificial intelligence. Deep autoencoder is one representative method of the deep learning methods, and can effectively extract abstract the information of datasets. However, it does not consider the complementarity between the deep features and original features during deep feature transformation. Besides, it suffers from small sample problem. In order to solve these problems, a novel deep autoencoder - hybrid feature embedded stacked sparse aut…
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…
Columbia University（哥伦比亚大学）；Nanyang Technological University（南洋理工大学）；Toyota Technological Institute at Chicago（芝加哥丰田工业大学）；Carnegie Mellon University（卡内基梅隆大学）
We study the space complexity of solving the bias-regularized SVM problem in the streaming model. This is a classic supervised learning problem that has drawn lots of attention, including for developing fast algorithms for solving the problem approximately. One of the most widely used algorithms for approximately optimizing the SVM objective is Stochastic Gradient Descent (SGD), which requires only $O(\frac{1}{λε})$ random samples, and which immediately yields a streaming algorithm that uses $O(\frac{d}{λε})$ space. For related problems, better streaming algorithms are only known for smooth fu…
Princeton University（普林斯顿大学）；Institute for Advanced Study（高等研究院）；Carnegie Mellon University（卡内基梅隆大学）
Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient algorithm to compute the NTK, as well as its convolutional counterparts, appears in Arora et al. (2019a), which allowed studying performance of infinitely wide nets on datasets like CIFAR-10. However, super-quadratic running time of kernel methods makes them best suited for small-data tasks. W…
The Ohio State University（俄亥俄州立大学）；Dalian University of Technology（大连理工大学）
We study the implicit bias of AdaGrad on separable linear classification problems. We show that AdaGrad converges to a direction that can be characterized as the solution of a quadratic optimization problem with the same feasible set as the hard SVM problem. We also give a discussion about how different choices of the hyperparameters of AdaGrad might impact this direction. This provides a deeper understanding of why adaptive methods do not seem to have the generalization ability as good as gradient descent does in practice.
Aristotle University of Thessaloniki（塞萨洛尼基亚里士多德大学）
We reconsider the stochastic (sub)gradient approach to the unconstrained primal L1-SVM optimization. We observe that if the learning rate is inversely proportional to the number of steps, i.e., the number of times any training pattern is presented to the algorithm, the update rule may be transformed into the one of the classical perceptron with margin in which the margin threshold increases linearly with the number of steps. Moreover, if we cycle repeatedly through the possibly randomly permuted training set the dual variables defined naturally via the expansion of the weight vector as a linea…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image descriptors, as well as computational and memory efficiency. This paper introduces a novel kernel, which serves such issues well. The kernel is learned by exploiting a large amount of low-complex, randomized binary mappings of the input feature. This leads to an efficient SVM, while also alleviating the task of kernel selection. We demonstrate the capabilities of …
Subsampled Randomized Hadamard Transform (SRHT), a popular random projection method that can efficiently project a $d$-dimensional data into $r$-dimensional space ($r \ll d$) in $O(dlog(d))$ time, has been widely used to address the challenge of high-dimensionality in machine learning. SRHT works by rotating the input data matrix $\mathbf{X} \in \mathbb{R}^{n \times d}$ by Randomized Walsh-Hadamard Transform followed with a subsequent uniform column sampling on the rotated matrix. Despite the advantages of SRHT, one limitation of SRHT is that it generates the new low-dimensional embedding with…
Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université Paul Sabatier（保尔·萨巴蒂埃大学）
We consider the binary classification problem when data are large and subject to unknown but bounded uncertainties. We address the problem by formulating the nonlinear support vector machine training problem with robust optimization. To do so, we analyze and propose two bounding schemes for uncertainties associated to random approximate features in low dimensional spaces. The proposed techniques are based on Random Fourier Features and the Nyström methods. The resulting formulations can be solved with efficient stochastic approximation techniques such as stochastic (sub)-gradient, stochastic p…
Indian Institute of Technology Indore（印度理工学院印多尔分校）；University of Manitoba（曼尼托巴大学）
Machine learning models have been successfully employed in the diagnosis of Schizophrenia disease. The impact of classification models and the feature selection techniques on the diagnosis of Schizophrenia have not been evaluated. Here, we sought to access the performance of classification models along with different feature selection approaches on the structural magnetic resonance imaging data. The data consist of 72 subjects with Schizophrenia and 74 healthy control subjects. We evaluated different classification algorithms based on support vector machine (SVM), random forest, kernel ridge r…
In the era of big data, an important weapon in a machine learning researcher's arsenal is a scalable Support Vector Machine (SVM) algorithm. SVMs are extensively used for solving classification problems. Traditional algorithms for learning SVMs often scale super linearly with training set size which becomes infeasible very quickly for large data sets. In recent years, scalable algorithms have been designed which study the primal or dual formulations of the problem. This often suggests a way to decompose the problem and facilitate development of distributed algorithms. In this paper, we present…
Univ Lyon（里昂大学）；UJM-Saint-Etienne（圣埃蒂安让·莫内大学）；CNRS（法国国家科学研究中心）；Institut d Optique Graduate School（法国光学研究生院）
For their ability to capture non-linearities in the data and to scale to large training sets, local Support Vector Machines (SVMs) have received a special attention during the past decade. In this paper, we introduce a new local SVM method, called L$^3$-SVMs, which clusters the input space, carries out dimensionality reduction by projecting the data on landmarks, and jointly learns a linear combination of local models. Simple and effective, our algorithm is also theoretically well-founded. Using the framework of Uniform Stability, we show that our SVM formulation comes with generalization guar…
Microbial clades modeling is a challenging problem in biology based on microarray genome sequences, especially in new species gene isolates discovery and category. Marker family genome sequences play important roles in describing specific microbial clades within species, a framework of support vector machine (SVM) based microbial species classification with N-best algorithm is constructed to classify the centroid marker genome fragments randomly generated from marker genome sequences on MetaRef. A time series feature extraction method is proposed by segmenting the centroid gene sequences and m…
University of Toronto（多伦多大学）；Microsoft Research（微软研究院）
We propose a novel algorithm for optimizing multivariate linear threshold functions as split functions of decision trees to create improved Random Forest classifiers. Standard tree induction methods resort to sampling and exhaustive search to find good univariate split functions. In contrast, our method computes a linear combination of the features at each node, and optimizes the parameters of the linear combination (oblique) split functions by adopting a variant of latent variable SVM formulation. We develop a convex-concave upper bound on the classification loss for a one-level decision tree…
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, fits into the framework of RC-FDM. We prove linear convergence for both R-FDM and RC-FDM under the weak strong convexity assumption. Moreover, we show that the duality gap converges linearly for RC-FDM, which implies that the duality gap also converges linearly for SDCA applied to…
University of Siena（锡耶纳大学）；Xidian University（西安电子科技大学）
We investigate if the random feature selection approach proposed in [1] to improve the robustness of forensic detectors to targeted attacks, can be extended to detectors based on deep learning features. In particular, we study the transferability of adversarial examples targeting an original CNN image manipulation detector to other detectors (a fully connected neural network and a linear SVM) that rely on a random subset of the features extracted from the flatten layer of the original network. The results we got by considering three image manipulation detection tasks (resizing, median filterin…
Centers for Disease Control and Prevention（美国疾病控制与预防中心）
The Centers for Disease Control and Prevention (CDC) coordinates a labor-intensive process to measure the prevalence of autism spectrum disorder (ASD) among children in the United States. Random forests methods have shown promise in speeding up this process, but they lag behind human classification accuracy by about 5%. We explore whether more recently available document classification algorithms can close this gap. We applied 8 supervised learning algorithms to predict whether children meet the case definition for ASD based solely on the words in their evaluations. We compared the algorithms'…
IIIT Kalyani（卡利亚尼印度信息技术学院）；University of Padova（帕多瓦大学）；INRIA（法国国家信息与自动化研究所）；ENS | PSL（巴黎高等师范学院（巴黎文理研究大学））
We propose a symbolic representation for support vector machines (SVMs) by means of abstract interpretation, a well-known and successful technique for designing and implementing static program analyses. We leverage this abstraction in two ways: (1) to enhance the interpretability of SVMs by deriving a novel feature importance measure, called abstract feature importance (AFI), that does not depend in any way on a given dataset of the accuracy of the SVM and is very fast to compute, and (2) for verifying stability, notably individual fairness, of SVMs and producing concrete counterexamples when …
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear non-linearities such as the commonly used ReLU and max-pool, and an SVM classifier as the final layer. The key observation of our approach is that the problem corresponding to the parameter estimation of a layer can be formulated as a difference-of-convex (DC) program, which happens to be a latent structured SVM. We optimize the DC program using the concave-convex…
University of Chinese Academy of Sciences（中国科学院大学）；Chinese Academy of Sciences（中国科学院）；Beijing Union University（北京联合大学）
Multi-label classification studies the task where each example belongs to multiple labels simultaneously. As a representative method, Ranking Support Vector Machine (Rank-SVM) aims to minimize the Ranking Loss and can also mitigate the negative influence of the class-imbalance issue. However, due to its stacking-style way for thresholding, it may suffer error accumulation and thus reduces the final classification performance. Binary Relevance (BR) is another typical method, which aims to minimize the Hamming Loss and only needs one-step learning. Nevertheless, it might have the class-imbalance…
We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpreting our algorithm as online equilibrium-finding dynamics in a certain two-player min-max game. Evaluations on synthetic and real-world datasets demonstrate scalability and consistent improvements over related random features-based methods.
Middle Tennessee State University（中田纳西州立大学）；Goats（三羊公司）
Nowadays, CAPTCHAs are computer generated tests that human can pass but current computer systems can not. They have common usage in various web services in order to be able to detect a human from computer programs autonomously. In this way, owners can protect their web services from bots. In addition to visual CAPTCHAs which consist of distorted images, mostly test images, that a user must write some description about that image, there are a significant amount of audio CAPTCHAs as well. Briefly, audio CAPTCHAs are sound files which consist of human sound under heavy noise where the speaker pro…
Machine learning is widely used in developing computer-aided diagnosis (CAD) schemes of medical images. However, CAD usually computes large number of image features from the targeted regions, which creates a challenge of how to identify a small and optimal feature vector to build robust machine learning models. In this study, we investigate feasibility of applying a random projection algorithm to build an optimal feature vector from the initially CAD-generated large feature pool and improve performance of machine learning model. We assemble a retrospective dataset involving 1,487 cases of mamm…
Computing Institute（计算研究所）；University of Campinas（坎皮纳斯大学）
We tested 14 very different classification algorithms (random forest, gradient boosting machines, SVM - linear, polynomial, and RBF - 1-hidden-layer neural nets, extreme learning machines, k-nearest neighbors and a bagging of knn, naive Bayes, learning vector quantization, elastic net logistic regression, sparse linear discriminant analysis, and a boosting of linear classifiers) on 115 real life binary datasets. We followed the Demsar analysis and found that the three best classifiers (random forest, gbm and RBF SVM) are not significantly different from each other. We also discuss that a chang…
Several recent studies in privacy-preserving learning have considered the trade-off between utility or risk and the level of differential privacy guaranteed by mechanisms for statistical query processing. In this paper we study this trade-off in private Support Vector Machine (SVM) learning. We present two efficient mechanisms, one for the case of finite-dimensional feature mappings and one for potentially infinite-dimensional feature mappings with translation-invariant kernels. For the case of translation-invariant kernels, the proposed mechanism minimizes regularized empirical risk in a rand…
University of Tennessee at Chattanooga（田纳西大学查塔努加分校）
It is estimated that the number of IoT devices will reach 75 billion in the next five years. Most of those currently, and to be deployed, lack sufficient security to protect themselves and their networks from attack by malicious IoT devices that masquerade as authorized devices to circumvent digital authentication approaches. This work presents a PHY layer IoT authentication approach capable of addressing this critical security need through the use of feature reduced Radio Frequency-Distinct Native Attributes (RF-DNA) fingerprints and Support Vector Machines (SVM). This work successfully demon…
Amrita Vishwa Vidyapeetham（阿姆里塔·维什瓦·维迪亚皮塔姆大学）；Amrita School of Engineering（阿姆里塔工程学院）
Irrespective of the fact that Machine learning has produced groundbreaking results, it demands an enormous amount of data in order to perform so. Even though data production has been in its all-time high, almost all the data is unlabelled, hence making them unsuitable for training the algorithms. This paper proposes a novel method of extracting the features using Dynamic Mode Decomposition (DMD). The experiment is performed using data samples from Imagenet. The learning is done using SVM-linear, SVM-RBF, Random Kitchen Sink approach (RKS). The results have shown that DMD features with RKS give…
Hajee Mohammad Danesh Science and Technology University（哈吉·穆罕默德·达内什科技大学）
Bangla Handwritten Digit recognition is a significant step forward in the development of Bangla OCR. However, intricate shape, structural likeness and distinctive composition style of Bangla digits makes it relatively challenging to distinguish. Thus, in this paper, we benchmarked four rigorous classifiers to recognize Bangla Handwritten Digit: K-Nearest Neighbor (KNN), Support Vector Machine (SVM), Random Forest (RF), and Gradient-Boosted Decision Trees (GBDT) based on three handcrafted feature extraction techniques: Histogram of Oriented Gradients (HOG), Local Binary Pattern (LBP), and Gabor…
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）
Approximating non-linear kernels using feature maps has gained a lot of interest in recent years due to applications in reducing training and testing times of SVM classifiers and other kernel based learning algorithms. We extend this line of work and present low distortion embeddings for dot product kernels into linear Euclidean spaces. We base our results on a classical result in harmonic analysis characterizing all dot product kernels and use it to define randomized feature maps into explicit low dimensional Euclidean spaces in which the native dot product provides an approximation to the do…
École Polytechnique（巴黎综合理工学院）；Pennsylvania State University（宾夕法尼亚州立大学）
Random Fourier features (RFF) represent one of the most popular and wide-spread techniques in machine learning to scale up kernel algorithms. Despite the numerous successful applications of RFFs, unfortunately, quite little is understood theoretically on their optimality and limitations of their performance. Only recently, precise statistical-computational trade-offs have been established for RFFs in the approximation of kernel values, kernel ridge regression, kernel PCA and SVM classification. Our goal is to spark the investigation of optimality of RFF-based approximations in tasks involving …
Georgia Institute of Technology（佐治亚理工学院）；University of Washington（华盛顿大学）；University of California Berkeley（加州大学伯克利分校）；UC San Diego（加州大学圣地亚哥分校）；Columbia University（哥伦比亚大学）
We compare classification and regression tasks in an overparameterized linear model with Gaussian features. On the one hand, we show that with sufficient overparameterization all training points are support vectors: solutions obtained by least-squares minimum-norm interpolation, typically used for regression, are identical to those produced by the hard-margin support vector machine (SVM) that minimizes the hinge loss, typically used for training classifiers. On the other hand, we show that there exist regimes where these interpolating solutions generalize well when evaluated by the 0-1 test lo…
The University of Adelaide（阿德莱德大学）；The Australian National University（澳大利亚国立大学）；NICTA（澳大利亚国家信息与通信技术研究院）
We propose a novel hybrid loss for multiclass and structured prediction problems that is a convex combination of log loss for Conditional Random Fields (CRFs) and a multiclass hinge loss for Support Vector Machines (SVMs). We provide a sufficient condition for when the hybrid loss is Fisher consistent for classification. This condition depends on a measure of dominance between labels - specifically, the gap in per observation probabilities between the most likely labels. We also prove Fisher consistency is necessary for parametric consistency when learning models such as CRFs. We demonstrate e…
The method of random projections has become very popular for large-scale applications in statistical learning, information retrieval, bio-informatics and other applications. Using a well-designed coding scheme for the projected data, which determines the number of bits needed for each projected value and how to allocate these bits, can significantly improve the effectiveness of the algorithm, in storage cost as well as computational speed. In this paper, we study a number of simple coding schemes, focusing on the task of similarity estimation and on an application to training linear classifier…
