[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors.

Sparse Online Learning With Kernels Using Random Features for Estimating Nonlinear Dynamic Graphs

We propose a novel Neyman-Pearson (NP) classifier that is both online and nonlinear as the first time in the literature. The proposed classifier operates on a binary labeled data stream in an online manner, and maximizes the detection power about a user-specified and controllable false positive rate. Our NP classifier is a single hidden layer feedforward neural network (SLFN), which is initialized with random Fourier features (RFFs) to construct the kernel space of the radial basis function at its hidden layer with sinusoidal activation. Not only does this use of RFFs provide an excellent initialization with great nonlinear modeling capability, but it also exponentially reduces the parameter complexity and compactifies the network to mitigate overfitting while improving the processing efficiency substantially. We sequentially learn the SLFN with stochastic gradient descent updates based on a Lagrangian NP objective. As a result, we obtain an expedited online adaptation and powerful nonlinear Neyman-Pearson modeling. Our algorithm is appropriate for large scale data applications and provides a decent false positive rate controllability with real time processing since it only has $O(N)$ computational and $O(1)$ space complexity ( $N$ : number of data instances). In our extensive set of experiments on several real datasets, our algorithm is highly superior over the competing state-of-the-art techniques, either by outperforming in terms of the NP classification objective with a comparable computational as well as space complexity or by achieving a comparable performance with significantly lower complexity.

/pdf/a-neural-network-approach-for-online-nonlinear-neyman-3wsbm0qxh6.pdf

A Neural Network Approach for Online Nonlinear Neyman-Pearson Classification

Compared with the classical constant false alarm ratio (CFAR) detector, the neural network (NN) based detector has data-driven representation learning ability, which can improve the detection performance of weak targets in a nonhomogeneous environment. Under the extreme sample imbalance scenario (ESIS) for marine radar, it is difficult to control the probability of false alarm (PFA) by a variable threshold for the network output by adopting the cross-entropy loss function. The Neyman Pearson (NP) criterion is used to find the optimal detector under the constraint of PFA in radar detection and may be used as a loss function for NN to realize false-alarm-controllable detection. However, it is nondifferentiable and cannot be used directly for NN. Therefore, firstly, we theoretically deduce two differentiable-NP loss functions for NNs under the ESIS to realize the NP criterion approximately. Secondly, we theoretically analyze the differentiable-NP loss under the ESIS from the gradient perspective. Thirdly, based on the differentiable-NP loss, we achieve the false-alarm-controllable detection under the ESIS by utilizing a lightweight U-Net segmentation network. Fourthly, to improve the PFA control capability of the segmentation network, we adopt a smaller fixed-size label for each target to reduce the influence of target random size, and we dynamically adjust the regular loss term to diminish the deviation caused by the nondifferentiable operation. The experimental results show that the proposed method can accurately control PFA and get a better detection performance compared to other methods in the measurement data from marine navigation radar. 

False-Alarm-Controllable Radar Target Detection by Differentiable Neyman Pearson Criterion for Neural Network

Online topology estimation of graph-connected time series is challenging in practice, particularly because the dependencies between the time series in many real-world scenarios are nonlinear. To address this challenge, we introduce a novel kernel-based algorithm for online graph topology estimation. Our proposed algorithm also performs a Fourier-based random feature approximation to tackle the curse of dimensionality associated with kernel representations. Exploiting the fact that real-world networks often exhibit sparse topologies, we propose a group-Lasso based optimization framework, which is solved using an iterative composite objective mirror descent method, yielding an online algorithm with fixed computational complexity per iteration. We provide theoretical guarantees for our algorithm and prove that it can achieve sublinear dynamic regret under certain reasonable assumptions. In experiments conducted on both real and synthetic data, our method outperforms existing state-of-the-art competitors. 

/pdf/sparse-online-learning-with-kernels-using-random-features-1db3515r.pdf

In binary classification problems, such as network intrusion detection, class specific observations are unevenly distributed, and the target class (suspicious activity in the network) is rarely observed compared to the non-target (ordinary network operations). Therefore, type I error (prediction of a non-target observation as target) and type II error (failure to detect target) have different consequences. For example, a network security system that generates too many false alarms (type I error), loses its reliability as it will cause rigorous but unnecessary measures to be taken. For this reason, asymmetric class costs should be used in the designed classifiers and the type I error should be controlled directly. To this end, the Neyman-Pearson (NP) classification framework is suitable for binary classification problems under asymmetric error costs, since it minimizes type II error and keeps type I error below a user-specified threshold. In this paper, we propose an NP classification method that solves 1Bu calisma Turkiye Bilimsel ve Teknolojik Arastirma Kurumu (TUBITAK) tarafindan 118E268 sozlesme numarali arastirma projesi kapsaminda desteklenmektedir nonlinear problems via context trees in an online manner. The performance analysis of the proposed method is performed on well-known data sets and the classification behavior is investigated on the basis of ROC (receiver operating characteristics) curves as well as the capability to achieve the desired type I error. According to our analyzes, the proposed algorithm successfully provides an average of 66% increase in the area under the ROC curve along with a precise control over the desired type I error, compared to the algorithms that do not use context trees and can only solve linear problems.

Neyman-Pearson Classification Via Context Trees

We propose a novel Neyman-Pearson (NP) classification algorithm, which achieves the maximum detection rate and meanwhile keeps the false alarm rate around a user-specified threshold. The proposed method processes data in an online framework with nonlinear modeling capabilities by transforming the observations into a high dimensional space via the random Fourier features. After this transformation, we use a linear classifier whose parameters are sequentially learned. We emphasize that our algorithm is the first online Neyman-Pearson classifier in the literature, which is suitable for both linearly and nonlinearly separable datasets. In our experiments, we investigate the performance of our algorithm on well-known datasets and observe that the proposed online algorithm successfully learns the nonlinear class separations (by outperforming the linear models) while matching the desired false alarm rate.

Online Kernel-Based Nonlinear Neyman-Pearson Classification

We propose a novel Neyman-Pearson (NP) classifier that is both online and nonlinear as the first time in the literature. The proposed classifier operates on a binary labeled data stream in an online manner, and maximizes the detection power about a user-specified and controllable false positive rate. Our NP classifier is a single hidden layer feedforward neural network (SLFN), which is initialized with random Fourier features (RFFs) to construct the kernel space of the radial basis function at its hidden layer with sinusoidal activation. Not only does this use of RFFs provide an excellent initialization with great nonlinear modeling capability, but it also exponentially reduces the parameter complexity and compactifies the network to mitigate overfitting while improving the processing efficiency substantially. We sequentially learn the SLFN with stochastic gradient descent updates based on a Lagrangian NP objective. As a result, we obtain an expedited online adaptation and powerful nonlinear Neyman-Pearson modeling. Our algorithm is appropriate for large scale data applications and provides a decent false positive rate controllability with real time processing since it only has O(N) computational and O(1) space complexity (N: number of data instances). In our extensive set of experiments on several real datasets, our algorithm is highly superior over the competing state-of-the-art techniques, either by outperforming in terms of the NP classification objective with a comparable computational as well as space complexity or by achieving a comparable performance with significantly lower complexity.

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A Neural Network Approach for Online Nonlinear Neyman-Pearson Classification

Neyman-Pearson Classification Via Context Trees

Online Kernel-Based Nonlinear Neyman-Pearson Classification

A Neural Network Approach for Online Nonlinear Neyman-Pearson Classification