arXiv subjects

Atsushi Nitanda

Publications and source records attributed to Atsushi Nitanda.

45 records · Page 3Linked to original sources

arXiv2021

BODAME: Bilevel Optimization for Defense Against Model Extraction

Model extraction attacks have become serious issues for service providers using machine learning. We consider an adversarial setting to prevent model extraction under the assumption that attackers will make their best guess on the service provider's model using query accesses, and propose to build a surrogate model that significantly keeps away the predictions of the attacker's model from those of the true model. We formulate the problem as a non-convex constrained bilevel optimization problem and show that for kernel models, it can be transformed into a non-convex 1-quadratically constrained quadratic program with a polynomial-time algorithm to find the global optimum. Moreover, we give a tractable transformation and an algorithm for more complicated models that are learned by using stochastic gradient descent-based algorithms. Numerical experiments show that the surrogate model performs well compared with existing defense models when the difference between the attacker's and service provider's distributions is large. We also empirically confirm the generalization ability of the surrogate model.

cs.LG↗

arXiv2020

When Does Preconditioning Help or Hurt Generalization?

While second order optimizers such as natural gradient descent (NGD) often speed up optimization, their effect on generalization has been called into question. This work presents a more nuanced view on how the \textit{implicit bias} of first- and second-order methods affects the comparison of generalization properties. We provide an exact asymptotic bias-variance decomposition of the generalization error of overparameterized ridgeless regression under a general class of preconditioner $\boldsymbol{P}$, and consider the inverse population Fisher information matrix (used in NGD) as a particular example. We determine the optimal $\boldsymbol{P}$ for both the bias and variance, and find that the relative generalization performance of different optimizers depends on the label noise and the "shape" of the signal (true parameters): when the labels are noisy, the model is misspecified, or the signal is misaligned with the features, NGD can achieve lower risk; conversely, GD generalizes better than NGD under clean labels, a well-specified model, or aligned signal. Based on this analysis, we discuss several approaches to manage the bias-variance tradeoff, and the potential benefit of interpolating between GD and NGD. We then extend our analysis to regression in the reproducing kernel Hilbert space and demonstrate that preconditioned GD can decrease the population risk faster than GD. Lastly, we empirically compare the generalization error of first- and second-order optimizers in neural network experiments, and observe robust trends matching our theoretical analysis.

stat.ML↗

arXiv2020

A Novel Global Spatial Attention Mechanism in Convolutional Neural Network for Medical Image Classification

Spatial attention has been introduced to convolutional neural networks (CNNs) for improving both their performance and interpretability in visual tasks including image classification. The essence of the spatial attention is to learn a weight map which represents the relative importance of activations within the same layer or channel. All existing attention mechanisms are local attentions in the sense that weight maps are image-specific. However, in the medical field, there are cases that all the images should share the same weight map because the set of images record the same kind of symptom related to the same object and thereby share the same structural content. In this paper, we thus propose a novel global spatial attention mechanism in CNNs mainly for medical image classification. The global weight map is instantiated by a decision boundary between important pixels and unimportant pixels. And we propose to realize the decision boundary by a binary classifier in which the intensities of all images at a pixel are the features of the pixel. The binary classification is integrated into an image classification CNN and is to be optimized together with the CNN. Experiments on two medical image datasets and one facial expression dataset showed that with the proposed attention, not only the performance of four powerful CNNs which are GoogleNet, VGG, ResNet, and DenseNet can be improved, but also meaningful attended regions can be obtained, which is beneficial for understanding the content of images of a domain.

eess.IV↗

arXiv2020

Gradient Descent can Learn Less Over-parameterized Two-layer Neural Networks on Classification Problems

Recently, several studies have proven the global convergence and generalization abilities of the gradient descent method for two-layer ReLU networks. Most studies especially focused on the regression problems with the squared loss function, except for a few, and the importance of the positivity of the neural tangent kernel has been pointed out. On the other hand, the performance of gradient descent on classification problems using the logistic loss function has not been well studied, and further investigation of this problem structure is possible. In this work, we demonstrate that the separability assumption using a neural tangent model is more reasonable than the positivity condition of the neural tangent kernel and provide a refined convergence analysis of the gradient descent for two-layer networks with smooth activations. A remarkable point of our result is that our convergence and generalization bounds have much better dependence on the network width in comparison to related studies. Consequently, our theory provides a generalization guarantee for less over-parameterized two-layer networks, while most studies require much higher over-parameterization.

stat.ML↗

arXiv2019

Data Cleansing for Models Trained with SGD

Data cleansing is a typical approach used to improve the accuracy of machine learning models, which, however, requires extensive domain knowledge to identify the influential instances that affect the models. In this paper, we propose an algorithm that can suggest influential instances without using any domain knowledge. With the proposed method, users only need to inspect the instances suggested by the algorithm, implying that users do not need extensive knowledge for this procedure, which enables even non-experts to conduct data cleansing and improve the model. The existing methods require the loss function to be convex and an optimal model to be obtained, which is not always the case in modern machine learning. To overcome these limitations, we propose a novel approach specifically designed for the models trained with stochastic gradient descent (SGD). The proposed method infers the influential instances by retracing the steps of the SGD while incorporating intermediate models computed in each step. Through experiments, we demonstrate that the proposed method can accurately infer the influential instances. Moreover, we used MNIST and CIFAR10 to show that the models can be effectively improved by removing the influential instances suggested by the proposed method.

stat.ML↗

arXiv2018

Functional Gradient Boosting based on Residual Network Perception

Residual Networks (ResNets) have become state-of-the-art models in deep learning and several theoretical studies have been devoted to understanding why ResNet works so well. One attractive viewpoint on ResNet is that it is optimizing the risk in a functional space by combining an ensemble of effective features. In this paper, we adopt this viewpoint to construct a new gradient boosting method, which is known to be very powerful in data analysis. To do so, we formalize the gradient boosting perspective of ResNet mathematically using the notion of functional gradients and propose a new method called ResFGB for classification tasks by leveraging ResNet perception. Two types of generalization guarantees are provided from the optimization perspective: one is the margin bound and the other is the expected risk bound by the sample-splitting technique. Experimental results show superior performance of the proposed method over state-of-the-art methods such as LightGBM.

stat.ML↗

arXiv2018

Gradient Layer: Enhancing the Convergence of Adversarial Training for Generative Models

We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep network is expressed using a highly non-convex finite-dimensional model, and thus the parameter gets stuck in a local optimum. Because of this, methods often suffer not only from degeneration of the convergence speed but also from limitations in the representational power of the trained network. To overcome this issue, we propose an additional layer called the gradient layer to seek a descent direction in an infinite-dimensional space. Because the layer is constructed in the infinite-dimensional space, we are not restricted by the specific model structure of finite-dimensional models. As a result, we can get out of the local optima in finite-dimensional models and move towards the global optimal function more directly. In this paper, this phenomenon is explained from the functional gradient method perspective of the gradient layer. Interestingly, the optimization procedure using the gradient layer naturally constructs the deep structure of the network. Moreover, we demonstrate that this procedure can be regarded as a discretization method of the gradient flow that naturally reduces the objective function. Finally, the method is tested using several numerical experiments, which show its fast convergence.

stat.ML↗

arXiv2017

Stochastic Particle Gradient Descent for Infinite Ensembles

The superior performance of ensemble methods with infinite models are well known. Most of these methods are based on optimization problems in infinite-dimensional spaces with some regularization, for instance, boosting methods and convex neural networks use $L^1$-regularization with the non-negative constraint. However, due to the difficulty of handling $L^1$-regularization, these problems require early stopping or a rough approximation to solve it inexactly. In this paper, we propose a new ensemble learning method that performs in a space of probability measures, that is, our method can handle the $L^1$-constraint and the non-negative constraint in a rigorous way. Such an optimization is realized by proposing a general purpose stochastic optimization method for learning probability measures via parameterization using transport maps on base models. As a result of running the method, a transport map to output an infinite ensemble is obtained, which forms a residual-type network. From the perspective of functional gradient methods, we give a convergence rate as fast as that of a stochastic optimization method for finite dimensional nonconvex problems. Moreover, we show an interior optimality property of a local optimality condition used in our analysis.

stat.ML↗

arXiv2015

Accelerated Stochastic Gradient Descent for Minimizing Finite Sums

We propose an optimization method for minimizing the finite sums of smooth convex functions. Our method incorporates an accelerated gradient descent (AGD) and a stochastic variance reduction gradient (SVRG) in a mini-batch setting. Unlike SVRG, our method can be directly applied to non-strongly and strongly convex problems. We show that our method achieves a lower overall complexity than the recently proposed methods that supports non-strongly convex problems. Moreover, this method has a fast rate of convergence for strongly convex problems. Our experiments show the effectiveness of our method.

stat.ML↗