arXiv subjects

Zhi-Hua Zhou

Publications and source records attributed to Zhi-Hua Zhou.

At least 109 records · Page 6Linked to original sources

arXiv2019

Learning to Confuse: Generating Training Time Adversarial Data with Auto-Encoder

In this work, we consider one challenging training time attack by modifying training data with bounded perturbation, hoping to manipulate the behavior (both targeted or non-targeted) of any corresponding trained classifier during test time when facing clean samples. To achieve this, we proposed to use an auto-encoder-like network to generate the pertubation on the training data paired with one differentiable system acting as the imaginary victim classifier. The perturbation generator will learn to update its weights by watching the training procedure of the imaginary classifier in order to produce the most harmful and imperceivable noise which in turn will lead the lowest generalization power for the victim classifier. This can be formulated into a non-linear equality constrained optimization problem. Unlike GANs, solving such problem is computationally challenging, we then proposed a simple yet effective procedure to decouple the alternating updates for the two networks for stability. The method proposed in this paper can be easily extended to the label specific setting where the attacker can manipulate the predictions of the victim classifiers according to some predefined rules rather than only making wrong predictions. Experiments on various datasets including CIFAR-10 and a reduced version of ImageNet confirmed the effectiveness of the proposed method and empirical results showed that, such bounded perturbation have good transferability regardless of which classifier the victim is actually using on image data.

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arXiv2019

Forest Representation Learning Guided by Margin Distribution

In this paper, we reformulate the forest representation learning approach as an additive model which boosts the augmented feature instead of the prediction. We substantially improve the upper bound of generalization gap from $\mathcal{O}(\sqrt\frac{\ln m}{m})$ to $\mathcal{O}(\frac{\ln m}{m})$, while $λ$ - the margin ratio between the margin standard deviation and the margin mean is small enough. This tighter upper bound inspires us to optimize the margin distribution ratio $λ$. Therefore, we design the margin distribution reweighting approach (mdDF) to achieve small ratio $λ$ by boosting the augmented feature. Experiments and visualizations confirm the effectiveness of the approach in terms of performance and representation learning ability. This study offers a novel understanding of the cascaded deep forest from the margin-theory perspective and further uses the mdDF approach to guide the layer-by-layer forest representation learning.

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arXiv2019

Reliable Weakly Supervised Learning: Maximize Gain and Maintain Safeness

Weakly supervised data are widespread and have attracted much attention. However, since label quality is often difficult to guarantee, sometimes the use of weakly supervised data will lead to unsatisfactory performance, i.e., performance degradation or poor performance gains. Moreover, it is usually not feasible to manually increase the label quality, which results in weakly supervised learning being somewhat difficult to rely on. In view of this crucial issue, this paper proposes a simple and novel weakly supervised learning framework. We guide the optimization of label quality through a small amount of validation data, and to ensure the safeness of performance while maximizing performance gain. As validation set is a good approximation for describing generalization risk, it can effectively avoid the unsatisfactory performance caused by incorrect data distribution assumptions. We formalize this underlying consideration into a novel Bi-Level optimization and give an effective solution. Extensive experimental results verify that the new framework achieves impressive performance on weakly supervised learning with a small amount of validation data.

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arXiv2019

Stochastic Approximation of Smooth and Strongly Convex Functions: Beyond the $O(1/T)$ Convergence Rate

Stochastic approximation (SA) is a classical approach for stochastic convex optimization. Previous studies have demonstrated that the convergence rate of SA can be improved by introducing either smoothness or strong convexity condition. In this paper, we make use of smoothness and strong convexity simultaneously to boost the convergence rate. Let $λ$ be the modulus of strong convexity, $κ$ be the condition number, $F_*$ be the minimal risk, and $α>1$ be some small constant. First, we demonstrate that, in expectation, an $O(1/[λT^α] + κF_*/T)$ risk bound is attainable when $T = Ω(κ^α)$. Thus, when $F_*$ is small, the convergence rate could be faster than $O(1/[λT])$ and approaches $O(1/[λT^α])$ in the ideal case. Second, to further benefit from small risk, we show that, in expectation, an $O(1/2^{T/κ}+F_*)$ risk bound is achievable. Thus, the excess risk reduces exponentially until reaching $O(F_*)$, and if $F_*=0$, we obtain a global linear convergence. Finally, we emphasize that our proof is constructive and each risk bound is equipped with an efficient stochastic algorithm attaining that bound.

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arXiv2018

$\ell_1$-regression with Heavy-tailed Distributions

In this paper, we consider the problem of linear regression with heavy-tailed distributions. Different from previous studies that use the squared loss to measure the performance, we choose the absolute loss, which is capable of estimating the conditional median. To address the challenge that both the input and output could be heavy-tailed, we propose a truncated minimization problem, and demonstrate that it enjoys an $\widetilde{O}(\sqrt{d/n})$ excess risk, where $d$ is the dimensionality and $n$ is the number of samples. Compared with traditional work on $\ell_1$-regression, the main advantage of our result is that we achieve a high-probability risk bound without exponential moment conditions on the input and output. Furthermore, if the input is bounded, we show that the classical empirical risk minimization is competent for $\ell_1$-regression even when the output is heavy-tailed.

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arXiv2018

Adaptive Online Learning in Dynamic Environments

In this paper, we study online convex optimization in dynamic environments, and aim to bound the dynamic regret with respect to any sequence of comparators. Existing work have shown that online gradient descent enjoys an $O(\sqrt{T}(1+P_T))$ dynamic regret, where $T$ is the number of iterations and $P_T$ is the path-length of the comparator sequence. However, this result is unsatisfactory, as there exists a large gap from the $Ω(\sqrt{T(1+P_T)})$ lower bound established in our paper. To address this limitation, we develop a novel online method, namely adaptive learning for dynamic environment (Ader), which achieves an optimal $O(\sqrt{T(1+P_T)})$ dynamic regret. The basic idea is to maintain a set of experts, each attaining an optimal dynamic regret for a specific path-length, and combines them with an expert-tracking algorithm. Furthermore, we propose an improved Ader based on the surrogate loss, and in this way the number of gradient evaluations per round is reduced from $O(\log T)$ to $1$. Finally, we extend Ader to the setting that a sequence of dynamical models is available to characterize the comparators.

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arXiv2018

On the Resistance of Nearest Neighbor to Random Noisy Labels

Nearest neighbor has always been one of the most appealing non-parametric approaches in machine learning, pattern recognition, computer vision, etc. Previous empirical studies partly shows that nearest neighbor is resistant to noise, yet there is a lack of deep analysis. This work presents the finite-sample and distribution-dependent bounds on the consistency of nearest neighbor in the random noise setting. The theoretical results show that, for asymmetric noises, k-nearest neighbor is robust enough to classify most data correctly, except for a handful of examples, whose labels are totally misled by random noises. For symmetric noises, however, k-nearest neighbor achieves the same consistent rate as that of noise-free setting, which verifies the resistance of k-nearest neighbor to random noisy labels. Motivated by the theoretical analysis, we propose the Robust k-Nearest Neighbor (RkNN) approach to deal with noisy labels. The basic idea is to make unilateral corrections to examples, whose labels are totally misled by random noises, and classify the others directly by utilizing the robustness of k-nearest neighbor. We verify the effectiveness of the proposed algorithm both theoretically and empirically.

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arXiv2018

Handling Concept Drift via Model Reuse

In many real-world applications, data are often collected in the form of stream, and thus the distribution usually changes in nature, which is referred as concept drift in literature. We propose a novel and effective approach to handle concept drift via model reuse, leveraging previous knowledge by reusing models. Each model is associated with a weight representing its reusability towards current data, and the weight is adaptively adjusted according to the model performance. We provide generalization and regret analysis. Experimental results also validate the superiority of our approach on both synthetic and real-world datasets.

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arXiv2018

Dynamic Regret of Strongly Adaptive Methods

To cope with changing environments, recent developments in online learning have introduced the concepts of adaptive regret and dynamic regret independently. In this paper, we illustrate an intrinsic connection between these two concepts by showing that the dynamic regret can be expressed in terms of the adaptive regret and the functional variation. This observation implies that strongly adaptive algorithms can be directly leveraged to minimize the dynamic regret. As a result, we present a series of strongly adaptive algorithms that have small dynamic regrets for convex functions, exponentially concave functions, and strongly convex functions, respectively. To the best of our knowledge, this is the first time that exponential concavity is utilized to upper bound the dynamic regret. Moreover, all of those adaptive algorithms do not need any prior knowledge of the functional variation, which is a significant advantage over previous specialized methods for minimizing dynamic regret.

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arXiv2018

Multi-Layered Gradient Boosting Decision Trees

Multi-layered representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical representations by stacking several layers of regression GBDTs as its building block. The model can be jointly trained by a variant of target propagation across layers, without the need to derive back-propagation nor differentiability. Experiments and visualizations confirmed the effectiveness of the model in terms of performance and representation learning ability.

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arXiv2018

Matrix Co-completion for Multi-label Classification with Missing Features and Labels

We consider a challenging multi-label classification problem where both feature matrix $\X$ and label matrix $\Y$ have missing entries. An existing method concatenated $\X$ and $\Y$ as $[\X; \Y]$ and applied a matrix completion (MC) method to fill the missing entries, under the assumption that $[\X; \Y]$ is of low-rank. However, since entries of $\Y$ take binary values in the multi-label setting, it is unlikely that $\Y$ is of low-rank. Moreover, such assumption implies a linear relationship between $\X$ and $\Y$ which may not hold in practice. In this paper, we consider a latent matrix $\Z$ that produces the probability $σ(Z_{ij})$ of generating label $Y_{ij}$, where $σ(\cdot)$ is nonlinear. Considering label correlation, we assume $[\X; \Z]$ is of low-rank, and propose an MC algorithm based on subgradient descent named co-completion (COCO) motivated by elastic net and one-bit MC. We give a theoretical bound on the recovery effect of COCO and demonstrate its practical usefulness through experiments.

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arXiv2018

Efficient Training for Positive Unlabeled Learning

Positive unlabeled (PU) learning is useful in various practical situations, where there is a need to learn a classifier for a class of interest from an unlabeled data set, which may contain anomalies as well as samples from unknown classes. The learning task can be formulated as an optimization problem under the framework of statistical learning theory. Recent studies have theoretically analyzed its properties and generalization performance, nevertheless, little effort has been made to consider the problem of scalability, especially when large sets of unlabeled data are available. In this work we propose a novel scalable PU learning algorithm that is theoretically proven to provide the optimal solution, while showing superior computational and memory performance. Experimental evaluation confirms the theoretical evidence and shows that the proposed method can be successfully applied to a large variety of real-world problems involving PU learning.

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arXiv2018

Unorganized Malicious Attacks Detection

Recommender system has attracted much attention during the past decade. Many attack detection algorithms have been developed for better recommendations, mostly focusing on shilling attacks, where an attack organizer produces a large number of user profiles by the same strategy to promote or demote an item. This work considers a different attack style: unorganized malicious attacks, where attackers individually utilize a small number of user profiles to attack different items without any organizer. This attack style occurs in many real applications, yet relevant study remains open. We first formulate the unorganized malicious attacks detection as a matrix completion problem, and propose the Unorganized Malicious Attacks detection (UMA) approach, a proximal alternating splitting augmented Lagrangian method. We verify, both theoretically and empirically, the effectiveness of our proposed approach.

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arXiv2018

Tunneling Neural Perception and Logic Reasoning through Abductive Learning

Perception and reasoning are basic human abilities that are seamlessly connected as part of human intelligence. However, in current machine learning systems, the perception and reasoning modules are incompatible. Tasks requiring joint perception and reasoning ability are difficult to accomplish autonomously and still demand human intervention. Inspired by the way language experts decoded Mayan scripts by joining two abilities in an abductive manner, this paper proposes the abductive learning framework. The framework learns perception and reasoning simultaneously with the help of a trial-and-error abductive process. We present the Neural-Logical Machine as an implementation of this novel learning framework. We demonstrate that--using human-like abductive learning--the machine learns from a small set of simple hand-written equations and then generalizes well to complex equations, a feat that is beyond the capability of state-of-the-art neural network models. The abductive learning framework explores a new direction for approaching human-level learning ability.

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arXiv2018

Learning with Feature Evolvable Streams

Learning with streaming data has attracted much attention during the past few years. Though most studies consider data stream with fixed features, in real practice the features may be evolvable. For example, features of data gathered by limited-lifespan sensors will change when these sensors are substituted by new ones. In this paper, we propose a novel learning paradigm: \emph{Feature Evolvable Streaming Learning} where old features would vanish and new features would occur. Rather than relying on only the current features, we attempt to recover the vanished features and exploit it to improve performance. Specifically, we learn two models from the recovered features and the current features, respectively. To benefit from the recovered features, we develop two ensemble methods. In the first method, we combine the predictions from two models and theoretically show that with the assistance of old features, the performance on new features can be improved. In the second approach, we dynamically select the best single prediction and establish a better performance guarantee when the best model switches. Experiments on both synthetic and real data validate the effectiveness of our proposal.

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arXiv2017

Improved Dynamic Regret for Non-degenerate Functions

Recently, there has been a growing research interest in the analysis of dynamic regret, which measures the performance of an online learner against a sequence of local minimizers. By exploiting the strong convexity, previous studies have shown that the dynamic regret can be upper bounded by the path-length of the comparator sequence. In this paper, we illustrate that the dynamic regret can be further improved by allowing the learner to query the gradient of the function multiple times, and meanwhile the strong convexity can be weakened to other non-degenerate conditions. Specifically, we introduce the squared path-length, which could be much smaller than the path-length, as a new regularity of the comparator sequence. When multiple gradients are accessible to the learner, we first demonstrate that the dynamic regret of strongly convex functions can be upper bounded by the minimum of the path-length and the squared path-length. We then extend our theoretical guarantee to functions that are semi-strongly convex or self-concordant. To the best of our knowledge, this is the first time that semi-strong convexity and self-concordance are utilized to tighten the dynamic regret.

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arXiv2017

AutoEncoder by Forest

Auto-encoding is an important task which is typically realized by deep neural networks (DNNs) such as convolutional neural networks (CNN). In this paper, we propose EncoderForest (abbrv. eForest), the first tree ensemble based auto-encoder. We present a procedure for enabling forests to do backward reconstruction by utilizing the equivalent classes defined by decision paths of the trees, and demonstrate its usage in both supervised and unsupervised setting. Experiments show that, compared with DNN autoencoders, eForest is able to obtain lower reconstruction error with fast training speed, while the model itself is reusable and damage-tolerable.

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arXiv2017

A Unified View of Multi-Label Performance Measures

Multi-label classification deals with the problem where each instance is associated with multiple class labels. Because evaluation in multi-label classification is more complicated than single-label setting, a number of performance measures have been proposed. It is noticed that an algorithm usually performs differently on different measures. Therefore, it is important to understand which algorithms perform well on which measure(s) and why. In this paper, we propose a unified margin view to revisit eleven performance measures in multi-label classification. In particular, we define label-wise margin and instance-wise margin, and prove that through maximizing these margins, different corresponding performance measures will be optimized. Based on the defined margins, a max-margin approach called LIMO is designed and empirical results verify our theoretical findings.

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