通常，用于训练排名模型的数据受到标签噪声。例如，在Web搜索中，由于ClickStream数据创建的标签是嘈杂的，这是因为诸如SERP上的项目描述中的信息不足，用户查询重新进行的，以及不稳定的或意外的用户行为。在实践中，很难处理标签噪声而不对标签生成过程做出强烈的假设。结果，如果不考虑标签噪声，从业人员通常会直接在此嘈杂的数据上训练他们的学习到秩（LTR）模型。令人惊讶的是，我们经常看到以这种方式训练的LTR模型的出色表现。在这项工作中，我们描述了一类耐噪声的LTR损失，即使在类条件标签噪声的背景下，经验风险最小化也是一致的程序。我们还开发了常用损失函数的耐噪声类似物。实验结果进一步支持了我们理论发现的实际意义。

In this paper, we theoretically study the problem of binary classification in the presence of random classification noise -the learner, instead of seeing the true labels, sees labels that have independently been flipped with some small probability. Moreover, random label noise is class-conditional -the flip probability depends on the class. We provide two approaches to suitably modify any given surrogate loss function. First, we provide a simple unbiased estimator of any loss, and obtain performance bounds for empirical risk minimization in the presence of iid data with noisy labels. If the loss function satisfies a simple symmetry condition, we show that the method leads to an efficient algorithm for empirical minimization. Second, by leveraging a reduction of risk minimization under noisy labels to classification with weighted 0-1 loss, we suggest the use of a simple weighted surrogate loss, for which we are able to obtain strong empirical risk bounds. This approach has a very remarkable consequence -methods used in practice such as biased SVM and weighted logistic regression are provably noise-tolerant. On a synthetic non-separable dataset, our methods achieve over 88% accuracy even when 40% of the labels are corrupted, and are competitive with respect to recently proposed methods for dealing with label noise in several benchmark datasets.

We introduce a tunable loss function called $\alpha$-loss, parameterized by $\alpha \in (0,\infty]$, which interpolates between the exponential loss ($\alpha = 1/2$), the log-loss ($\alpha = 1$), and the 0-1 loss ($\alpha = \infty$), for the machine learning setting of classification. Theoretically, we illustrate a fundamental connection between $\alpha$-loss and Arimoto conditional entropy, verify the classification-calibration of $\alpha$-loss in order to demonstrate asymptotic optimality via Rademacher complexity generalization techniques, and build-upon a notion called strictly local quasi-convexity in order to quantitatively characterize the optimization landscape of $\alpha$-loss. Practically, we perform class imbalance, robustness, and classification experiments on benchmark image datasets using convolutional-neural-networks. Our main practical conclusion is that certain tasks may benefit from tuning $\alpha$-loss away from log-loss ($\alpha = 1$), and to this end we provide simple heuristics for the practitioner. In particular, navigating the $\alpha$ hyperparameter can readily provide superior model robustness to label flips ($\alpha > 1$) and sensitivity to imbalanced classes ($\alpha < 1$).

In this paper, we study a classification problem in which sample labels are randomly corrupted. In this scenario, there is an unobservable sample with noise-free labels. However, before being observed, the true labels are independently flipped with a probability ρ ∈ [0, 0.5), and the random label noise can be class-conditional. Here, we address two fundamental problems raised by this scenario. The first is how to best use the abundant surrogate loss functions designed for the traditional classification problem when there is label noise. We prove that any surrogate loss function can be used for classification with noisy labels by using importance reweighting, with consistency assurance that the label noise does not ultimately hinder the search for the optimal classifier of the noise-free sample. The other is the open problem of how to obtain the noise rate ρ. We show that the rate is upper bounded by the conditional probability P ( Ŷ |X) of the noisy sample. Consequently, the rate can be estimated, because the upper bound can be easily reached in classification problems. Experimental results on synthetic and real datasets confirm the efficiency of our methods.

We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data, recovering as a special case Nystrom approaches for kernel methods. Considering random subspaces naturally leads to computational savings, but the question is whether the corresponding learning accuracy is degraded. These statistical-computational tradeoffs have been recently explored for the least squares loss and self-concordant loss functions, such as the logistic loss. Here, we work to extend these results to convex Lipschitz loss functions, that might not be smooth, such as the hinge loss used in support vector machines. This unified analysis requires developing new proofs, that use different technical tools, such as sub-gaussian inputs, to achieve fast rates. Our main results show the existence of different settings, depending on how hard the learning problem is, for which computational efficiency can be improved with no loss in performance.

在负面的感知问题中，我们给出了$ n $数据点$（{\ boldsymbol x} _i，y_i）$，其中$ {\ boldsymbol x} _i $是$ d $ -densional vector和$ y_i \ in \ { + 1，-1 \} $是二进制标签。数据不是线性可分离的，因此我们满足自己的内容，以找到最大的线性分类器，具有最大的\ emph {否定}余量。换句话说，我们想找到一个单位常规矢量$ {\ boldsymbol \ theta} $，最大化$ \ min_ {i \ le n} y_i \ langle {\ boldsymbol \ theta}，{\ boldsymbol x} _i \ rangle $ 。这是一个非凸优化问题（它相当于在Polytope中找到最大标准矢量），我们在两个随机模型下研究其典型属性。我们考虑比例渐近，其中$ n，d \ to \ idty $以$ n / d \ to \ delta $，并在最大边缘$ \ kappa _ {\ text {s}}（\ delta）上证明了上限和下限）$或 - 等效 - 在其逆函数$ \ delta _ {\ text {s}}（\ kappa）$。换句话说，$ \ delta _ {\ text {s}}（\ kappa）$是overparametization阈值：以$ n / d \ le \ delta _ {\ text {s}}（\ kappa） - \ varepsilon $一个分类器实现了消失的训练错误，具有高概率，而以$ n / d \ ge \ delta _ {\ text {s}}（\ kappa）+ \ varepsilon $。我们在$ \ delta _ {\ text {s}}（\ kappa）$匹配，以$ \ kappa \ to - \ idty $匹配。然后，我们分析了线性编程算法来查找解决方案，并表征相应的阈值$ \ delta _ {\ text {lin}}（\ kappa）$。我们观察插值阈值$ \ delta _ {\ text {s}}（\ kappa）$和线性编程阈值$ \ delta _ {\ text {lin {lin}}（\ kappa）$之间的差距，提出了行为的问题其他算法。

我们研究了基于分布强大的机会约束的对抗性分类模型。我们表明，在Wasserstein模糊性下，该模型旨在最大限度地减少距离分类距离的条件值 - 风险，并且我们探讨了前面提出的对抗性分类模型和最大限度的分类机的链接。我们还提供了用于线性分类的分布鲁棒模型的重构，并且表明它相当于最小化正则化斜坡损失目标。数值实验表明，尽管这种配方的非凸起，但是标准的下降方法似乎会聚到全球最小值器。灵感来自这种观察，我们表明，对于某一类分布，正则化斜坡损失最小化问题的唯一静止点是全球最小化器。

In many applications of classifier learning, training data suffers from label noise. Deep networks are learned using huge training data where the problem of noisy labels is particularly relevant. The current techniques proposed for learning deep networks under label noise focus on modifying the network architecture and on algorithms for estimating true labels from noisy labels. An alternate approach would be to look for loss functions that are inherently noise-tolerant. For binary classification there exist theoretical results on loss functions that are robust to label noise. In this paper, we provide some sufficient conditions on a loss function so that risk minimization under that loss function would be inherently tolerant to label noise for multiclass classification problems. These results generalize the existing results on noise-tolerant loss functions for binary classification. We study some of the widely used loss functions in deep networks and show that the loss function based on mean absolute value of error is inherently robust to label noise. Thus standard back propagation is enough to learn the true classifier even under label noise. Through experiments, we illustrate the robustness of risk minimization with such loss functions for learning neural networks.

收购数据是机器学习的许多应用中的一项艰巨任务，只有一个人希望并且预期人口风险在单调上汇率增加（更好的性能）。事实证明，甚至对于最小化经验风险的最大限度的算法，甚至不令人惊讶的情况。在训练中的风险和不稳定的非单调行为表现出并出现在双重血统描述中的流行深度学习范式中。这些问题突出了目前对学习算法和泛化的理解缺乏了解。因此，追求这种行为的表征是至关重要的，这是至关重要的。在本文中，我们在弱假设下获得了一致和风险的单调算法，从而解决了一个打开问题Viering等。 2019关于如何避免风险曲线的非单调行为。我们进一步表明，风险单调性不一定以更糟糕的风险率的价格出现。为实现这一目标，我们推出了持有某些非I.I.D的独立利益的新经验伯恩斯坦的浓度不等式。鞅差异序列等进程。

转移学习或域适应性与机器学习问题有关，在这些问题中，培训和测试数据可能来自可能不同的概率分布。在这项工作中，我们在Russo和Xu发起的一系列工作之后，就通用错误和转移学习算法的过量风险进行了信息理论分析。我们的结果也许表明，也许正如预期的那样，kullback-leibler（kl）Divergence $ d（\ mu || \ mu'）$在$ \ mu $和$ \ mu'$表示分布的特征中起着重要作用。培训数据和测试测试。具体而言，我们为经验风险最小化（ERM）算法提供了概括误差上限，其中两个分布的数据在训练阶段都可用。我们进一步将分析应用于近似的ERM方法，例如Gibbs算法和随机梯度下降方法。然后，我们概括了与$ \ phi $ -Divergence和Wasserstein距离绑定的共同信息。这些概括导致更紧密的范围，并且在$ \ mu $相对于$ \ mu' $的情况下，可以处理案例。此外，我们应用了一套新的技术来获得替代的上限，该界限为某些学习问题提供了快速（最佳）的学习率。最后，受到派生界限的启发，我们提出了Infoboost算法，其中根据信息测量方法对源和目标数据的重要性权重进行了调整。经验结果表明了所提出的算法的有效性。

标准均匀收敛导致在假设类别上预期损失的概括差距。对风险敏感学习的出现需要超出预期损失分布的功能的概括保证。虽然先前的工作专门从事特定功能的均匀收敛，但我们的工作为一般的H \'较旧风险功能提供了统一的收敛，累积分配功能（CDF）的亲密关系（CDF）需要接近风险。我们建立了第一个统一的融合估计损失分布的CDF的结果，可以保证在所有H \“较旧的风险功能和所有假设上）同时保持。因此，我们获得了实现经验风险最小化的许可，我们开发了基于梯度的实用方法，以最大程度地减少失真风险（广泛研究的H \'H \'较旧风险涵盖了光谱风险，包括平均值，有条件价值，风险的有条件价值，累积前景理论风险和累积前景理论风险，以及其他）并提供融合保证。在实验中，我们证明了学习程序的功效，这是在均匀收敛结果和具有深层网络的高维度的设置中。

我们提出了一种基于优化的基于优化的框架，用于计算差异私有M估算器以及构建差分私立置信区的新方法。首先，我们表明稳健的统计数据可以与嘈杂的梯度下降或嘈杂的牛顿方法结合使用，以便分别获得具有全局线性或二次收敛的最佳私人估算。我们在局部强大的凸起和自我协调下建立当地和全球融合保障，表明我们的私人估算变为对非私人M估计的几乎最佳附近的高概率。其次，我们通过构建我们私有M估计的渐近方差的差异私有估算来解决参数化推断的问题。这自然导致近​​似枢轴统计，用于构建置信区并进行假设检测。我们展示了偏置校正的有效性，以提高模拟中的小样本实证性能。我们说明了我们在若干数值例子中的方法的好处。

We define notions of stability for learning algorithms and show how to use these notions to derive generalization error bounds based on the empirical error and the leave-one-out error. The methods we use can be applied in the regression framework as well as in the classification one when the classifier is obtained by thresholding a real-valued function. We study the stability properties of large classes of learning algorithms such as regularization based algorithms. In particular we focus on Hilbert space regularization and Kullback-Leibler regularization. We demonstrate how to apply the results to SVM for regression and classification.1. For a qualitative discussion about sensitivity analysis with links to other resources see e.g. http://sensitivity-analysis.jrc.cec.eu.int/

解决机器学习模型的公平关注是朝着实际采用现实世界自动化系统中的至关重要的一步。尽管已经开发了许多方法来从数据培训公平模型，但对这些方法对数据损坏的鲁棒性知之甚少。在这项工作中，我们考虑在最坏情况下的数据操作下进行公平意识学习。我们表明，在某些情况下，对手可能会迫使任何学习者返回过度偏见的分类器，无论样本量如何，有或没有降解的准确性，并且多余的偏见的强度会增加数据中数据不足的受保护组的学习问题，而数据中有代表性不足的组。我们还证明，我们的硬度结果紧密到不断的因素。为此，我们研究了两种自然学习算法，以优化准确性和公平性，并表明这些算法在损坏比和较大数据限制中受保护的群体频率方面享有订单最佳的保证。

We show that parametric models trained by a stochastic gradient method (SGM) with few iterations have vanishing generalization error. We prove our results by arguing that SGM is algorithmically stable in the sense of Bousquet and Elisseeff. Our analysis only employs elementary tools from convex and continuous optimization. We derive stability bounds for both convex and non-convex optimization under standard Lipschitz and smoothness assumptions.Applying our results to the convex case, we provide new insights for why multiple epochs of stochastic gradient methods generalize well in practice. In the non-convex case, we give a new interpretation of common practices in neural networks, and formally show that popular techniques for training large deep models are indeed stability-promoting. Our findings conceptually underscore the importance of reducing training time beyond its obvious benefit.

Privacy-preserving machine learning algorithms are crucial for the increasingly common setting in which personal data, such as medical or financial records, are analyzed. We provide general techniques to produce privacy-preserving approximations of classifiers learned via (regularized) empirical risk minimization (ERM). These algorithms are private under the ǫ-differential privacy definition due to Dwork et al. (2006). First we apply the output perturbation ideas of Dwork et al. (2006), to ERM classification. Then we propose a new method, objective perturbation, for privacy-preserving machine learning algorithm design. This method entails perturbing the objective function before optimizing over classifiers. If the loss and regularizer satisfy certain convexity and differentiability criteria, we prove theoretical results showing that our algorithms preserve privacy, and provide generalization bounds for linear and nonlinear kernels. We further present a privacy-preserving technique for tuning the parameters in general machine learning algorithms, thereby providing end-to-end privacy guarantees for the training process. We apply these results to produce privacy-preserving analogues of regularized logistic regression and support vector machines. We obtain encouraging results from evaluating their performance on real demographic and benchmark data sets. Our results show that both theoretically and empirically, objective perturbation is superior to the previous state-of-the-art, output perturbation, in managing the inherent tradeoff between privacy and learning performance.

大多数监督学习数据集的构建围绕着为每个实例收集多个标签，然后将标签汇总以形成``金标准''的类型。我们通过开发该过程的（风格化的）理论模型并分析其统计后果的理论模型来质疑该管道的智慧，并显示了如何访问非聚集标签信息的信息可以使培训良好的模型更加容易，或者在某些情况下 - 甚至在某些情况下 - 可行，而只有金标准标签是不可能的。然而，整个故事都是微妙的，汇总和填充标签信息之间的对比取决于问题的细节，在该信息中，使用汇总信息的估计器表现出强大但较慢的收敛速度，而估计器可以有效地利用所有标签的收敛性更高。如果他们有忠诚（或可以学习）真实的标签过程，很快。我们在风格化模型中开发的理论对现实世界数据集进行了一些预测，包括何时非聚集标签应改善学习绩效，我们测试以证实我们的预测有效性。

成对学习正在接受越来越多的关注，因为它涵盖了许多重要的机器学习任务，例如度量学习，AUC最大化和排名。研究成对学习的泛化行为是重要的。然而，现有的泛化分析主要侧重于凸面的目标函数，使非挖掘学习远远较少。此外，导出用于成对学习的泛化性能的当前学习速率主要是较慢的顺序。通过这些问题的动机，我们研究了非透露成对学习的泛化性能，并提供了改进的学习率。具体而言，我们基于其分析经验风险最小化器，梯度下降和随机梯度下降成对比对学习的不同假设，在不同假设下产生不同均匀的梯度梯度收敛。我们首先在一般的非核心环境中成功地为这些算法建立了学习率，在普通非核心环境中，分析揭示了优化和泛化之间的权衡的见解以及早期停止的作用。然后，我们调查非凸起学习的概括性表现，具有梯度优势曲率状态。在此设置中，我们推出了更快的订单$ \ mathcal {o}（1 / n）$的学习速率，其中$ n $是样本大小。如果最佳人口风险很小，我们进一步将学习率提高到$ \ mathcal {o}（1 / n ^ 2）$，这是我们的知识，是第一个$ \ mathcal {o}（ 1 / n ^ 2）$ - 成对学习的速率类型，无论是凸面还是非渗透学习。总的来说，我们系统地分析了非凸显成对学习的泛化性能。

Network data are ubiquitous in modern machine learning, with tasks of interest including node classification, node clustering and link prediction. A frequent approach begins by learning an Euclidean embedding of the network, to which algorithms developed for vector-valued data are applied. For large networks, embeddings are learned using stochastic gradient methods where the sub-sampling scheme can be freely chosen. Despite the strong empirical performance of such methods, they are not well understood theoretically. Our work encapsulates representation methods using a subsampling approach, such as node2vec, into a single unifying framework. We prove, under the assumption that the graph is exchangeable, that the distribution of the learned embedding vectors asymptotically decouples. Moreover, we characterize the asymptotic distribution and provided rates of convergence, in terms of the latent parameters, which includes the choice of loss function and the embedding dimension. This provides a theoretical foundation to understand what the embedding vectors represent and how well these methods perform on downstream tasks. Notably, we observe that typically used loss functions may lead to shortcomings, such as a lack of Fisher consistency.

我们研究了称为“乐观速率”（Panchenko 2002; Srebro等，2010）的统一收敛概念，用于与高斯数据的线性回归。我们的精致分析避免了现有结果中的隐藏常量和对数因子，这已知在高维设置中至关重要，特别是用于了解插值学习。作为一个特殊情况，我们的分析恢复了Koehler等人的保证。（2021年），在良性过度的过度条件下，严格地表征了低规范内插器的人口风险。但是，我们的乐观速度绑定还分析了具有任意训练错误的预测因子。这使我们能够在随机设计下恢复脊和套索回归的一些经典统计保障，并有助于我们在过度参数化制度中获得精确了解近端器的过度风险。