Real-world machine learning applications often have complex test metrics, and may have training and test data that follow different distributions. We propose addressing these issues by using a weighted loss function with a standard convex loss, but with weights on the training examples that are learned to optimize the test metric of interest on the validation set. These metric-optimized example weights can be learned for any test metric, including black box losses and customized metrics for specific applications. We illustrate the performance of our proposal with public benchmark datasets and real-world applications with domain shift and custom loss functions that balance multiple objectives, impose fairness policies, and are non-convex and non-decomposable.
Maximum likelihood based inference is the classical approach to address the issue with non-constant noise levels in the training data. For example, maximizing Gaussian likelihood is equivalent to minimizing squared loss with training weights that are inversely proportional to the variance of the training examples. In the case with over-dispersed binary data, beta-binomial models are often used. In addition, several common machine learning techniques, such as ensemble and graph-based methods, are found to be robust to binary label noise; see @cite_14 for a survey of these methods.
@cite_14
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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 show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multicategory classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this autoencoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns. When training the parameters for a natural language system, one would prefer to minimize 1-best loss (error) on an evaluation set. Since the error surface for many natural language problems is piecewise constant and riddled with local minima, many systems instead optimize log-likelihood, which is conveniently differentiable and convex. We propose training instead to minimize the expected loss, or risk. We define this expectation using a probability distribution over hypotheses that we gradually sharpen (anneal) to focus on the 1-best hypothesis. Besides the linear loss functions used in previous work, we also describe techniques for optimizing nonlinear functions such as precision or the BLEU metric. We present experiments training log-linear combinations of models for dependency parsing and for machine translation. In machine translation, annealed minimum risk training achieves significant improvements in BLEU over standard minimum error training. We also show improvements in labeled dependency parsing. We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the categories is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns.