Weakly supervised object detection (WSOD) focuses on training object detector with only image-level annotations, and is challenging due to the gap between the supervision and the objective. Most of existing approaches model WSOD as a multiple instance learning (MIL) problem. However, we observe that the result of MIL based detector is unstable, i.e., the most confident bounding boxes change significantly when using different initializations. We quantitatively demonstrate the instability by introducing a metric to measure it, and empirically analyze the reason of instability. Although the instability seems harmful for detection task, we argue that it can be utilized to improve the performance by fusing the results of differently initialized detectors. To implement this idea, we propose an end-to-end framework with multiple detection branches, and introduce a simple fusion strategy. We further propose an orthogonal initialization method to increase the difference between detection branches. By utilizing the instability, we achieve 52.6 and 48.0 mAP on the challenging PASCAL VOC 2007 and 2012 datasets, which are both the new state-of-the-arts.
However, the loss function of MIL is non-convex, and the optimization of MIL is sensitive to initialization @cite_15 @cite_0 @cite_25 @cite_23 . In order to solve this issue, some works introduce better initialization methods. Deselaers al @cite_15 propose to initialize object locations based on the objectness score. Cinbis al @cite_0 propose to split the training data into multi folds to escape local optima. Beyond generating better initialization, some works propose to smooth the optimization of MIL to alleviate the non-convexity problem. Bilen al @cite_25 introduce a smoothed version of MIL that softly labels object instances. Song al @cite_23 propose to use Nesterov's smoothing technique in latent SVM model. The proposed method is also related to the non-convexity of MIL, but we propose to utilize the instability, which is partly caused by the non-convexity.
@cite_0 @cite_15 @cite_25 @cite_23
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While convex losses for binary classification are attractive due to the existence of numerous (provably) efficient methods for finding their global optima, they are sensitive to outliers. On the other hand, while the nonconvex 0-1 loss is robust to outliers, it is NP-hard to optimize and thus rarely directly optimized in practice. In this paper, however, we do just that: we explore a variety of practical methods for direct (approximate) optimization of the 0-1 loss based on branch and bound search, combinatorial search, and coordinate descent on smooth, differentiable relaxations of 0-1 loss. Empirically, we compare our proposed algorithms to logistic regression, SVM, and the Bayes point machine showing that the proposed 0-1 loss optimization algorithms perform at least as well and offer a clear advantage in the presence of outliers. To this end, we believe this work reiterates the importance of 0-1 loss and its robustness properties while challenging the notion that it is difficult to directly optimize. In this letter, we investigate the impact of choosing different loss functions from the viewpoint of statistical learning theory. We introduce a convexity assumption, which is met by all loss functions commonly used in the literature, and study how the bound on the estimation error changes with the loss. We also derive a general result on the minimizer of the expected risk for a convex loss function in the case of classification. The main outcome of our analysis is that for classification, the hinge loss appears to be the loss of choice. Other things being equal, the hinge loss leads to a convergence rate practically indistinguishable from the logistic loss rate and much better than the square loss rate. Furthermore, if the hypothesis space is sufficiently rich, the bounds obtained for the hinge loss are not loosened by the thresholding stage. Problems of data classification can be studied in the framework of regularization theory as ill-posed problems. In this framework, loss functions play an important role in the application of regularization theory to classification. In this paper, we review some important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, @math -loss, ramp loss, normalized sigmoid loss, and the loss function of 2 layer neural network. Based on the analysis of these loss functions, we propose a new differentiable non-convex loss function, called smoothed 0-1 loss function, which is a natural approximation of the 0-1 loss function. To compare the performance of different loss functions, we propose two binary classification algorithms for binary classification, one for convex loss functions, the other for non-convex loss functions. A set of experiments are launched on several binary data sets from the UCI repository. The results show that the proposed smoothed 0-1 loss function is robust, especially for those noisy data sets with many outliers. Learning with non-modular losses is an important problem when sets of predictions are made simultaneously. The main tools for constructing convex surrogate loss functions for set prediction are margin rescaling and slack rescaling. In this work, we show that these strategies lead to tight convex surrogates iff the underlying loss function is increasing in the number of incorrect predictions. However, gradient or cutting-plane computation for these functions is NP-hard for nonsupermodular loss functions. We propose instead a novel convex surrogate loss function for submodular losses, the Lovasz hinge, which leads to O(p log p) complexity with O(p) oracle accesses to the loss function to compute a gradient or cutting-plane. As a result, we have developed the first tractable convex surrogates in the literature for submodular losses. We demonstrate the utility of this novel convex surrogate through a real world image labeling task.