In many classification systems, sensing modalities have different acquisition costs. It is often unnecessary to use every modality to classify a majority of examples. We study a multi-stage system in a prediction time cost reduction setting, where the full data is available for training, but for a test example, measurements in a new modality can be acquired at each stage for an additional cost. We seek decision rules to reduce the average measurement acquisition cost. We formulate an empirical risk minimization problem (ERM) for a multi-stage reject classifier, wherein the stage @math classifier either classifies a sample using only the measurements acquired so far or rejects it to the next stage where more attributes can be acquired for a cost. To solve the ERM problem, we show that the optimal reject classifier at each stage is a combination of two binary classifiers, one biased towards positive examples and the other biased towards negative examples. We use this parameterization to construct stage-by-stage global surrogate risk, develop an iterative algorithm in the boosting framework and present convergence and generalization results. We test our work on synthetic, medical and explosives detection datasets. Our results demonstrate that substantial cost reduction without a significant sacrifice in accuracy is achievable.
Detection Cascades: Our multi-stage sequential reject classifiers bears close resemblance to detection cascades. There is much literature on cascade design (see @cite_19 @cite_4 and references therein) but most cascades roughly follow the set-up introduced by @cite_13 to reduce computation cost during classification. At each stage in a cascade, there is a binary classifier with a very high detection rate and a mediocre false alarm rate. Each stage makes a partial decision; it either detects an instance as negative or passes it on to the next stage. Only the last stage in the cascade makes a full decision, namely, whether the example belongs to a positive or negative class.
@cite_13 @cite_19 @cite_4
2007272817 2135502357 2100807570 2101217650
Cascade classifiers are widely used in real-time object detection. Different from conventional classifiers that are designed for a low overall classification error rate, a classifier in each node of the cascade is required to achieve an extremely high detection rate and moderate false positive rate. Although there are a few reported methods addressing this requirement in the context of object detection, there is no principled feature selection method that explicitly takes into account this asymmetric node learning objective. We provide such an algorithm here. We show that a special case of the biased minimax probability machine has the same formulation as the linear asymmetric classifier (LAC) of (linear asymmetric classifier for cascade detectors, 2005). We then design a new boosting algorithm that directly optimizes the cost function of LAC. The resulting totally-corrective boosting algorithm is implemented by the column generation technique in convex optimization. Experimental results on object detection verify the effectiveness of the proposed boosting algorithm as a node classifier in cascade object detection, and show performance better than that of the current state-of-the-art. Cascade detectors have been shown to operate extremely rapidly, with high accuracy, and have important applications such as face detection. Driven by this success, cascade learning has been an area of active research in recent years. Nevertheless, there are still challenging technical problems during the training process of cascade detectors. In particular, determining the optimal target detection rate for each stage of the cascade remains an unsolved issue. In this paper, we propose the multiple instance pruning (MIP) algorithm for soft cascades. This algorithm computes a set of thresholds which aggressively terminate computation with no reduction in detection rate or increase in false positive rate on the training dataset. The algorithm is based on two key insights: i) examples that are destined to be rejected by the complete classifier can be safely pruned early; ii) face detection is a multiple instance learning problem. The MIP process is fully automatic and requires no assumptions of probability distributions, statistical independence, or ad hoc intermediate rejection targets. Experimental results on the MIT+CMU dataset demonstrate significant performance advantages. This paper presents a novel learning framework for training boosting cascade based object detector from large scale dataset. The framework is derived from the well-known Viola-Jones (VJ) framework but distinguished by three key differences. First, the proposed framework adopts multi-dimensional SURF features instead of single dimensional Haar features to describe local patches. In this way, the number of used local patches can be reduced from hundreds of thousands to several hundreds. Second, it adopts logistic regression as weak classifier for each local patch instead of decision trees in the VJ framework. Third, we adopt AUC as a single criterion for the convergence test during cascade training rather than the two trade-off criteria (false-positive-rate and hit-rate) in the VJ framework. The benefit is that the false-positive-rate can be adaptive among different cascade stages, and thus yields much faster convergence speed of SURF cascade. Combining these points together, the proposed approach has three good properties. First, the boosting cascade can be trained very efficiently. Experiments show that the proposed approach can train object detectors from billions of negative samples within one hour even on personal computers. Second, the built detector is comparable to the state-of-the-art algorithm not only on the accuracy but also on the processing speed. Third, the built detector is small in model-size due to short cascade stages. The problem of learning classifier cascades is considered. A new cascade boosting algorithm, fast cascade boosting (FCBoost), is proposed. FCBoost is shown to have a number of interesting properties, namely that it 1) minimizes a Lagrangian risk that jointly accounts for classification accuracy and speed, 2) generalizes adaboost, 3) can be made cost-sensitive to support the design of high detection rate cascades, and 4) is compatible with many predictor structures suitable for sequential decision making. It is shown that a rich family of such structures can be derived recursively from cascade predictors of two stages, denoted cascade generators. Generators are then proposed for two new cascade families, last-stage and multiplicative cascades, that generalize the two most popular cascade architectures in the literature. The concept of neutral predictors is finally introduced, enabling FCBoost to automatically determine the cascade configuration, i.e., number of stages and number of weak learners per stage, for the learned cascades. Experiments on face and pedestrian detection show that the resulting cascades outperform current state-of-the-art methods in both detection accuracy and speed.