Non-linear functions such as neural networks can be locally approximated by affine planes. Recent works make use of input-Jacobians, which describe the normal to these planes. In this paper, we introduce full-Jacobians, which includes this normal along with an additional intercept term called the bias-Jacobians, that together completely describe local planes. For ReLU neural networks, bias-Jacobians correspond to sums of gradients of outputs w.r.t. intermediate layer activations. We first use these full-Jacobians for distillation by aligning gradients of their intermediate representations. Next, we regularize bias-Jacobians alone to improve generalization. Finally, we show that full-Jacobian maps can be viewed as saliency maps. Experimental results show improved distillation on small data-sets, improved generalization for neural network training, and sharper saliency maps.

Classical Boosting algorithms, such as AdaBoost, build a strong classifier without concern about the computational cost. Some applications, in particular in computer vision, may involve up to millions of training examples and features. In such contexts, the training time may become prohibitive. Several methods exist to accelerate training, typically either by sampling the features, or the examples, used to train the weak learners. Even if those methods can precisely quantify the speed improvement they deliver, they offer no guarantee of being more efficient than any other, given the same amount of time. This paper aims at shading some light on this problem, i.e. given a fixed amount of time, for a particular problem, which strategy is optimal in order to reduce the training loss the most. We apply this analysis to the design of new algorithms which estimate on the fly at every iteration the optimal trade-off between the number of samples and the number of features to look at in order to maximize the expected loss reduction. Experiments in object recognition with two standard computer vision data-sets show that the adaptive methods we propose outperform basic sampling and state-of-the-art bandit methods.

The standard strategy for efficient object detection consists of building a cascade composed of several binary classifiers. The detection process takes the form of a lazy evaluation of the conjunction of the responses of these classifiers, and concentrates the computation on difficult parts of the image which can not be trivially rejected. We introduce a novel algorithm to construct jointly the classifiers of such a cascade. We interpret the response of a classifier as a probability of a positive prediction, and the overall response of the cascade as the probability that all the predictions are positive. From this noisy-AND model, we derive a consistent loss and a Boosting procedure to optimize that global probability on the training set. Such a joint learning allows the individual predictors to focus on a more restricted modeling problem, and improves the performance compared to a standard cascade. We demonstrate the efficiency of this approach on face and pedestrian detection with standard data-sets and comparisons with reference baselines.

We investigate the learning of the appearance of an object from a single image of it. Instead of using a large number of pictures of the object to recognize, we use a labeled reference database of pictures of other objects to learn invariance to noise and variations in pose and illumination. This acquired knowledge is then used to predict if two pictures of new objects, which do not appear on the training pictures, actually display the same object. We propose a generic scheme called chopping to address this task. It relies on hundreds of random binary splits of the training set chosen to keep together the images of any given object. Those splits are extended to the complete image space with a simple learning algorithm. Given two images, the responses of the split predictors are combined with a Bayesian rule into a posterior probability of similarity.

We investigate the learning of the appearance of an object from a single image of it. Instead of using a large number of pictures of the object to recognize, we use a labeled reference database of pictures of other objects to learn invariance to noise and variations in pose and illumination. This acquired knowledge is then used to predict if two pictures of new objects, which do not appear on the training pictures, actually display the same object. We propose a generic scheme called chopping to address this task. It relies on hundreds of random binary splits of the training set chosen to keep together the images of any given object. Those splits are extended to the complete image space with a simple learning algorithm. Given two images, the responses of the split predictors are combined with a Bayesian rule into a posterior probability of similarity.

We investigate the learning of the appearance of an object from a single image of it. Instead of using a large number of pictures of the object to recognize, we use a labeled reference database of pictures of other objects tolearn invariance to noise and variations in pose and illumination. This acquired knowledge is then used to predict if two pictures of new objects, which do not appear on the training pictures, actually display the same object. We propose a generic scheme called chopping to address this task. It relies on hundreds of random binary splits of the training set chosen to keep together the images of any given object. Those splits are extended to the complete image space with a simple learning algorithm. Given two images, the responses of the split predictors are combined with a Bayesian rule into a posterior probability of similarity.