Estimating 3D pose from monocular images is a highly ambiguous problem. Physical constraints can be exploited to restrict the space of feasible configurations. In this paper we propose an approach to constraining the prediction of a discriminative predictor. We first show that the mean prediction of a Gaussian process implicitly satisfies linear constraints if those constraints are satisfied by the training examples. We then show how, by performing a change of variables, a GP can be forced to satisfy quadratic constraints. As evidenced by the experiments, our method outperforms state-of-the-art approaches on the tasks of rigid and non-rigid pose estimation.

We propose an approach to multiple-instance learning that reformulates the problem as a convex optimization on the likelihood ratio between the positive and the negative class for each training instance. This is casted as joint estimation of both a likelihood ratio predictor and the target (likelihood ratio variable) for instances. Theoretically, we prove a quantitative relationship between the risk estimated under the 0-1 classification loss, and under a loss function for likelihood ratio. It is shown that likelihood ratio estimation is generally a good surrogate for the 0-1 loss, and separates positive and negative instances well. The likelihood ratio estimates provide a ranking of instances within a bag and are used as input features to learn a linear classifier on bags of instances. Instance-level classification is achieved from the bag-level predictions and the individual likelihood ratios. Experiments on synthetic and real datasets demonstrate the competitiveness of the approach.

We introduce an approach to learn discriminative visual representations while exploiting external semantic knowledge about object category relationships. Given a hierarchical taxonomy that captures semantic similarity between the objects, we learn a corresponding tree of metrics (ToM). In this tree, we have one metric for each non-leaf node of the object hierarchy, and each metric is responsible for discriminating among its immediate subcategory children. Specifically, a Mahalanobis metric learned for a given node must satisfy the appropriate (dis)similarity constraints generated only among its subtree members' training instances. To further exploit the semantics, we introduce a novel regularizer coupling the metrics that prefers a sparse disjoint set of features to be selected for each metric relative to its ancestor (supercategory) nodes' metrics. Intuitively, this reflects that visual cues most useful to distinguish the generic classes (e.g., feline vs. canine) should be different than those cues most useful to distinguish their component fine-grained classes (e.g., Persian cat vs. Siamese cat). We validate our approach with multiple image datasets using the WordNet taxonomy, show its advantages over alternative metric learning approaches, and analyze the meaning of attribute features selected by our algorithm.

Despite the recent trend of increasingly large datasets for object detection, there still exist many classes with few training examples. To overcome this lack of training data for certain classes, we propose a novel way of augmenting the training data for each class by borrowing and transforming examples from other classes. Our model learns which training instances from other classes to borrow and how to transform the borrowed examples so that they become more similar to instances from the target class. Our experimental results demonstrate that our new object detector, with borrowed and transformed examples, improves upon the current state-of-the-art detector on the challenging SUN09 object detection dataset.

For most scene understanding tasks (such as object detection or depth estimation), the classifiers need to consider contextual information in addition to the local features. We can capture such contextual information by taking as input the features/attributes from all the regions in the image. However, this contextual dependence also varies with the spatial location of the region of interest, and we therefore need a different set of parameters for each spatial location.

This paper studies the problem of semi-supervised learning from the vector field perspective. Many of the existing work use the graph Laplacian to ensure the smoothness of the prediction function on the data manifold. However, beyond smoothness, it is suggested by recent theoretical work that we should ensure second order smoothness for achieving faster rates of convergence for semisupervised regression problems. To achieve this goal, we show that the second order smoothness measures the linearity of the function, and the gradient field of a linear function has to be a parallel vector field. Consequently, we propose to find a function which minimizes the empirical error, and simultaneously requires its gradient field to be as parallel as possible. We give a continuous objective function on the manifold and discuss how to discretize it by using random points. The discretized optimization problem turns out to be a sparse linear system which can be solved very efficiently. The experimental results have demonstrated the effectiveness of our proposed approach.

We present a novel regularization-based Multitask Learning (MTL) formulation for Structured Output (SO) prediction for the case of hierarchical task relations. Structured output prediction often leads to difficult inference problems and hence requires large amounts of training data to obtain accurate models. We propose to use MTL to exploit additional information from related learning tasks by means of hierarchical regularization. Training SO models on the combined set of examples from multiple tasks can easily become infeasible for real world applications. To be able to solve the optimization problems underlying multitask structured output learning, we propose an efficient algorithm based on bundle-methods. We demonstrate the performance of our approach in applications from the domain of computational biology addressing the key problem of gene finding. We show that 1) our proposed solver achieves much faster convergence than previous methods and 2) that the Hierarchical SO-MTL approach outperforms considered non-MTL methods.

We study the problem of learning to track a large quantity of homogeneous objects such as cell tracking in cell culture study and developmental biology. Reliable cell tracking in time-lapse microscopic image sequences is important for modern biomedical research. Existing cell tracking methods are usually kept simple and use only a small number of features to allow for manual parameter tweaking or grid search. We propose a structured learning approach that allows to learn optimum parameters automatically from a training set. This allows for the use of a richer set of features which in turn affords improved tracking compared to recently reported methods on two public benchmark sequences.

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.

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