For autonomous agents to successfully operate in the real world, anticipation of future events and states of their environment is a key competence. This problem has been formalized as a sequence extrapolation problem, where a number of observations are used to predict the sequence into the future. Real-world scenarios demand a model of uncertainty of such predictions, as predictions become increasingly uncertain -- in particular on long time horizons. While impressive results have been shown on point estimates, scenarios that induce multi-modal distributions over future sequences remain challenging. Our work addresses these challenges in a Gaussian Latent Variable model for sequence prediction. Our core contribution is a "Best of Many" sample objective that leads to more accurate and more diverse predictions that better capture the true variations in real-world sequence data. Beyond our analysis of improved model fit, our models also empirically outperform prior work on three diverse tasks ranging from traffic scenes to weather data.
Multiple Choice Learning. In @cite_25 a Multiple Choice Learning framework is presented where multiple models are learned to produce diverse predictions. During training, training examples are iteratively reassigned to the minimum loss model. The models are trained to convergence using these samples. Similarly in @cite_24 multiple diverse models are iteratively learned to solve submodular optimization tasks. As these frameworks require expensive retraining, in @cite_7 a Stochastic Multiple Choice Learning framework is proposed. Here instead of iterative reassignment, for each example in a mini-batch, the error is back-propagated to only the model with the minimum loss (best) model. In contrast to our approach, these approaches require the learning of multiple models while our approach efficiently learns only one model without compromising on diversity of predictions.
@cite_24 @cite_25 @cite_7
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The recently proposed semi-supervised learning methods exploit consistency loss between different predictions under random perturbations. Typically, a student model is trained to predict consistently with the targets generated by a noisy teacher. However, they ignore the fact that not all training data provide meaningful and reliable information in terms of consistency. For misclassified data, blindly minimizing the consistency loss around them can hinder learning. In this paper, we propose a novel certainty-driven consistency loss (CCL) to dynamically select data samples that have relatively low uncertainty. Specifically, we measure the variance or entropy of multiple predictions under random augmentations and dropout as an estimation of uncertainty. Then, we introduce two approaches, i.e. Filtering CCL and Temperature CCL to guide the student learn more meaningful and certain reliable targets, and hence improve the quality of the gradients backpropagated to the student. Experiments demonstrate the advantages of the proposed method over the state-of-the-art semi-supervised deep learning methods on three benchmark datasets: SVHN, CIFAR10, and CIFAR100. Our method also shows robustness to noisy labels. We consider a special type of multi-label learning where class assignments of training examples are incomplete. As an example, an instance whose true class assignment is (c 1 , c 2 , c 3 ) is only assigned to class c 1 when it is used as a training sample. We refer to this problem as multi-label learning with incomplete class assignment. Incompletely labeled data is frequently encountered when the number of classes is very large (hundreds as in MIR Flickr dataset) or when there is a large ambiguity between classes (e.g., jet vs plane). In both cases, it is difficult for users to provide complete class assignments for objects. We propose a ranking based multi-label learning framework that explicitly addresses the challenge of learning from incompletely labeled data by exploiting the group lasso technique to combine the ranking errors. We present a learning algorithm that is empirically shown to be efficient for solving the related optimization problem. Our empirical study shows that the proposed framework is more effective than the state-of-the-art algorithms for multi-label learning in dealing with incompletely labeled data. Our first contribution in this paper is a theoretical investigation of curriculum learning in the context of stochastic gradient descent when optimizing the least squares loss function. We prove that the rate of convergence of an ideal curriculum learning method in monotonically increasing with the difficulty of the examples, and that this increase in convergence rate is monotonically decreasing as training proceeds. In our second contribution we analyze curriculum learning in the context of training a CNN for image classification. Here one crucial problem is the means to achieve a curriculum. We describe a method which infers the curriculum by way of transfer learning from another network, pre-trained on a different task. While this approach can only approximate the ideal curriculum, we observe empirically similar behavior to the one predicted by the theory, namely, a significant boost in convergence speed at the beginning of training. When the task is made more difficult, improvement in generalization performance is observed. Finally, curriculum learning exhibits robustness against unfavorable conditions such as strong regularization. We describe an end-to-end framework for learning parameters of min-cost flow multitarget tracking problem with quadratic trajectory interactions including suppression of overlapping tracks and contextual cues about co-occurrence of different objects. Our approach utilizes structured prediction with a tracking-specific loss function to learn the complete set of model parameters. Under our learning framework, we evaluate two different approaches to finding an optimal set of tracks under quadratic model objective based on an LP relaxation and a novel greedy extension to dynamic programming that handles pairwise interactions. We find the greedy algorithm achieves almost equivalent accuracy to the LP relaxation while being 2-7x faster than a commercial solver. We evaluate trained models on the challenging MOT and KITTI benchmarks. Surprisingly, we find that with proper parameter learning, our simple data-association model without explicit appearance motion reasoning is able to outperform many state-of-the-art methods that use far more complex motion features and affinity metric learning.