You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
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.

Cited Abstract(s):
[1]: We present a simple approach for producing a small number of structured visual outputs which have high recall, for a variety of tasks including monocular pose estimation and semantic scene segmentation. Current state-of-the-art approaches learn a single model and modify inference procedures to produce a small number of diverse predictions. We take the alternate route of modifying the learning procedure to directly optimize for good, high recall sequences of structured-output predictors. Our approach introduces no new parameters, naturally learns diverse predictions and is not tied to any specific structured learning or inference procedure. We leverage recent advances in the contextual submodular maximization literature to learn a sequence of predictors and empirically demonstrate the simplicity and performance of our approach on multiple challenging vision tasks including achieving state-of-the-art results on multiple predictions for monocular pose-estimation and image foreground background segmentation.

[2]: We address the problem of generating multiple hypotheses for structured prediction tasks that involve interaction with users or successive components in a cascaded architecture. Given a set of multiple hypotheses, such components users typically have the ability to retrieve the best (or approximately the best) solution in this set. The standard approach for handling such a scenario is to first learn a single-output model and then produce M-Best Maximum a Posteriori (MAP) hypotheses from this model. In contrast, we learn to produce multiple outputs by formulating this task as a multiple-output structured-output prediction problem with a loss-function that effectively captures the setup of the problem. We present a max-margin formulation that minimizes an upper-bound on this loss-function. Experimental results on image segmentation and protein side-chain prediction show that our method outperforms conventional approaches used for this type of scenario and leads to substantial improvements in prediction accuracy.

[3]: Many practical perception systems exist within larger processes that include interactions with users or additional components capable of evaluating the quality of predicted solutions. In these contexts, it is beneficial to provide these oracle mechanisms with multiple highly likely hypotheses rather than a single prediction. In this work, we pose the task of producing multiple outputs as a learning problem over an ensemble of deep networks -- introducing a novel stochastic gradient descent based approach to minimize the loss with respect to an oracle. Our method is simple to implement, agnostic to both architecture and loss function, and parameter-free. Our approach achieves lower oracle error compared to existing methods on a wide range of tasks and deep architectures. We also show qualitatively that the diverse solutions produced often provide interpretable representations of task ambiguity.
Multiple Choice Learning. In [2] 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 [1] multiple diverse models are iteratively learned to solve submodular optimization tasks. As these frameworks require expensive retraining, in [3] 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.