Future prediction is a fundamental principle of intelligence that helps plan actions and avoid possible dangers. As the future is uncertain to a large extent, modeling the uncertainty and multimodality of the future states is of great relevance. Existing approaches are rather limited in this regard and mostly yield a single hypothesis of the future or, at the best, strongly constrained mixture components that suffer from instabilities in training and mode collapse. In this work, we present an approach that involves the prediction of several samples of the future with a winner-takes-all loss and iterative grouping of samples to multiple modes. Moreover, we discuss how to evaluate predicted multimodal distributions, including the common real scenario, where only a single sample from the ground-truth distribution is available for evaluation. We show on synthetic and real data that the proposed approach triggers good estimates of multimodal distributions and avoids mode collapse.
Another option is to estimate a complete mixture distribution from a network, like the Mixture Density Networks (MDNs) by Bishop @cite_48 . @cite_3 used MDNs with von Mises distributions for pose estimation. @cite_25 utilized MDNs for uncertainties in autonomous driving by using mixture components as samples alternative to dropout @cite_41 . However, optimizing for a general mixture distribution comes with problems, such as numerical instability, requirement for good initializations, and collapsing to a single mode @cite_30 @cite_33 @cite_11 @cite_5 @cite_44 @cite_28 . The Evolving WTA loss and two stage approach proposed in this work addresses these problems.
@cite_30 @cite_33 @cite_41 @cite_48 @cite_28 @cite_3 @cite_44 @cite_5 @cite_25 @cite_11
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Many prediction tasks contain uncertainty. In some cases, uncertainty is inherent in the task itself. In future prediction, for example, many distinct outcomes are equally valid. In other cases, uncertainty arises from the way data is labeled. For example, in object detection, many objects of interest often go unlabeled, and in human pose estimation, occluded joints are often labeled with ambiguous values. In this work we focus on a principled approach for handling such scenarios. In particular, we propose a frame-work for reformulating existing single-prediction models as multiple hypothesis prediction (MHP) models and an associated meta loss and optimization procedure to train them. To demonstrate our approach, we consider four diverse applications: human pose estimation, future prediction, image classification and segmentation. We find that MHP models outperform their single-hypothesis counterparts in all cases, and that MHP models simultaneously expose valuable insights into the variability of predictions. Autonomous driving presents one of the largest problems that the robotics and artificial intelligence communities are facing at the moment, both in terms of difficulty and potential societ al impact. Self-driving vehicles (SDVs) are expected to prevent road accidents and save millions of lives while improving the livelihood and life quality of many more. However, despite large interest and a number of industry players working in the autonomous domain, there is still more to be done in order to develop a system capable of operating at a level comparable to best human drivers. One reason for this is high uncertainty of traffic behavior and large number of situations that an SDV may encounter on the roads, making it very difficult to create a fully generalizable system. To ensure safe and efficient operations, an autonomous vehicle is required to account for this uncertainty and to anticipate a multitude of possible behaviors of traffic actors in its surrounding. In this work, we address this critical problem and present a method to predict multiple possible trajectories of actors while also estimating their probabilities. The method encodes each actor's surrounding context into a raster image, used as input by deep convolutional networks to automatically derive relevant features for the task. Following extensive offline evaluation and comparison to state-of-the-art baselines, as well as closed course tests, the method was successfully deployed to a fleet of SDVs. Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets. Minimization of a sum-of-squares or cross-entropy error function leads to network outputs which approximate the conditional averages of the target data, conditioned on the input vector. For classifications problems, with a suitably chosen target coding scheme, these averages represent the posterior probabilities of class membership, and so can be regarded as optimal. For problems involving the prediction of continuous variables, however, the conditional averages provide only a very limited description of the properties of the target variables. This is particularly true for problems in which the mapping to be learned is multi-valued, as often arises in the solution of inverse problems, since the average of several correct target values is not necessarily itself a correct value. In order to obtain a complete description of the data, for the purposes of predicting the outputs corresponding to new input vectors, we must model the conditional probability distribution of the target data, again conditioned on the input vector. In this paper we introduce a new class of network models obtained by combining a conventional neural network with a mixture density model. The complete system is called a Mixture Density Network, and can in principle represent arbitrary conditional probability distributions in the same way that a conventional neural network can represent arbitrary functions. We demonstrate the effectiveness of Mixture Density Networks using both a toy problem and a problem involving robot inverse kinematics. Modern deep learning systems successfully solve many perception tasks such as object pose estimation when the input image is of high quality. However, in challenging imaging conditions such as on low resolution images or when the image is corrupted by imaging artifacts, current systems degrade considerably in accuracy. While a loss in performance is unavoidable, we would like our models to quantify their uncertainty to achieve robustness against images of varying quality. Probabilistic deep learning models combine the expressive power of deep learning with uncertainty quantification. In this paper we propose a novel probabilistic deep learning model for the task of angular regression. Our model uses von Mises distributions to predict a distribution over object pose angle. Whereas a single von Mises distribution is making strong assumptions about the shape of the distribution, we extend the basic model to predict a mixture of von Mises distributions. We show how to learn a mixture model using a finite and infinite number of mixture components. Our model allows for likelihood-based training and efficient inference at test time. We demonstrate on a number of challenging pose estimation datasets that our model produces calibrated probability predictions and competitive or superior point estimates compared to the current state-of-the-art. This paper shows how Long Short-term Memory recurrent neural networks can be used to generate complex sequences with long-range structure, simply by predicting one data point at a time. The approach is demonstrated for text (where the data are discrete) and online handwriting (where the data are real-valued). It is then extended to handwriting synthesis by allowing the network to condition its predictions on a text sequence. The resulting system is able to generate highly realistic cursive handwriting in a wide variety of styles. In this paper, we propose an uncertainty-aware learning from demonstration method by presenting a novel uncertainty estimation method utilizing a mixture density network appropriate for modeling complex and noisy human behaviors. The proposed uncertainty acquisition can be done with a single forward path without Monte Carlo sampling and is suitable for real-time robotics applications. Then, we show that it can be decomposed into explained variance and unexplained variance where the connections between aleatoric and epistemic uncertainties are addressed. The properties of the proposed uncertainty measure are analyzed through three different synthetic examples, absence of data, heavy measurement noise, and composition of functions scenarios. We show that each case can be distinguished using the proposed uncertainty measure and presented an uncertainty-aware learning from demonstration method for autonomous driving using this property. The proposed uncertainty-aware learning from demonstration method outperforms other compared methods in terms of safety using a complex real-world driving dataset. Artificial Neural Networks (ANNs) are increasingly used in modeling and prediction due to advances in deep learning architecture and training. As ANNs become a viable option for making state or measurement predictions in navigation algorithms, special care must be taken in order to determine the confidence (covariance) of the predictions. A special kind of ANN called a Mixture Density Network (MDN) approximates the prediction distribution with a mixture of distributions such as Gaussian distributions. This allows the MDN to output a full Probability Distribution Function (PDF) rather than just a mean estimate. The prediction mixtures can also be converted into other forms for processing by a filter. In this paper, MDN are trained to model a measurement equation which converts measurements to state estimates represented as a Gaussian Mixture Model (GMM). The GMM distributions are simplified into a single Gaussian distribution for each measurement for inclusion into an EKF. An experiment was conducted using magnetic field measurements and Very Low Frequency (VLF) signals to estimate position using an EKF with measurements from a MDN. This method shows a performance improvement using the MDN covariance estimate to determine measurement noise when compared to using static estimates for measurement noise. Thus, the MDN output allows the modeling and prediction power of ANN to be used in standard navigation filters with minimal changes to the filter.