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Estimating and reacting to external disturbances is of fundamental importance for robust control of quadrotors. Existing estimators typically require significant tuning or training with a large amount of data, including the ground truth, to achieve satisfactory performance. This paper proposes a data-efficient differentiable moving horizon estimation (DMHE) algorithm that can automatically tune the MHE parameters online and also adapt to different scenarios. We achieve this by deriving the analytical gradient of the estimated trajectory from MHE with respect to the tuning parameters, enabling end-to-end learning for auto-tuning. Most interestingly, we show that the gradient can be calculated efficiently from a Kalman filter in a recursive form. Moreover, we develop a model-based policy gradient algorithm to learn the parameters directly from the trajectory tracking errors without the need for the ground truth. The proposed DMHE can be further embedded as a layer with other neural networks for joint optimization. Finally, we demonstrate the effectiveness of the proposed method via both simulation and experiments on quadrotors, where challenging scenarios such as sudden payload change and flying in downwash are examined.

We consider the problem of discovering $K$ related Gaussian directed acyclic graphs (DAGs), where the involved graph structures share a consistent causal order and sparse unions of supports. Under the multi-task learning setting, we propose a $l_1/l_2$-regularized maximum likelihood estimator (MLE) for learning $K$ linear structural equation models. We theoretically show that the joint estimator, by leveraging data across related tasks, can achieve a better sample complexity for recovering the causal order (or topological order) than separate estimations. Moreover, the joint estimator is able to recover non-identifiable DAGs, by estimating them together with some identifiable DAGs. Lastly, our analysis also shows the consistency of union support recovery of the structures. To allow practical implementation, we design a continuous optimization problem whose optimizer is the same as the joint estimator and can be approximated efficiently by an iterative algorithm. We validate the theoretical analysis and the effectiveness of the joint estimator in experiments.

This paper focuses on the expected difference in borrower's repayment when there is a change in the lender's credit decisions. Classical estimators overlook the confounding effects and hence the estimation error can be magnificent. As such, we propose another approach to construct the estimators such that the error can be greatly reduced. The proposed estimators are shown to be unbiased, consistent, and robust through a combination of theoretical analysis and numerical testing. Moreover, we compare the power of estimating the causal quantities between the classical estimators and the proposed estimators. The comparison is tested across a wide range of models, including linear regression models, tree-based models, and neural network-based models, under different simulated datasets that exhibit different levels of causality, different degrees of nonlinearity, and different distributional properties. Most importantly, we apply our approaches to a large observational dataset provided by a global technology firm that operates in both the e-commerce and the lending business. We find that the relative reduction of estimation error is strikingly substantial if the causal effects are accounted for correctly.

Neural Architecture Search (NAS) was first proposed to achieve state-of-the-art performance through the discovery of new architecture patterns, without human intervention. An over-reliance on expert knowledge in the search space design has however led to increased performance (local optima) without significant architectural breakthroughs, thus preventing truly novel solutions from being reached. In this work we 1) are the first to investigate casting NAS as a problem of finding the optimal network generator and 2) we propose a new, hierarchical and graph-based search space capable of representing an extremely large variety of network types, yet only requiring few continuous hyper-parameters. This greatly reduces the dimensionality of the problem, enabling the effective use of Bayesian Optimisation as a search strategy. At the same time, we expand the range of valid architectures, motivating a multi-objective learning approach. We demonstrate the effectiveness of this strategy on six benchmark datasets and show that our search space generates extremely lightweight yet highly competitive models.

Interpretation of Deep Neural Networks (DNNs) training as an optimal control problem with nonlinear dynamical systems has received considerable attention recently, yet the algorithmic development remains relatively limited. In this work, we make an attempt along this line by reformulating the training procedure from the trajectory optimization perspective. We first show that most widely-used algorithms for training DNNs can be linked to the Differential Dynamic Programming (DDP), a celebrated second-order trajectory optimization algorithm rooted in the Approximate Dynamic Programming. In this vein, we propose a new variant of DDP that can accept batch optimization for training feedforward networks, while integrating naturally with the recent progress in curvature approximation. The resulting algorithm features layer-wise feedback policies which improve convergence rate and reduce sensitivity to hyper-parameter over existing methods. We show that the algorithm is competitive against state-ofthe-art first and second order methods. Our work opens up new avenues for principled algorithmic design built upon the optimal control theory.

Graph deep learning has recently emerged as a powerful ML concept allowing to generalize successful deep neural architectures to non-Euclidean structured data. Such methods have shown promising results on a broad spectrum of applications ranging from social science, biomedicine, and particle physics to computer vision, graphics, and chemistry. One of the limitations of the majority of the current graph neural network architectures is that they are often restricted to the transductive setting and rely on the assumption that the underlying graph is known and fixed. In many settings, such as those arising in medical and healthcare applications, this assumption is not necessarily true since the graph may be noisy, partially- or even completely unknown, and one is thus interested in inferring it from the data. This is especially important in inductive settings when dealing with nodes not present in the graph at training time. Furthermore, sometimes such a graph itself may convey insights that are even more important than the downstream task. In this paper, we introduce Differentiable Graph Module (DGM), a learnable function predicting the edge probability in the graph relevant for the task, that can be combined with convolutional graph neural network layers and trained in an end-to-end fashion. We provide an extensive evaluation of applications from the domains of healthcare (disease prediction), brain imaging (gender and age prediction), computer graphics (3D point cloud segmentation), and computer vision (zero-shot learning). We show that our model provides a significant improvement over baselines both in transductive and inductive settings and achieves state-of-the-art results.

Reasoning with knowledge expressed in natural language and Knowledge Bases (KBs) is a major challenge for Artificial Intelligence, with applications in machine reading, dialogue, and question answering. General neural architectures that jointly learn representations and transformations of text are very data-inefficient, and it is hard to analyse their reasoning process. These issues are addressed by end-to-end differentiable reasoning systems such as Neural Theorem Provers (NTPs), although they can only be used with small-scale symbolic KBs. In this paper we first propose Greedy NTPs (GNTPs), an extension to NTPs addressing their complexity and scalability limitations, thus making them applicable to real-world datasets. This result is achieved by dynamically constructing the computation graph of NTPs and including only the most promising proof paths during inference, thus obtaining orders of magnitude more efficient models. Then, we propose a novel approach for jointly reasoning over KBs and textual mentions, by embedding logic facts and natural language sentences in a shared embedding space. We show that GNTPs perform on par with NTPs at a fraction of their cost while achieving competitive link prediction results on large datasets, providing explanations for predictions, and inducing interpretable models. Source code, datasets, and supplementary material are available online at //github.com/uclnlp/gntp.

We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

We study active object tracking, where a tracker takes as input the visual observation (i.e., frame sequence) and produces the camera control signal (e.g., move forward, turn left, etc.). Conventional methods tackle the tracking and the camera control separately, which is challenging to tune jointly. It also incurs many human efforts for labeling and many expensive trial-and-errors in realworld. To address these issues, we propose, in this paper, an end-to-end solution via deep reinforcement learning, where a ConvNet-LSTM function approximator is adopted for the direct frame-toaction prediction. We further propose an environment augmentation technique and a customized reward function, which are crucial for a successful training. The tracker trained in simulators (ViZDoom, Unreal Engine) shows good generalization in the case of unseen object moving path, unseen object appearance, unseen background, and distracting object. It can restore tracking when occasionally losing the target. With the experiments over the VOT dataset, we also find that the tracking ability, obtained solely from simulators, can potentially transfer to real-world scenarios.

During the recent years, correlation filters have shown dominant and spectacular results for visual object tracking. The types of the features that are employed in these family of trackers significantly affect the performance of visual tracking. The ultimate goal is to utilize robust features invariant to any kind of appearance change of the object, while predicting the object location as properly as in the case of no appearance change. As the deep learning based methods have emerged, the study of learning features for specific tasks has accelerated. For instance, discriminative visual tracking methods based on deep architectures have been studied with promising performance. Nevertheless, correlation filter based (CFB) trackers confine themselves to use the pre-trained networks which are trained for object classification problem. To this end, in this manuscript the problem of learning deep fully convolutional features for the CFB visual tracking is formulated. In order to learn the proposed model, a novel and efficient backpropagation algorithm is presented based on the loss function of the network. The proposed learning framework enables the network model to be flexible for a custom design. Moreover, it alleviates the dependency on the network trained for classification. Extensive performance analysis shows the efficacy of the proposed custom design in the CFB tracking framework. By fine-tuning the convolutional parts of a state-of-the-art network and integrating this model to a CFB tracker, which is the top performing one of VOT2016, 18% increase is achieved in terms of expected average overlap, and tracking failures are decreased by 25%, while maintaining the superiority over the state-of-the-art methods in OTB-2013 and OTB-2015 tracking datasets.