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In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric structures to solve these problems efficiently. We show that a wide range of geometric theories emerge naturally in these fields, ranging from measure-preserving processes, information divergences, Poisson geometry, and geometric integration. Specifically, we explain how (i) leveraging the symplectic geometry of Hamiltonian systems enable us to construct (accelerated) sampling and optimisation methods, (ii) the theory of Hilbertian subspaces and Stein operators provides a general methodology to obtain robust estimators, (iii) preserving the information geometry of decision-making yields adaptive agents that perform active inference. Throughout, we emphasise the rich connections between these fields; e.g., inference draws on sampling and optimisation, and adaptive decision-making assesses decisions by inferring their counterfactual consequences. Our exposition provides a conceptual overview of underlying ideas, rather than a technical discussion, which can be found in the references herein.

Adapting Deep Learning (DL) techniques to automate non-trivial coding activities, such as code documentation and defect detection, has been intensively studied recently. Learning to predict code changes is one of the popular and essential investigations. Prior studies have shown that DL techniques such as Neural Machine Translation (NMT) can benefit meaningful code changes, including bug fixing and code refactoring. However, NMT models may encounter bottleneck when modeling long sequences, thus are limited in accurately predicting code changes. In this work, we design a Transformer-based approach, considering that Transformer has proven effective in capturing long-term dependencies. Specifically, we propose a novel model named DTrans. For better incorporating the local structure of code, i.e., statement-level information in this paper, DTrans is designed with dynamically relative position encoding in the multi-head attention of Transformer. Experiments on benchmark datasets demonstrate that DTrans can more accurately generate patches than the state-of-the-art methods, increasing the performance by at least 5.45\%-46.57\% in terms of the exact match metric on different datasets. Moreover, DTrans can locate the lines to change with 1.75\%-24.21\% higher accuracy than the existing methods.

General purpose optimization techniques can be used to solve many problems in engineering computations, although their cost is often prohibitive when the number of degrees of freedom is very large. We describe a multilevel approach to speed up the computation of the solution of a large-scale optimization problem by a given optimization technique. By embedding the problem within Harten's Multiresolution Framework (MRF), we set up a procedure that leads to the desired solution, after the computation of a finite sequence of sub-optimal solutions, which solve auxiliary optimization problems involving a smaller number of variables. For convex optimization problems having smooth solutions, we prove that the distance between the optimal solution and each sub-optimal approximation is related to the accuracy of the interpolation technique used within the MRF and analyze its relation with the performance of the proposed algorithm. Several numerical experiments confirm that our technique provides a computationally efficient strategy that allows the end user to treat both the optimizer and the objective function as black boxes throughout the optimization process.

Face clustering is a promising way to scale up face recognition systems using large-scale unlabeled face images. It remains challenging to identify small or sparse face image clusters that we call hard clusters, which is caused by the heterogeneity, \ie, high variations in size and sparsity, of the clusters. Consequently, the conventional way of using a uniform threshold (to identify clusters) often leads to a terrible misclassification for the samples that should belong to hard clusters. We tackle this problem by leveraging the neighborhood information of samples and inferring the cluster memberships (of samples) in a probabilistic way. We introduce two novel modules, Neighborhood-Diffusion-based Density (NDDe) and Transition-Probability-based Distance (TPDi), based on which we can simply apply the standard Density Peak Clustering algorithm with a uniform threshold. Our experiments on multiple benchmarks show that each module contributes to the final performance of our method, and by incorporating them into other advanced face clustering methods, these two modules can boost the performance of these methods to a new state-of-the-art. Code is available at: //github.com/echoanran/On-Mitigating-Hard-Clusters.

We present a generic framework for scale-aware direct monocular odometry based on depth prediction from a deep neural network. In contrast with previous methods where depth information is only partially exploited, we formulate a novel depth prediction residual which allows us to incorporate multi-view depth information. In addition, we propose to use a truncated robust cost function which prevents considering inconsistent depth estimations. The photometric and depth-prediction measurements are integrated into a tightly-coupled optimization leading to a scale-aware monocular system which does not accumulate scale drift. Our proposal does not particularize for a concrete neural network, being able to work along with the vast majority of the existing depth prediction solutions. We demonstrate the validity and generality of our proposal evaluating it on the KITTI odometry dataset, using two publicly available neural networks and comparing it with similar approaches and the state-of-the-art for monocular and stereo SLAM. Experiments show that our proposal largely outperforms classic monocular SLAM, being 5 to 9 times more precise, beating similar approaches and having an accuracy which is closer to that of stereo systems.

Event cameras are bio-inspired sensors that offer advantages over traditional cameras. They work asynchronously, sampling the scene with microsecond resolution and producing a stream of brightness changes. This unconventional output has sparked novel computer vision methods to unlock the camera's potential. We tackle the problem of event-based stereo 3D reconstruction for SLAM. Most event-based stereo methods try to exploit the camera's high temporal resolution and event simultaneity across cameras to establish matches and estimate depth. By contrast, we investigate how to estimate depth without explicit data association by fusing Disparity Space Images (DSIs) originated in efficient monocular methods. We develop fusion theory and apply it to design multi-camera 3D reconstruction algorithms that produce state-of-the-art results, as we confirm by comparing against four baseline methods and testing on a variety of available datasets.

Estimating human motion from video is an active research area due to its many potential applications. Most state-of-the-art methods predict human shape and posture estimates for individual images and do not leverage the temporal information available in video. Many "in the wild" sequences of human motion are captured by a moving camera, which adds the complication of conflated camera and human motion to the estimation. We therefore present BodySLAM, a monocular SLAM system that jointly estimates the position, shape, and posture of human bodies, as well as the camera trajectory. We also introduce a novel human motion model to constrain sequential body postures and observe the scale of the scene. Through a series of experiments on video sequences of human motion captured by a moving monocular camera, we demonstrate that BodySLAM improves estimates of all human body parameters and camera poses when compared to estimating these separately.

Current methods for video activity localisation over time assume implicitly that activity temporal boundaries labelled for model training are determined and precise. However, in unscripted natural videos, different activities mostly transit smoothly, so that it is intrinsically ambiguous to determine in labelling precisely when an activity starts and ends over time. Such uncertainties in temporal labelling are currently ignored in model training, resulting in learning mis-matched video-text correlation with poor generalisation in test. In this work, we solve this problem by introducing Elastic Moment Bounding (EMB) to accommodate flexible and adaptive activity temporal boundaries towards modelling universally interpretable video-text correlation with tolerance to underlying temporal uncertainties in pre-fixed annotations. Specifically, we construct elastic boundaries adaptively by mining and discovering frame-wise temporal endpoints that can maximise the alignment between video segments and query sentences. To enable both more accurate matching (segment content attention) and more robust localisation (segment elastic boundaries), we optimise the selection of frame-wise endpoints subject to segment-wise contents by a novel Guided Attention mechanism. Extensive experiments on three video activity localisation benchmarks demonstrate compellingly the EMB's advantages over existing methods without modelling uncertainty.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

We introduce a new language representation model called BERT, which stands for Bidirectional Encoder Representations from Transformers. Unlike recent language representation models, BERT is designed to pre-train deep bidirectional representations by jointly conditioning on both left and right context in all layers. As a result, the pre-trained BERT representations can be fine-tuned with just one additional output layer to create state-of-the-art models for a wide range of tasks, such as question answering and language inference, without substantial task-specific architecture modifications. BERT is conceptually simple and empirically powerful. It obtains new state-of-the-art results on eleven natural language processing tasks, including pushing the GLUE benchmark to 80.4% (7.6% absolute improvement), MultiNLI accuracy to 86.7 (5.6% absolute improvement) and the SQuAD v1.1 question answering Test F1 to 93.2 (1.5% absolute improvement), outperforming human performance by 2.0%.