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We present a geometric framework for constructing additive and non-additive stabiliser codes which encompasses stabiliser codes and graphical non-additive stabiliser codes.

We consider parameter estimation in distributed networks, where each sensor in the network observes an independent sample from an underlying distribution and has $k$ bits to communicate its sample to a centralized processor which computes an estimate of a desired parameter. We develop lower bounds for the minimax risk of estimating the underlying parameter for a large class of losses and distributions. Our results show that under mild regularity conditions, the communication constraint reduces the effective sample size by a factor of $d$ when $k$ is small, where $d$ is the dimension of the estimated parameter. Furthermore, this penalty reduces at most exponentially with increasing $k$, which is the case for some models, e.g., estimating high-dimensional distributions. For other models however, we show that the sample size reduction is re-mediated only linearly with increasing $k$, e.g. when some sub-Gaussian structure is available. We apply our results to the distributed setting with product Bernoulli model, multinomial model, Gaussian location models, and logistic regression which recover or strengthen existing results. Our approach significantly deviates from existing approaches for developing information-theoretic lower bounds for communication-efficient estimation. We circumvent the need for strong data processing inequalities used in prior work and develop a geometric approach which builds on a new representation of the communication constraint. This approach allows us to strengthen and generalize existing results with simpler and more transparent proofs.

Complex, high-dimensional data is used in a wide range of domains to explore problems and make decisions. Analysis of high-dimensional data, however, is vulnerable to the hidden influence of confounding variables, especially as users apply ad hoc filtering operations to visualize only specific subsets of an entire dataset. Thus, visual data-driven analysis can mislead users and encourage mistaken assumptions about causality or the strength of relationships between features. This work introduces a novel visual approach designed to reveal the presence of confounding variables via counterfactual possibilities during visual data analysis. It is implemented in CoFact, an interactive visualization prototype that determines and visualizes \textit{counterfactual subsets} to better support user exploration of feature relationships. Using publicly available datasets, we conducted a controlled user study to demonstrate the effectiveness of our approach; the results indicate that users exposed to counterfactual visualizations formed more careful judgments about feature-to-outcome relationships.

Real-world videos contain many complex actions with inherent relationships between action classes. In this work, we propose an attention-based architecture that models these action relationships for the task of temporal action localization in untrimmed videos. As opposed to previous works that leverage video-level co-occurrence of actions, we distinguish the relationships between actions that occur at the same time-step and actions that occur at different time-steps (i.e. those which precede or follow each other). We define these distinct relationships as action dependencies. We propose to improve action localization performance by modeling these action dependencies in a novel attention-based Multi-Label Action Dependency (MLAD)layer. The MLAD layer consists of two branches: a Co-occurrence Dependency Branch and a Temporal Dependency Branch to model co-occurrence action dependencies and temporal action dependencies, respectively. We observe that existing metrics used for multi-label classification do not explicitly measure how well action dependencies are modeled, therefore, we propose novel metrics that consider both co-occurrence and temporal dependencies between action classes. Through empirical evaluation and extensive analysis, we show improved performance over state-of-the-art methods on multi-label action localization benchmarks(MultiTHUMOS and Charades) in terms of f-mAP and our proposed metric.

Intersection over Union (IoU) is the most popular evaluation metric used in the object detection benchmarks. However, there is a gap between optimizing the commonly used distance losses for regressing the parameters of a bounding box and maximizing this metric value. The optimal objective for a metric is the metric itself. In the case of axis-aligned 2D bounding boxes, it can be shown that $IoU$ can be directly used as a regression loss. However, $IoU$ has a plateau making it infeasible to optimize in the case of non-overlapping bounding boxes. In this paper, we address the weaknesses of $IoU$ by introducing a generalized version as both a new loss and a new metric. By incorporating this generalized $IoU$ ($GIoU$) as a loss into the state-of-the art object detection frameworks, we show a consistent improvement on their performance using both the standard, $IoU$ based, and new, $GIoU$ based, performance measures on popular object detection benchmarks such as PASCAL VOC and MS COCO.

Network embedding is the process of learning low-dimensional representations for nodes in a network, while preserving node features. Existing studies only leverage network structure information and focus on preserving structural features. However, nodes in real-world networks often have a rich set of attributes providing extra semantic information. It has been demonstrated that both structural and attribute features are important for network analysis tasks. To preserve both features, we investigate the problem of integrating structure and attribute information to perform network embedding and propose a Multimodal Deep Network Embedding (MDNE) method. MDNE captures the non-linear network structures and the complex interactions among structures and attributes, using a deep model consisting of multiple layers of non-linear functions. Since structures and attributes are two different types of information, a multimodal learning method is adopted to pre-process them and help the model to better capture the correlations between node structure and attribute information. We employ both structural proximity and attribute proximity in the loss function to preserve the respective features and the representations are obtained by minimizing the loss function. Results of extensive experiments on four real-world datasets show that the proposed method performs significantly better than baselines on a variety of tasks, which demonstrate the effectiveness and generality of our method.

We propose novel Stacked Spatio-Temporal Graph Convolutional Networks (Stacked-STGCN) for action segmentation, i.e., predicting and localizing a sequence of actions over long videos. We extend the Spatio-Temporal Graph Convolutional Network (STGCN) originally proposed for skeleton-based action recognition to enable nodes with different characteristics (e.g., scene, actor, object, action, etc.), feature descriptors with varied lengths, and arbitrary temporal edge connections to account for large graph deformation commonly associated with complex activities. We further introduce the stacked hourglass architecture to STGCN to leverage the advantages of an encoder-decoder design for improved generalization performance and localization accuracy. We explore various descriptors such as frame-level VGG, segment-level I3D, RCNN-based object, etc. as node descriptors to enable action segmentation based on joint inference over comprehensive contextual information. We show results on CAD120 (which provides pre-computed node features and edge weights for fair performance comparison across algorithms) as well as a more complex real-world activity dataset, Charades. Our Stacked-STGCN in general achieves 4.1% performance improvement over the best reported results in F1 score on CAD120 and 1.3% in mAP on Charades using VGG features.

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning. In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty to be learned. Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. Finally, we propose to apply optimal mass transportation theory to control the probability distribution in the latent space.

Image-level feature descriptors obtained from convolutional neural networks have shown powerful representation capabilities for image retrieval. In this paper, we present an unsupervised method to aggregate deep convolutional features into compact yet discriminative image vectors by simulating the dynamics of heat diffusion. A distinctive problem in image retrieval is that repetitive or bursty features tend to dominate feature representations, leading to less than ideal matches. We show that by leveraging elegant properties of the heat equation, our method is able to select informative features while avoiding over-representation of bursty features. We additionally present a theoretical time complexity analysis showing the efficiency of our method, which is further demonstrated in our experimental evaluation. Finally, we extensively evaluate the proposed approach with pre-trained and fine-tuned deep networks on common public benchmarks, and show superior performance compared to previous work.

Interest point descriptors have fueled progress on almost every problem in computer vision. Recent advances in deep neural networks have enabled task-specific learned descriptors that outperform hand-crafted descriptors on many problems. We demonstrate that commonly used metric learning approaches do not optimally leverage the feature hierarchies learned in a Convolutional Neural Network (CNN), especially when applied to the task of geometric feature matching. While a metric loss applied to the deepest layer of a CNN, is often expected to yield ideal features irrespective of the task, in fact the growing receptive field as well as striding effects cause shallower features to be better at high precision matching tasks. We leverage this insight together with explicit supervision at multiple levels of the feature hierarchy for better regularization, to learn more effective descriptors in the context of geometric matching tasks. Further, we propose to use activation maps at different layers of a CNN, as an effective and principled replacement for the multi-resolution image pyramids often used for matching tasks. We propose concrete CNN architectures employing these ideas, and evaluate them on multiple datasets for 2D and 3D geometric matching as well as optical flow, demonstrating state-of-the-art results and generalization across datasets.