**Randomized Block Cubic Newton (RBCN)**

We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\cal O}(1/\epsilon)$, ${\cal O}(1/\sqrt{\epsilon})$ and ${\cal O}(\log (1/\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression. … **Gaussian Process Latent Variable Alignment Learning**

We present a model that can automatically learn alignments between high-dimensional data in an unsupervised manner. Learning alignments is an ill-constrained problem as there are many different ways of defining a good alignment. Our proposed method casts alignment learning in a framework where both alignment and data are modelled simultaneously. We derive a probabilistic model built on non-parametric priors that allows for flexible warps while at the same time providing means to specify interpretable constraints. We show results on several datasets, including different motion capture sequences and show that the suggested model outperform the classical algorithmic approaches to the alignment task. … **Multimodal Deep Network Embedding (MDNE)**

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. … **Scale-Adaptive Neural Dense Features (SAND Features)**

How do computers and intelligent agents view the world around them? Feature extraction and representation constitutes one the basic building blocks towards answering this question. Traditionally, this has been done with carefully engineered hand-crafted techniques such as HOG, SIFT or ORB. However, there is no “one size fits all” approach that satisfies all requirements. In recent years, the rising popularity of deep learning has resulted in a myriad of end-to-end solutions to many computer vision problems. These approaches, while successful, tend to lack scalability and can’t easily exploit information learned by other systems. Instead, we propose SAND features, a dedicated deep learning solution to feature extraction capable of providing hierarchical context information. This is achieved by employing sparse relative labels indicating relationships of similarity/dissimilarity between image locations. The nature of these labels results in an almost infinite set of dissimilar examples to choose from. We demonstrate how the selection of negative examples during training can be used to modify the feature space and vary it’s properties. To demonstrate the generality of this approach, we apply the proposed features to a multitude of tasks, each requiring different properties. This includes disparity estimation, semantic segmentation, self-localisation and SLAM. In all cases, we show how incorporating SAND features results in better or comparable results to the baseline, whilst requiring little to no additional training. Code can be found at: https://…/SAND_features …

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Sep 2020

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