Related papers: Simplified derivations for high-dimensional convex…

The article explores an encoding and structural information processing approach using sparse bit vectors and fixed-length linear vectors. The following are presented: a discrete method of speculative stochastic dimensionality reduction of…

A graph-based classification method is proposed for semi-supervised learning in the case of Euclidean data and for classification in the case of graph data. Our manifold learning technique is based on a convex optimization problem involving…

While visual imitation learning offers one of the most effective ways of learning from visual demonstrations, generalizing from them requires either hundreds of diverse demonstrations, task specific priors, or large, hard-to-train…

Traditional feature extraction and projection techniques, such as Principal Component Analysis, struggle to adequately represent X-Ray Transmission (XRT) Multi-Energy (ME) images, limiting the performance of neural networks in…

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite…

We present a general framework of semi-supervised dimensionality reduction for manifold learning which naturally generalizes existing supervised and unsupervised learning frameworks which apply the spectral decomposition. Algorithms derived…

On the long-established classification problems in general relativity we take a novel perspective by adopting fruitful techniques from machine learning and modern data-science. In particular, we model Petrov's classification of spacetimes,…

Simplicial complexes prove effective in modeling data with multiway dependencies, such as data defined along the edges of networks or within other higher-order structures. Their spectrum can be decomposed into three interpretable subspaces…

One of the most fundamental problems in machine learning is to compare examples: Given a pair of objects we want to return a value which indicates degree of (dis)similarity. Similarity is often task specific, and pre-defined distances can…

Solving geometric tasks involving point clouds by using machine learning is a challenging problem. Standard feed-forward neural networks combine linear or, if the bias parameter is included, affine layers and activation functions. Their…

We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the…

A fundamental problem in manifold learning is to approximate a functional relationship in a data chosen randomly from a probability distribution supported on a low dimensional sub-manifold of a high dimensional ambient Euclidean space. The…

In these lecture notes we present different methods and concepts developed in statistical physics to analyze gradient descent dynamics in high-dimensional non-convex landscapes. Our aim is to show how approaches developed in physics, mainly…

Capsule networks were proposed as an alternative approach to Convolutional Neural Networks (CNNs) for learning object-centric representations, which can be leveraged for improved generalization and sample complexity. Unlike CNNs, capsule…

We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…

Recently, there has been much interest in spectral approaches to learning manifolds---so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

Human brain connectome studies aim at extracting and analyzing relevant features associated to pathologies of interest. Usually this consists in modeling the brain connectome as a graph and in using graph metrics as features. A fine brain…

High-dimensional data with intrinsic low-dimensional structure is ubiquitous in machine learning and data science. While various approaches allow one to learn a data manifold with a Riemannian structure from finite samples, performing…

Robust optimization has been established as a leading methodology to approach decision problems under uncertainty. To derive a robust optimization model, a central ingredient is to identify a suitable model for uncertainty, which is called…