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Consistent in-focus input imagery is an essential precondition for machine vision systems to perceive the dynamic environment. A defocus blur severely degrades the performance of vision systems. To tackle this problem, we propose a…

A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…

Bayesian inference problems require sampling or approximating high-dimensional probability distributions. The focus of this paper is on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely…

Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of data. More importantly, they are proven invariant to…

In the compressive learning theory, instead of solving a statistical learning problem from the input data, a so-called sketch is computed from the data prior to learning. The sketch has to capture enough information to solve the problem…

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel…

Creating representations of shapes that are invari-ant to isometric or almost-isometric transforma-tions has long been an area of interest in shape anal-ysis, since enforcing invariance allows the learningof more effective and robust shape…

Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…

The need for large amounts of training data in modern machine learning is one of the biggest challenges of the field. Compared to the brain, current artificial algorithms are much less capable of learning invariance transformations and…

Measuring and testing dependence between complex objects is of great importance in modern statistics. Most existing work relied on the distance between random variables, which inevitably required the moment conditions to guarantee the…

This paper presents new and effective algorithms for learning kernels. In particular, as shown by our empirical results, these algorithms consistently outperform the so-called uniform combination solution that has proven to be difficult to…

The computational complexity of kernel methods has often been a major barrier for applying them to large-scale learning problems. We argue that this barrier can be effectively overcome. In particular, we develop methods to scale up kernel…

The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…

Symmetry plays a central role in the sciences, machine learning, and statistics. While statistical tests for the presence of distributional invariance with respect to groups have a long history, tests for conditional symmetry in the form of…

It is widely believed that the success of deep networks lies in their ability to learn a meaningful representation of the features of the data. Yet, understanding when and how this feature learning improves performance remains a challenge:…

Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble…

Quantum kernel methods are a promising method in quantum machine learning thanks to the guarantees connected to them. Their accessibility for analytic considerations also opens up the possibility of prescreening datasets based on their…

The creation of unstable heavy particles at the Large Hadron Collider is the most direct way to address some of the deepest open questions in physics. Collisions typically produce variable-size sets of observed particles which have inherent…

Symmetry is present in nature and science. In image processing, kernels for spatial filtering possess some symmetry (e.g. Sobel operators, Gaussian, Laplacian). Convolutional layers in artificial feed-forward neural networks have typically…

Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…