Related papers: Fast Randomized Kernel Methods With Statistical Gu…
Tensor algebras give rise to one of the most powerful measures of similarity for sequences of arbitrary length called the signature kernel accompanied with attractive theoretical guarantees from stochastic analysis. Previous algorithms to…
Kernel methods provide an elegant framework for developing nonlinear learning algorithms from simple linear methods. Though these methods have superior empirical performance in several real data applications, their usefulness is inhibited…
The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…
Reinforcement Learning (RL) problems are being considered under increasingly more complex structures. While tabular and linear models have been thoroughly explored, the analytical study of RL under nonlinear function approximation,…
The graphlet kernel is a classical method in graph classification. It however suffers from a high computation cost due to the isomorphism test it includes. As a generic proxy, and in general at the cost of losing some information, this test…
This paper presents a practical, and theoretically well-founded, approach to improve the speed of kernel manifold learning algorithms relying on spectral decomposition. Utilizing recent insights in kernel smoothing and learning with…
In learning-to-learn the goal is to infer a learning algorithm that works well on a class of tasks sampled from an unknown meta distribution. In contrast to previous work on batch learning-to-learn, we consider a scenario where tasks are…
We present space-efficient linear sketches for estimating trimmed statistics of an $n$-dimensional frequency vector $x$, e.g., the sum of $p$-th powers of the largest $k$ frequencies (i.e., entries) in absolute value, or the $k$-trimmed…
We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…
In this work, we propose a method for speeding up linear regression distributively, while ensuring security. We leverage randomized sketching techniques, and improve straggler resilience in asynchronous systems. Specifically, we apply a…
Despite being a key bottleneck in many machine learning tasks, the cost of solving large linear systems has proven challenging to quantify due to problem-dependent quantities such as condition numbers. To tackle this, we consider a…
The Grassmannian manifold G(k, n) serves as a fundamental tool in signal processing, computer vision, and machine learning, where problems often involve classifying, clustering, or comparing subspaces. In this work, we propose a…
We develop an approach for feature elimination in statistical learning with kernel machines, based on recursive elimination of features.We present theoretical properties of this method and show that it is uniformly consistent in finding the…
This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…
In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the…
It has been found that stochastic algorithms often find good solutions much more rapidly than inherently-batch approaches. Indeed, a very useful rule of thumb is that often, when solving a machine learning problem, an iterative technique…
We study the fixed design segmented regression problem: Given noisy samples from a piecewise linear function $f$, we want to recover $f$ up to a desired accuracy in mean-squared error. Previous rigorous approaches for this problem rely on…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
Leverage score sampling is a powerful technique that originates from theoretical computer science, which can be used to speed up a large number of fundamental questions, e.g. linear regression, linear programming, semi-definite programming,…