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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…
The kernel polynomial method (KPM) is a powerful numerical method for approximating spectral densities. Typical implementations of the KPM require an a prior estimate for an interval containing the support of the target spectral density,…
In this paper we present a simple but powerful subgraph sampling primitive that is applicable in a variety of computational models including dynamic graph streams (where the input graph is defined by a sequence of edge/hyperedge insertions…
This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical…
Understanding the singular value spectrum of a matrix $A \in \mathbb{R}^{n \times n}$ is a fundamental task in countless applications. In matrix multiplication time, it is possible to perform a full SVD and directly compute the singular…
Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…
In this work, the concept of quasi-type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. The…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
In this paper, we analyze the spatial information of deep features, and propose two complementary regressions for robust visual tracking. First, we propose a kernelized ridge regression model wherein the kernel value is defined as the…
We develop an exact and scalable algorithm for one-dimensional Gaussian process regression with Mat\'ern correlations whose smoothness parameter $\nu$ is a half-integer. The proposed algorithm only requires $\mathcal{O}(\nu^3 n)$ operations…
In this paper, we introduce an iterative speckle filtering method for polarimetric SAR (PolSAR) images based on the bilateral filter. To locally adapt to the spatial structure of images, this filter relies on pixel similarities in both…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for…
Kernel ridge regression (KRR) is a standard method for performing non-parametric regression over reproducing kernel Hilbert spaces. Given $n$ samples, the time and space complexity of computing the KRR estimate scale as $\mathcal{O}(n^3)$…
We provide a number of algorithmic results for the following family of problems: For a given binary m\times n matrix A and integer k, decide whether there is a "simple" binary matrix B which differs from A in at most k entries. For an…
To date, the histogram-based running median filter of Perreault and H\'ebert is considered the fastest for 8-bit images, being roughly O(1) in average case. We present here another approximately constant time algorithm which further…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
State-of-the-art methods for computer vision rely heavily on the translation equivariance and spatial sharing properties of convolutional layers without explicitly taking into consideration the input content. Modern techniques employ deep…
Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…