Related papers: Rotation Invariant Angular Descriptor Via A Bandli…
Rahimi and Recht (2007) introduced the idea of decomposing positive definite shift-invariant kernels by randomly sampling from their spectral distribution for machine learning applications. This famous technique, known as Random Fourier…
Although Convolutional Neural Networks (CNNs) have achieved promising results in image classification, they still are vulnerable to affine transformations including rotation, translation, flip and shuffle. The drawback motivates us to…
The analytic inference, e.g. predictive distribution being in closed form, may be an appealing benefit for machine learning practitioners when they treat wide neural networks as Gaussian process in Bayesian setting. The realistic widths,…
The velocity distributions of stellar tracers in general exhibit weak non-Gaussianity encoding information on the orbital composition of a galaxy and the underlying potential. The standard solution for measuring non-Gaussianity involves…
We consider nonparametric estimation of the derivative of a probability density function with the bounded support on $[0,\infty)$. Estimates are looked up in the class of estimates with asymmetric gamma kernel functions. The use of gamma…
This study proposes multivariate kernel density estimation by stagewise minimization algorithm based on $U$-divergence and a simple dictionary. The dictionary consists of an appropriate scalar bandwidth matrix and a part of the original…
We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
This paper studies Kernel Density Estimation for a high-dimensional distribution $\rho(x)$. Traditional approaches have focused on the limit of large number of data points $n$ and fixed dimension $d$. We analyze instead the regime where…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
We introduce a new approach for estimating the invariant density of a multidimensional diffusion when dealing with high-frequency observations blurred by independent noises. We consider the intermediate regime, where observations occur at…
Recent progress in variational inference has paid much attention to the flexibility of variational posteriors. One promising direction is to use implicit distributions, i.e., distributions without tractable densities as the variational…
We present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we…
Simulating a Gaussian process requires sampling from a high-dimensional Gaussian distribution, which scales cubically with the number of sample locations. Spectral methods address this challenge by exploiting the Fourier representation,…
This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides…
Convolutional neural networks have shown great success on feature extraction from raw input data such as images. Although convolutional neural networks are invariant to translations on the inputs, they are not invariant to other…
We analyze in this paper a random feature map based on a theory of invariance I-theory introduced recently. More specifically, a group invariant signal signature is obtained through cumulative distributions of group transformed random…
Image acquisition and segmentation are likely to introduce noise. Further image processing such as image registration and parameterization can introduce additional noise. It is thus imperative to reduce noise measurements and boost signal.…
We consider a family of gradient Gaussian vector fields on the torus $(\mathbb{Z}/L^N\mathbb{Z})^d$. Adams, Koteck\'{y}, M\"{u}ller and independently Bauerschmidt established the existence of a uniform finite range decomposition of the…
We study change-point detection for high-dimensional data in regimes where inference must be performed from small batches of observations. Our primary focus is the high-dimensional, low sample size (HDLSS) regime, where the sequence length…