Related papers: Kernel entropy estimation for long memory linear p…
Kernel methods form a theoretically-grounded, powerful and versatile framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the \emph{kernel trick} to perform pairwise evaluations of…
In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly…
In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and…
Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have…
We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…
In this paper, we present a framework for fitting multivariate Hawkes processes for large-scale problems both in the number of events in the observed history $n$ and the number of event types $d$ (i.e. dimensions). The proposed Low-Rank…
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 propose a nonparametric parameter estimation of confidence intervals when the underlying has large or infinite variance. We explain the method by a simple numerical example and provide an application to estimate the coupling strength in…
We describe a quantum algorithm to estimate the $\alpha$-Renyi entropy of an unknown density matrix $\rho\in\mathcal{C}^{d\times d}$ for $\alpha\neq 1$ by combining the recent technique of quantum singular value transformations with the…
Reinforcement learning (RL) algorithms based on high-dimensional function approximation have achieved tremendous empirical success in large-scale problems with an enormous number of states. However, most analysis of such algorithms gives…
We propose an inference procedure for estimators defined by mathematical programming problems, focusing on the important special cases of linear programming (LP) and quadratic programming (QP). In these settings, the coefficients in both…
Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive…
An important feature of kernel mean embeddings (KME) is that the rate of convergence of the empirical KME to the true distribution KME can be bounded independently of the dimension of the space, properties of the distribution and smoothness…
Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We establish the asymptotic normality of the kernel type estimator for the regression function constructed from quasi-associated data when the explanatory variable takes its values in a separable Hilbert space.
We consider discrete time models for asset prices with a stationary volatility process. We aim at estimating the multivariate density of this process at a set of consecutive time instants. A Fourier type deconvolution kernel density…
We introduce an estimation method for the scaled skewness coefficient of the sample mean of short and long memory linear processes. This method can be extended to estimate higher moments such as curtosis coefficient of the sample mean. Also…
We study a quantity called discrete layered entropy, which approximates the Shannon entropy within a logarithmic gap. Compared to the Shannon entropy, the discrete layered entropy is piecewise linear, approximates the expected length of the…