Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHMC, an Algorithms in Data Mining, the Functional Analysis approach
90
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The main purpose of this paper is to facilitate the communication between the Analytic, Probabilistic and Algorithmic communities. We present a proof of convergence of the Hamiltonian (Hybrid) Monte Carlo algorithm from the point of view of the Dynamical Systems, where the evolving objects are densities of probability distributions and the tool are derived from the Functional Analysis.
rate research
Read More
We present a proof of convergence of the Hamiltonian Monte Carlo algorithm in terms of Functional Analysis. We represent the algorithm as an operator on the density functions, and prove the convergence of iterations of this operator in $L^p$, for $1<p<infty$, and strong convergence for $2le p<infty$.
Process data refer to data recorded in the log files of computer-based items. These data, represented as timestamped action sequences, keep track of respondents response processes of solving the items. Process data analysis aims at enhancing educational assessment accuracy and serving other assessment purposes by utilizing the rich information contained in response processes. The R package ProcData presented in this article is designed to provide tools for processing, describing, and analyzing process data. We define an S3 class proc for organizing process data and extend generic methods summary and print for class proc. Two feature extraction methods for process data are implemented in the package for compressing information in the irregular response processes into regular numeric vectors. ProcData also provides functions for fitting and making predictions from a neural-network-based sequence model. These functions call relevant functions in package keras for constructing and training neural networks. In addition, several response process generators and a real dataset of response processes of the climate control item in the 2012 Programme for International Student Assessment are included in the package.
Functional data analysis (FDA) methods have computational and theoretical appeals for some high dimensional data, but lack the scalability to modern large sample datasets. To tackle the challenge, we develop randomized algorithms for two important FDA methods: functional principal component analysis (FPCA) and functional linear regression (FLR) with scalar response. The two methods are connected as they both rely on the accurate estimation of functional principal subspace. The proposed algorithms draw subsamples from the large dataset at hand and apply FPCA or FLR over the subsamples to reduce the computational cost. To effectively preserve subspace information in the subsamples, we propose a functional principal subspace sampling probability, which removes the eigenvalue scale effect inside the functional principal subspace and properly weights the residual. Based on the operator perturbation analysis, we show the proposed probability has precise control over the first order error of the subspace projection operator and can be interpreted as an importance sampling for functional subspace estimation. Moreover, concentration bounds for the proposed algorithms are established to reflect the low intrinsic dimension nature of functional data in an infinite dimensional space. The effectiveness of the proposed algorithms is demonstrated upon synthetic and real datasets.
We present and describe the GPFDA package for R. The package provides flexible functionalities for dealing with Gaussian process regression (GPR) models for functional data. Multivariate functional data, functional data with multidimensional inputs, and nonseparable and/or nonstationary covariance structures can be modeled. In addition, the package fits functional regression models where the mean function depends on scalar and/or functional covariates and the covariance structure is modeled by a GPR model. In this paper, we present the versatility of GPFDA with respect to mean function and covariance function specifications and illustrate the implementation of estimation and prediction of some models through reproducible numerical examples.
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form low-dimensional data sketches. We apply conventional statistical methods to compare probabilistic algorithms based on storing either selected order statistics, or random projections. We derive estimators of the cardinality in both cases, and show that the maximal-term estimator is recursively computable and has exponentially decreasing error bounds. Furthermore, we show that the estimators have comparable asymptotic efficiency, and explain this result by demonstrating an unexpected connection between the two approaches.
suggested questions
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
