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FastGaSP (version 0.6.0)

Fast and Exact Computation of Gaussian Stochastic Process

Description

Implements fast and exact computation of Gaussian stochastic process with the Matern kernel using forward filtering and backward smoothing algorithm. It includes efficient implementations of the inverse Kalman filter, with applications such as estimating particle interaction functions. These tools support models with or without noise. Additionally, the package offers algorithms for fast parameter estimation in latent factor models, where the factor loading matrix is orthogonal, and latent processes are modeled by Gaussian processes. See the references: 1) Mengyang Gu and Yanxun Xu (2020), Journal of Computational and Graphical Statistics; 2) Xinyi Fang and Mengyang Gu (2024), ; 3) Mengyang Gu and Weining Shen (2020), Journal of Machine Learning Research; 4) Yizi Lin, Xubo Liu, Paul Segall and Mengyang Gu (2025), .

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Version

Install

install.packages('FastGaSP')

Monthly Downloads

267

Version

0.6.0

License

GPL (>= 2)

Maintainer

Mengyang Gu

Last Published

February 12th, 2025

Functions in FastGaSP (0.6.0)

Construct_W_matern_5_2

The conditional covariance matrix for matern covariance with roughness parameter 2.5

f_Vicsek_variation

Modified Vicsek Interaction Function

IKF_CG_particle

IKF-CG algorithm for one-interaction physical model with 1D output

the natural logarithm of the determinant of the correlation matrix and the estimated sum of squares in the exponent of the profile likelihood

Fast GaSP class

Setting up the Fast GaSP model

Sample the prior process using a dynamic linear model

The multiplication of the transpose of L with y

The multiplication of L with y

Sample the posterior distribution of the process using the backward smoothing algorithm

IKF_CG_particle_cell

Inverse Kalman Filter with Conjugate Gradient for Particle Systems

Fit Particle Interaction Models

particle.est-class

Particle interaction estimation class

Prediction and uncertainty quantification on the testing input using a GaSP model.

Setting up the FMOU model

get_consecutive_data

Extract consecutive time steps data from particle trajectories

Kalman_smoother

the predictive mean and predictive variance by Kalman Smoother

Natural logarithm of profile likelihood by the fast computing algorithm

particle.data-class

Particle trajectory data class

simulate_particle

Simulate particle trajectories

The fast EM algorithm of multivariate Ornstein-Uhlenbeck processes

Parameter estimation for generalized probabilistic principal component analysis of correlated data.

show.particle.data

Show method for particle data class

trajectory_data

Convert experimental particle tracking data to particle.data object

extract_time_window

Extract time window from particle data

Vicsek Model Simulation

show.particle.est

Show method for particle estimation class

Setting up the GPPCA model

predictobj.fgasp-class

Predictive results for the Fast GaSP class

fit.particle.data

Fit method for particle data

Prediction and uncertainty quantification on the future observations using GPPCA.

Prediction and uncertainty quantification on the future observations using a FMOU model.

Show an fgasp object.

FastGaSP-package

tools:::Rd_package_title("FastGaSP")

Construct_W_exp

The conditional covariance matrix of the state in the dynamic linear model when kernel is the exponential covariance

A_t_times_x_particle

Transpose matrix-vector multiplication for particle systems

Construct_W0_exp

covariance of the stationary distribution of the state when kernel is the exponential covariance.

matrices and vectors for the inverse covariance in the predictive distribution

Construct_G_exp

The coefficient matrix in the dynamic linear model when kernel is the exponential covariance

Construct_G_matern_5_2

The coefficient matrix in the dynamic linear model when kernel is the Matern covariance with roughness parameter 2.5.

The multiplication of the inverse of L with y

Construct_W0_matern_5_2

covariance of the stationary distribution of the state when kernel is the Matern covariance with roughness parameter 2.5.

A_times_x_particle

Matrix-vector multiplication for particle systems

The multiplication of the inverse of the transpose of L with y

The multiplication of R with y

one-step-ahead predictive variance and Kalman gain