Variational Flow-Based Inference for Rare Events and Large Deviations

Variational flow-based methods for modeling rare events using Kullback–Leibler (KL) divergence, normalizing flows, Girsanov change of measure, and Freidlin–Wentzell action functionals. The package provides tools for rare-event inference, minimum-action paths, and quasi-potential computation in stochastic dynamical systems. Methods are based on Rezende and Mohamed (2015) , Girsanov (1960) , and Freidlin and Wentzell (2012, ISBN:978-0387955477).

rareflow

Normalizing Flows for Rare-Event Inference

Overview

rareflow provides a unified framework for rare-event inference by combining:

• Sanov theory for empirical distributions
• Girsanov change of measure for SDEs
• Freidlin–Wentzell large deviations for small-noise diffusions
• Normalizing flows for flexible variational inference

The package includes:

• modular flow models (planar, radial, MAF, spline)
• variational optimization via ELBO
• wrappers for Girsanov tilting and FW quasi-potentials
• tools for rare-event simulation and analysis

Installation

From GitHub

# install.packages("devtools")
devtools::install_github("PietroPiu-labstats/rareflow")

Quick Example

A minimal workflow for fitting a variational posterior using a planar flow:

library(rareflow)

Qobs <- c(0.05, 0.90, 0.05)
px <- function(z) c(0.3, 0.4, 0.3)

flow <- makeflow("planar")
fit <- fitflowvariational(Qobs, pxgivenz = px, nmc = 500)

fit$elbo

Girsanov Tilting

b <- function(x) -x
dt <- 0.01
T <- 1000
Winc <- rnorm(T, sd = sqrt(dt))

fit_gir <- fitflow_girsanov(
  observed = Qobs,
  drift = b,
  Winc = Winc,
  dt = dt,
  pxgivenz = px
)

Freidlin–Wentzell Quasi-Potential

b <- function(x) x - x^3
qp <- FW_quasipotential(-1, 1, drift = b, T = 200, dt = 0.01)
qp$action

Documentation

Full documentation and examples are available in the package vignette:

vignette("rareflow")

Features

• Variational inference with normalizing flows

• Rare-event tilting via Girsanov

• Minimum-action paths and quasi-potentials

• Support for 1D and 2D systems

• Modular flow architecture