Update README.md

Author: NikitinaMaria

README.md

@@ -19,9 +19,41 @@
 
 This repository implements an educational project for the Bayesian Multimodeling course. It implements algorithms for sampling from various distributions, using the implicit reparameterization trick.
 
-## Описание
-
-В этом репозитории реализован учебный проект для курса Байесовское мультимоделирование. В нем реализуются алгоритмы сэмплирования из различных распределений, используя implicit reparametriation trick.
+## Scope
+We plan to implement the following distributions in our library:
+- Gaussian normal distribution (*)
+- Dirichlet distribution (Beta distributions)(\*)
+- Sampling from a mixture of distributions
+- Sampling from the Student's t-distribution (**) (\*)
+- Sampling from an arbitrary factorized distribution (***)
+
+(\*) - this distribution is already implemented in torch using the explicit reparameterization trick, we will implement it for comparison
+
+(\*\*) - this distribution is added as a backup, their inclusion is questionable
+
+(\*\*\*) - this distribution is not very clear in implementation, its inclusion is questionable
+
+## Stack
+
+We plan to inherit from the torch.distribution.Distribution class, so we need to implement all the methods that are present in that class.
+
+##  Usage
+In this example, we demonstrate the application of our library using a Variational Autoencoder (VAE) model, where the latent layer is modified by a normal distribution.
+```
+>>> import torch.distributions.implicit as irt
+>>> params = Encoder(inputs)
+>>> gauss = irt.Normal(*params)
+>>> deviated = gauss.rsample()
+>>> outputs = Decoder(deviated)
+```
+In this example, we demonstrate the use of a mixture of distributions using our library.
+```
+>>> import irt
+>>> params = Encoder(inputs)
+>>> mix = irt.Mixture([irt.Normal(*params), irt.Dirichlet(*params)])
+>>> deviated = mix.rsample()
+>>> outputs = Decoder(deviated)
+```
 
 ## Links
 - [LinkReview](https://github.com/intsystems/implitic-reparametrization-trick/blob/main/linkreview.md)