Pyrax Documentation

Introduction

Welcome to the Pyrax documentation! This guide is structured to help you get started with probabilistic programming, Bayesian inference, and deep learning models using Pyrax. Pyrax also features $PYR, a Solana-based token designed for model sharing and incentivized contributions.

---

Table of Contents

1. Getting Started

2. Bayesian Inference and SVI

3. Deep Generative Models

4. Time Series Forecasting

5. Discrete Latent Variable Models

6. Integration with $PYR Token

7. Featured Tutorials

8. Community and Documentation

---

Getting Started

Pyrax provides an intuitive API for building probabilistic models.

Example: Simple Probabilistic Model

import pyrax as px

def model():
    weight = px.sample("weight", px.distributions.Normal(0, 1))
    bias = px.sample("bias", px.distributions.Normal(0, 1))
    x = px.param("x", [1.0, 2.0, 3.0])
    y = weight * x + bias
    return px.sample("obs", px.distributions.Normal(y, 0.1), obs=[1.5, 2.5, 3.5])

svi = px.SVI(model, px.optim.Adam(learning_rate=0.01), px.loss.ELBO())
for step in range(1000):
    loss = svi.step()
    print(f"Step {step}, Loss: {loss}")

---

Bayesian Inference and SVI

Pyrax supports Bayesian inference through Stochastic Variational Inference (SVI) to handle complex posterior distributions.

Bayesian Linear Regression Example

class BayesianLinearModel(px.Module):
    def __init__(self):
        self.weight = px.sample("weight", px.distributions.Normal(0, 1))
        self.bias = px.sample("bias", px.distributions.Normal(0, 1))

    def forward(self, x):
        return self.weight * x + self.bias

x_data = [0.5, 1.0, 1.5]
y_data = [2.0, 2.5, 3.0]

svi = px.SVI(BayesianLinearModel(), px.optim.Adam(0.005), px.loss.Trace_ELBO())
svi.train(x_data, y_data)

---

Deep Generative Models

Deep generative models such as Variational Autoencoders (VAEs) are powerful for high-dimensional data.

VAE Example

class VAE(px.Module):
    def __init__(self, input_dim, latent_dim):
        self.encoder = px.Linear(input_dim, latent_dim)
        self.decoder = px.Linear(latent_dim, input_dim)

    def forward(self, x):
        z_mean, z_log_var = self.encoder(x)
        z = px.sample("latent", px.distributions.Normal(z_mean, px.exp(0.5 * z_log_var)))
        return self.decoder(z)

---

Time Series Forecasting

Pyrax simplifies the modeling of time-dependent data.

Time Series Example

class ARModel(px.Module):
    def __init__(self):
        self.coefficients = px.sample("coefficients", px.distributions.Normal(0, 1))

    def forward(self, previous_values):
        return sum(c * v for c, v in zip(self.coefficients, previous_values))

---

Discrete Latent Variable Models

Hidden Markov Models (HMMs) are an example of models supported by Pyrax.

HMM Example

class HMM(px.Module):
    def __init__(self):
        self.transition_matrix = px.sample("transitions", px.distributions.Dirichlet([0.5, 0.5]))
        self.emission_means = px.sample("emissions", px.distributions.Normal(0, 1, [2]))

    def forward(self, sequence_length):
        states = []
        for t in range(sequence_length):
            state = px.sample(f"state_{t}", px.distributions.Categorical(self.transition_matrix))
            observation = px.sample(f"obs_{t}", px.distributions.Normal(self.emission_means[state], 1))
            states.append((state, observation))
        return states

---

Integration with $PYR Token

The $PYR Solana token enhances Pyrax with blockchain-enabled capabilities:

• Model Marketplace: Monetize or share trained models.

• Incentivized Collaboration: Earn $PYR by contributing innovative models.

• Distributed Compute Access: Pay for scalable distributed compute nodes using $PYR.

Smart Contract Example

def handle_payment(amount, public_key):
    if amount >= required_pyr_balance:
        grant_access_to_model(public_key)

---

Featured Tutorials

• "Hello, Bayesian World!": A beginner-friendly introduction.

• Advanced Pyrax Applications: Explore hierarchical Bayesian models.

• Solana-Powered Inference: Learn to deploy models with secure payments.

---

Community and Documentation

Join the Pyrax developer community, explore detailed guides, and contribute your projects to expand the Pyrax ecosystem.

---

Start Your Journey

Build with Pyrax and leverage the power of Bayesian programming and blockchain-backed $PYR incentives.