# Abductive Reasoning and Probabilistic Programming

Hi!

I wondered where the best place to get started learning about how Abductive Reasoning has materialized in the Probabilistic Programming and Bayesian Inference worlds: any research papers or books not about Bayesian inferences and inductive reasoning? Should I read mainly about Beliefs revisions? I want to look at the math itself… I wonder how the Abduction, Deduction, and Induction cycle is being expressed and leveraged.

I was thinking something as follows:

• Abduction: Generative models (e.g., GANs, LSTMs)
• Deduction: Rule-based models (e.g., Decision Trees)
• Induction: Statistical models (e.g., Random Forest)
• Iterative Refinement: Reinforcement Learning models

For fun, I asked ChatGPT to program Adbudctive Reasoning with Pyro, and it spitted out something … fun! I’ve no experience with PyTorch or Pyro.

Sorry if that’s the weirdest/random/stupid question ever.

Here’s what ChatGPT printed out if curious ``````import torch
import pyro
import pyro.distributions as dist
import pyro.nn as pnn

class Attention(pnn.PyroModule):
def __init__(self, hidden_size):
super().__init__()
self.fc = pnn.PyroModule[torch.nn.Linear](hidden_size, 1)

def forward(self, rnn_output):
attention_weights = torch.nn.functional.softmax(self.fc(rnn_output).squeeze(-1), dim=1)
context_vector = torch.sum(attention_weights.unsqueeze(-1) * rnn_output, dim=1)
return context_vector

class AbductiveReasoningModel(pnn.PyroModule):
def __init__(self, num_explanations, num_categories, rnn_hidden_size):
super().__init__()
self.num_explanations = num_explanations
self.num_categories = num_categories
self.rnn = pnn.PyroModule[torch.nn.RNN](input_size=1, hidden_size=rnn_hidden_size, batch_first=True)
self.attention = Attention(rnn_hidden_size)

def forward(self, observations):
# Temporal reasoning using an RNN
rnn_output, _ = self.rnn(observations.unsqueeze(-1))
context_vector = self.attention(rnn_output)

# Hierarchical model: sample a category first
category_probs = pyro.param("category_probs", torch.ones(self.num_categories) / self.num_categories, constraint=dist.constraints.simplex)
category = pyro.sample("category", dist.Categorical(category_probs))

# Explanation probabilities depend on the chosen category
explanation_probs = pyro.param(f"explanation_probs_{category}", torch.ones(self.num_explanations) / self.num_explanations, constraint=dist.constraints.simplex)

# Sample an explanation based on the category
explanation = pyro.sample("explanation", dist.Categorical(explanation_probs))

# Simple Causal Model: Introduce a latent variable that affects the observations
latent_factor = pyro.sample("latent", dist.Normal(0, 1))
causal_effect = context_vector + latent_factor

# Placeholder: Combine the latent factor, attention context, and explanation.
combined_score = torch.dot(causal_effect, explanation.float())

return combined_score

# Placeholder data
observations = torch.tensor([0.1, 0.2, 0.3, 0.4])
num_explanations = 5
num_categories = 3
rnn_hidden_size = 10

model = AbductiveReasoningModel(num_explanations, num_categories, rnn_hidden_size)

# Placeholder guide for variational inference
def guide():
category_probs = pyro.param("category_probs", torch.ones(num_categories) / num_categories, constraint=dist.constraints.simplex)
category = pyro.sample("category", dist.Categorical(category_probs))

explanation_probs = pyro.param(f"explanation_probs_{category}", torch.ones(num_explanations) / num_explanations, constraint=dist.constraints.simplex)
explanation = pyro.sample("explanation", dist.Categorical(explanation_probs))

latent_factor = pyro.sample("latent", dist.Normal(0, 1))

# Placeholder loss and optimization
loss = pyro.infer.Trace_ELBO().differentiable_loss