Fundamentals

This section covers the core concepts and models in poisson-topicmodels, providing a deeper understanding of topic modeling and the different model variants available.

Fundamentals

• Core Concepts
  • What is Topic Modeling?
  • Document-Term Matrix
  • Vocabulary
  • Topics and Word Distributions
  • Document-Topic Mixtures
  • The Complete Picture
  • Poisson Factorization Model
  • Inference: Learning from Data
  • Hyperparameters
  • Convergence and Loss
  • Interpreting Topics
  • Model Assumptions
  • Common Pitfalls
  • Next Steps
• Poisson Factorization (PF)
  • When to Use PF
  • The Model
  • Example: Basic Usage
  • Interpreting Results
  • Example Interpretation Workflow
  • Hyperparameter Selection
  • Training Tips
  • Common Issues and Solutions
  • Evaluation Metrics
  • Next Steps
• Seeded Models (SPF & Keywords)
  • When to Use Seeded Models
  • The Model
  • Basic Usage
  • How Seeding Works
  • Advanced: Seed Strength
  • Designing Good Seeds
  • Mixing Seeded and Unseeded Topics
  • Iterative Seeding
  • Practical Example
  • Troubleshooting Seeds
  • Validation
  • Comparison with Unsupervised
  • Next Steps
• Covariate Models (CPF & CSPF)
  • Covariate Poisson Factorization (CPF)
  • Covariate Seeded PF (CSPF)
  • Tips for Covariate Modeling
  • Common Patterns
  • Visualization Examples
  • Troubleshooting
  • Next Steps
• Ideal Points Models (TBIP)
  • What Are Ideal Points?
  • Model Intuition
  • When to Use TBIP
  • Basic Usage
  • Interpreting Ideal Points
  • Topic-Word-Author Relationships
  • Practical Example: Political Speeches
  • Validating Ideal Points
  • Relationship to Other Models
  • Implementation Details
  • Troubleshooting
  • Next Steps
• Embedded Topic Models (ETM)
  • Why Use Embeddings?
  • When to Use ETM
  • Model Overview
  • Basic Usage
  • Loading Pre-trained Embeddings
  • Practical Example: News Classification
  • Comparing ETM vs Standard Models
  • Advanced: Custom ETM Variants
  • Embedding Quality Matters
  • Troubleshooting ETM
  • Evaluation
  • Relationship to Other Models
  • Next Steps

Overview of Available Models

The poisson-topicmodels package provides several related models addressing different use cases:

Unsupervised Baseline

• Poisson Factorization (PF): Discover topics without guidance or external information

Guided Discovery

• Seeded PF (SPF): Incorporate domain knowledge through keyword priors

Covariate Modeling

• Covariate PF (CPF): Model how topics are influenced by document-level covariates

• Covariate Seeded PF (CSPF): Combine covariate effects with keyword guidance

Advanced Models

• Text-Based Ideal Points (TBIP): Estimate author positions on latent dimensions

• Embedded Topic Models (ETM): Integrate pre-trained word embeddings

Which Model Should I Use?

Your question: “I want to discover topics in my text data”

→ Use: Poisson Factorization (PF) or Seeded PF (SPF)

• PF if you have no prior knowledge about topics

• SPF if you can define some keyword seeds for expected topics

Your question: “I want to understand how topics vary by document attributes”

→ Use: Covariate PF (CPF) or Covariate Seeded PF (CSPF)

• Use when you have metadata (author, date, category) and want to model how topics are affected by these attributes

Your question: “I want to estimate author or speaker positions”

→ Use: Text-Based Ideal Points (TBIP)

• Model ideal points (positions on a latent scale) based on language use

• Useful for political polarization, sentiment analysis across authors

Your question: “I want to use pre-trained word embeddings”

→ Use: Embedded Topic Models (ETM)

• Incorporates semantic information from embeddings like Word2Vec or FastText

• Often produces more semantically coherent topics

Model Comparison Table

Model Comparison

Model	Unsupervised?	Guides?	Covariates?	Embeddings?
PF	✓
SPF	✓ (guided)	✓
CPF	✓		✓
CSPF	✓ (guided)	✓	✓
TBIP	✓
ETM	✓			✓

Common Patterns

All models in poisson-topicmodels follow a consistent API:

Create: Initialize with data and parameters

model = PF(counts=counts, vocab=vocab, num_topics=10, batch_size=32)

Train: Fit the model to data

params = model.train_step(num_steps=200, lr=0.01, random_seed=42)

Summarize: Get a quick overview of the fitted model

model.summary()

Extract: Get interpretable results

categories, e_theta = model.return_topics()
beta = model.return_beta()
top_words = model.return_top_words_per_topic(n=10)

Evaluate: Quantitative diagnostics

coherence_df = model.compute_topic_coherence()
diversity = model.compute_topic_diversity()

Visualize: Built-in publication-ready plots

model.plot_model_loss()
model.plot_topic_prevalence()
model.plot_topic_correlation()
model.plot_document_topic_heatmap()
model.plot_topic_wordclouds()

Probabilistic Background

All models in this package are built on Poisson Factorization, a probabilistic framework for count data. Here’s the core idea:

Poisson Factorization Model

For each document d and word w:

• Observed: word count $C_{dw}$ (how many times word w appears in document d)

• Latent: topic z (which topic generated this word)

• Model: $C_{dw} sim text{Poisson}(sum_z beta_z^w theta_d^z)$

Where: - $beta_z^w$ = word w probability in topic z - $theta_d^z$ = topic z intensity in document d

Why Poisson?

• Natural for count data

• Mathematically elegant with exponential family

• Computationally efficient with SVI

• Flexible foundation for extensions

Bayesian Inference

We use Stochastic Variational Inference (SVI) to estimate posterior distributions:

• Place prior distributions on $beta$ and $theta$

• Learn approximate posterior through variational optimization

• Mini-batch training for scalability

Learn More

Each model variant has dedicated documentation:

• Core Concepts - Detailed statistical background

• Poisson Factorization (PF) - PF and understanding results

• Seeded Models (SPF & Keywords) - SPF for incorporating domain knowledge

• Covariate Models (CPF & CSPF) - CPF and CSPF for structured data

• Ideal Points Models (TBIP) - TBIP for position estimation

• Embedded Topic Models (ETM) - ETM for embedding integration

Ready to dive deeper? Start with Core Concepts.