Examples Gallery

Complete .qvr programs spanning probabilistic regressions, latent-variable models, state-space models, language models, encoder-decoder networks, and weighted deductions. Every example ships a ## Try it section with synthetic-data generation, an SVI fit, and a Bayesian posterior block; all snippets are executed in CI.

All source files live under docs/examples/source/.

Regressions

• Bayesian Linear Regression: Normal likelihood with Normal-prior weights.
• Beta Regression: Beta-distributed response with logit link.
• Gamma Regression: Gamma response with log link.
• Horseshoe Regression: sparse linear regression under the horseshoe prior.
• Negative Binomial Regression: overdispersed count response.
• Zero-Inflated Poisson Regression: count response with a separate zero-inflation channel.
• Item Response Theory (2PL): Rasch-style logistic IRT with item difficulty and discrimination.
• Weibull Survival: proportional-hazards survival with Weibull baseline.

Latent-variable models

• Factor Analysis: linear factor decomposition with free per-dimension noise.
• Probabilistic PCA: isotropic-noise special case of factor analysis.
• Latent Dirichlet Allocation: topic model with Dirichlet priors on per-document and per-topic distributions.
• Gaussian Mixture Model: finite mixture with grouped marginalization over the cluster label.
• Variational Autoencoder: amortized inference over a continuous latent with neural decoder.
• Bayesian Neural Network: feed-forward classifier with Normal priors over every weight.
• Probabilistic Matrix Factorization: low-rank Bayesian completion of a sparse rating matrix.

State-space and time-series models

• AR(1): first-order autoregressive Normal scalar series.
• Changepoint Model: piecewise-constant means with a sampled change point.
• Stochastic Volatility: AR(1) log-variance driving Normal returns.
• Linear-Gaussian SSM: Kalman-filter dynamics with learnable transition / emission.
• Hidden Markov Model (Discrete): row-stochastic transition and emission matrices over finite states.
• Hidden Markov Model (Continuous): Gaussian-emission HMM with continuous-state latent trajectory.
• Deep Markov Model: nonlinear-MLP transition and emission cells.

Language models

• Vanilla RNN LM: single-cell Elman RNN scored by a Categorical head.
• GRU LM: gated recurrent unit cell.
• LSTM LM: long short-term memory cell.
• Bidirectional RNN LM: forward + backward RNN with a masked-token target.
• Transformer LM: stacked self-attention with a Categorical head.

Encoder-decoder and structured outputs

• Sequence-to-Sequence: encoder-decoder with attention scored by a target-side Categorical.
• Tree-Structured Categorical: hierarchical Categorical observation over a parametric tree.

Weighted deductions

• PCFG: probabilistic context-free grammar with learnable production weights.
• CCG: combinatory categorial grammar with forward / backward application and composition.
• Type-Logical Grammar (Lambek): Lambek calculus with residuated slashes and tensor.
• PMCFG: probabilistic multiple context-free grammar with WH-movement via a rank-2 non-terminal.
• Multimodal TLG: Lambek calculus extended with diamond and box modalities.
• Custom Sequent Rules: user-defined sequents over a free residuated category.
• Quantifier Scope: continuation-monad lift for generalized quantifiers.
• Montague NLI: Montague-style lambda-term LFs plus modus-ponens NLI prover.