Examples Gallery

.qvr programs spanning probabilistic regressions, latent-variable models, state-space models, language models, encoder-decoder networks, and weighted deductions. Most full pages include a ## Try it section; CI executes runnable documentation blocks and skips blocks marked as illustrative. Pages with current model limitations identify them directly.

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 a log-shape predictor and unit rate.
• Horseshoe Regression: sparse linear regression under the horseshoe prior.
• Negative Binomial Regression: overdispersed count response.
• Continuous-gate Poisson Regression: differentiable relaxation of a zero-inflation gate.
• Item Response Theory (2PL): Rasch-style logistic IRT with item difficulty and discrimination.
• Weibull Survival: uncensored Weibull event-time regression; censored rows require an explicit survival-score term.

Latent-variable models

• Factor Analysis: current isotropic-noise factor model, equivalent in noise structure to PPCA.
• 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.
• Latent Decoder and Encoder Paths: prior-decoder program plus a separately exported encoder-decoder path; the current SVI block does not use the encoder as its guide.
• Bayesian Neural Network: nonlinear regression through an MLP-parameterised Normal kernel, made Bayesian after lifting priors over its weights.
• Parametric Partial Pooling: random effects from a parametric program template, with a labeled return tuple, a score-step sum-to-zero factor, and export selection.
• Probabilistic Matrix Factorization: low-rank Bayesian completion of a sparse rating matrix.
• Bilinear Tensor Contraction: neural-tensor-layer scoring of predicate-argument pairs via an operadic three-way contraction.

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.
• Gaussian-Kernel SSM: learned transition, emission, and filtering kernels; not a closed-form Kalman filter.
• Finite-State Path Composition: product-fuzzy transition and emission relations, plus a partial discrete-program sketch.
• Continuous-State Sequence Model: Gaussian transition, emission, and separately learned recognition kernels.
• Deep Markov Model: nonlinear-MLP transition and emission cells.

Language models

• Vanilla RNN LM: single-cell Elman RNN scored by a Categorical head.
• GRU-shaped LM: stochastic reset and update gates with a simplified candidate update.
• LSTM-shaped LM: stochastic gates without a separately threaded cell state.
• Dual-RNN Masked-Token Model: two left-to-right scans combined for a masked-token target.
• Transformer-shaped LM: parallel MLP-normal branches with a Categorical head; no dot-product self-attention or causal mask.

Encoder-decoder and structured outputs

• Sequence-to-Sequence: parallel encoder-decoder branches joined by a learned merge, without attention.
• Tree-Structured Score Tensor: recursive additive scores 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.
• Schema-Bundled Chart Parser: pattern-polymorphic rule schemas bundled into a differentiable CKY chart parser.
• Term Autoencoder: a signature, encoder, decoder, and loss compressing typed lambda terms.
• 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.