> ## Documentation Index
> Fetch the complete documentation index at: https://docs.verisynth.ai/llms.txt
> Use this file to discover all available pages before exploring further.

# Models

> Overview of the AI models supported by VeriSynth for generating synthetic data.

# Models in VeriSynth

VeriSynth uses machine learning models to learn the **statistical structure** of real data and generate **synthetic data** that behaves like the real world — without exposing sensitive records.

Each model is designed to balance **realism**, **privacy**, and **computational efficiency**.\
The system is modular, so users can plug in new synthesis engines over time.

***

## Current Model: Gaussian Copula (GC)

The **Gaussian Copula Synthesizer** is the first and default model in VeriSynth Core.\
It’s a fast, deterministic, and lightweight model for **tabular synthetic data** — perfect for most structured datasets.

### How It Works

1. **Learn relationships**\
   GC learns pairwise correlations between all columns in your dataset.\
   It transforms them into a continuous Gaussian space where relationships are easier to model.

2. **Model dependencies**\
   A multivariate Gaussian distribution is fit to the transformed data.\
   This captures how each variable depends on others (e.g., *age ↔ BMI ↔ blood pressure*).

3. **Sample synthetic data**\
   New synthetic samples are drawn from this learned distribution, then mapped back to the original data space.

4. **Output verification**\
   The generated dataset is post-processed and evaluated for correlation deltas, privacy risk, and consistency metrics.

***

### Example

Let’s say your real dataset has these correlations:

| Variable Pair     | Correlation |
| ----------------- | ----------- |
| Age ↔ BMI         | 0.42        |
| BMI ↔ Systolic BP | 0.61        |
| Age ↔ Glucose     | 0.58        |

The synthetic dataset produced by VeriSynth will preserve these relationships closely, often within a **correlation delta of ±0.1** — enough to be statistically realistic for most analytical and ML tasks.

> Instead of random noise, GC learns your dataset’s *statistical DNA* and regenerates it faithfully.

***

### Strengths

| Feature           | Description                                        |
| ----------------- | -------------------------------------------------- |
| **Lightweight**   | Runs entirely on CPU — no GPUs required            |
| **Deterministic** | Same seed → same result, ideal for reproducibility |
| **Explainable**   | Transparent mathematical model (no black box)      |
| **Fast**          | Generates up to 1M+ rows in seconds                |
| **Auditable**     | Outputs proof receipts with correlation metrics    |

***

### Limitations

| Limitation                             | Description                                             |
| -------------------------------------- | ------------------------------------------------------- |
| **Linear correlations only**           | GC struggles with nonlinear or multimodal relationships |
| **Limited categorical complexity**     | High-cardinality categories may be oversimplified       |
| **No temporal or sequential modeling** | Best for static, tabular datasets                       |

***

## Roadmap: Upcoming Models

VeriSynth Core is model-agnostic — future releases will expand into **deep generative** and **privacy-enhanced** models.

| Model          | Type                                   | Status         | Description                                                         |
| -------------- | -------------------------------------- | -------------- | ------------------------------------------------------------------- |
| **CTGAN**      | GAN-based tabular                      | 🧩 Planned     | Captures nonlinear relationships and rare categories                |
| **TVAE**       | Variational Autoencoder                | 🧩 Planned     | Produces smoother synthetic distributions and uncertainty estimates |
| **DP-GC**      | Differentially Private Gaussian Copula | 🧩 Planned     | Adds formal privacy bounds (ε) to correlation modeling              |
| **TimeSynth**  | Sequential/time-series                 | 🧩 Planned     | Models synthetic patient timelines, transactions, or sensor data    |
| **ImageSynth** | Generative Vision                      | 🚧 Exploratory | Extends proof-based synthesis to visual data                        |

***

## Model Selection Philosophy

We believe every synthetic data generator should be:

1. **Understandable** — transparent about how it learns and samples
2. **Reproducible** — deterministic seeds, reproducible metrics
3. **Verifiable** — accompanied by measurable fidelity and privacy proofs
4. **Modular** — easy to swap models as new techniques evolve

VeriSynth is built as a **modular framework**, so you can run:

```bash theme={null}
verisynth data/patients.csv -o out/ --model gaussian_copula
# (future)
verisynth data/patients.csv -o out/ --model ctgan
```

***

## Model Registry (Coming Soon)

We’re working on a **model registry system** that will let users:

* View available models (`verisynth models list`)
* Inspect metadata, dependencies, and required hardware
* Register custom synthesis engines via plugin
* Benchmark models on fidelity vs privacy

Example:

```bash theme={null}
verisynth models list
# → gaussian_copula, ctgan, tvae, dp_gc
```

***

## Model Validation Metrics

Each model is evaluated using:

| Metric                           | Description                                        |
| -------------------------------- | -------------------------------------------------- |
| **Correlation delta (Δ)**        | Measures difference in variable relationships      |
| **KS test (p-value)**            | Checks distributional similarity                   |
| **Naive re-identification risk** | Approximates privacy exposure                      |
| **Synthetic utility**            | Performance of ML models trained on synthetic data |

These metrics are logged to `proof.json` for transparency and reproducibility.

***

## Example CLI Run (GC Model)

```bash theme={null}
verisynth data/finance.csv -o out/ --rows 50000 --model gaussian_copula --seed 42
```

Produces:

```
📁 out/synthetic.csv
🧾 out/proof.json
```

With proof:

```json theme={null}
{
  "model": { "engine": "gaussian_copula", "seed": 42 },
  "metrics": { "corr_mean_abs_delta": 0.15, "naive_reid_risk": 0.0 }
}
```

***

## Summary

| Principle           | Description                                                             |
| ------------------- | ----------------------------------------------------------------------- |
| **Start simple**    | GC gives accurate, transparent tabular synthesis                        |
| **Build modularly** | New models can plug into the same proof pipeline                        |
| **Stay verifiable** | Every model, no matter how complex, will always produce a proof receipt |

***