---
title: "Information-filtering networks: TMFG and LoGo"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Information-filtering networks: TMFG and LoGo}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", fig.width = 6, fig.height = 5)
has_cograph <- requireNamespace("cograph", quietly = TRUE)
```

```{r}
library(psychnets)
```

**Information-filtering networks** take a different route to sparsity than the
graphical lasso. Instead of penalising edges, they keep a fixed, theoretically
motivated *topology* and let the data fill in the weights.

- **TMFG** (Triangulated Maximally Filtered Graph, `method = "tmfg"`) greedily
  builds a planar, chordal graph with exactly `3(p - 2)` edges -- the strongest
  associations that still form a triangulated structure.
- **LoGo** (Local-Global, `method = "logo"`) takes the TMFG topology and returns
  the *closed-form* sparse inverse covariance (a partial-correlation network) for
  that chordal graph -- no iteration, no tuning.

Both are deterministic and dependency-free, and both carry a structural
certificate.

```{r}
tmfg <- psychnet(SRL_GPT, method = "tmfg")
logo <- psychnet(SRL_GPT, method = "logo")

tmfg
logo
```

With only five nodes the filter is mild (a 5-node graph has 10 possible edges and
TMFG keeps `3(5 - 2) = 9`); the method shows its value on larger node sets, where
it drops the great majority of edges. The TMFG certificate confirms the graph has
the correct edge count and is chordal and connected:

```{r}
certificate(tmfg)
```

The LoGo edges are the partial correlations on the TMFG backbone:

```{r}
as.data.frame(logo)
```

## Plotting

LoGo weights the TMFG backbone with partial correlations. Pass the network
object to `cograph::splot()` with `psych_styling = TRUE` (spring layout,
green = positive, red = negative); ask for the predictability ring with
`predictability = TRUE`.

```{r logo-plot, eval = has_cograph}
cograph::splot(logo, psych_styling = TRUE, predictability = TRUE)
```

LoGo reproduces the sample correlation exactly on the TMFG support (its defining
property), so its constrained-MLE certificate is near zero:

```{r}
certificate(logo)
```