partition.Rmd

---
title: partition
author: 
  - name: Bodo Burger
date: 2018-06-14
output:
  html_document: 
    toc: yes
  github_document:
    toc: yes
  pdf_document: default
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = TRUE,
                      cache = TRUE, cache.path = "cache/partition/")
library("ggplot2")
library("intame")
theme_set(theme_light())
set.seed(4218)
```

## Toy example

```{r small-dataset}
set.seed(0815)
n = 6
x = sample(n) + 1.5
y = runif(n, 0, 10)
df = data.frame(x, y)
ggplot(data=df, mapping=aes(x = x, y = y)) + geom_point()
```

```{r small-partition}
ggplot() + geom_point(data=df, mapping=aes(x = x, y = y)) +
  geom_vline(mapping = aes(xintercept = partition(df$x, df$y, 4) - .03,
    color = "rpart")) +
  geom_vline(mapping = aes(xintercept = partition(df$x, df$y, 4,
    part_method = "cluster") + .03, color = "cluster"))
```

## More data

```{r more-data}
set.seed(123)
n = 100
x = runif(n, 0, 1000)
y = x * sin(.01*x) + rnorm(n, 0, 10)
df = data.frame(x, y)
poly12.mod = lm(y ~ poly(x, 12, raw = TRUE), data = df)
ggplot(data=df, mapping=aes(x = x, y = y)) + geom_point(alpha = .5, size = 3) +
  geom_line(mapping = aes(y = predict(poly12.mod)), color = "red")
me = derivative(x, "x", df, poly12.mod)
```

```{r more-partition}
p0 = ggplot() + geom_line(data=df, mapping=aes(x = x, y = y))
# gridExtra::grid.arrange(
#   p0 + geom_vline(mapping = aes(xintercept = partition(df$x, me, 8), color = "rpart")),
#   p0 + geom_vline(mapping = aes(xintercept = partition(df$x, me, 8, part_method = "cluster"), 
#     color = "cluster"))
# )
library(patchwork)
(p0 + geom_vline(mapping = aes(xintercept = partition(df$x, me, 8), color = "rpart"))) /
(p0 + geom_vline(mapping = aes(xintercept = partition(df$x, me, 8, part_method = "cluster"),
  color = "cluster")))
```


```{r mob}
mob.mod = partykit::lmtree(y ~ x | x, data = df, minsize = 10)
coef(mob.mod)
plot(mob.mod)
```


```{r}
library(ALEPlot)
ale = ALEPlot(df[, 1, drop=FALSE], poly12.mod, J = 1, pred.fun = function(X.model, newdata) predict(X.model, newdata))
ggplot(data=df, mapping=aes(x = x, y = y)) + geom_point(alpha = .5, size = 3) +
  geom_line(mapping = aes(y = predict(poly12.mod)), color = "red") +
  geom_line(data = data.frame(ale), mapping = aes(x = x.values, y = f.values), col = "blue")
```