Я строю поверхность в уценке R, используя
p1 <- plot_ly() %>% add_surface(z=z,x=wRange,y=yRange) %>% layout(showlegend=FALSE,scene=list(xaxis=list(title="wMult"),yaxis=list(title="yMult"),zaxis=list(title="MAE")))
p1
Позже я хочу добавить точку на эту поверхность, выполнив следующие действия:
p2 <- p1 %>% add_markers(z=MAE1,x=wMult1,y=yMult1) %>% layout(showlegend=FALSE)
p2
Чуть позже я пытаюсь нанести на карту p3, добавляя еще одну отметку поверх p2.
p3 <- p2 %>% add_markers(z=MAE2,x=wMult2,y=yMult2) %>% layout(showlegend=FALSE)
p3
К сожалению, только p1 отображается как интерактивная диаграмма в HTML. p2 и p3 отображаются как пустое белое пространство, размер которого примерно соответствует размеру диаграммы, но внутри которого ничего нет, как в средстве просмотра, так и в браузере. Если я использую веб-инспектор, я вижу, что он пытается отобразить сюжетный объект, но он выглядит пустым.
Если я запускаю тот же код непосредственно в RStudio, я могу просматривать графики с добавленными дополнительными маркерами, но они не отображаются, когда я вяжу уценку.
Что здесь происходит?
Набор данных доступен здесь: https://archive.ics.uci.edu/ml/datasets/auto+mpg
Вот полный код уценки на данный момент:
---
title: "Gradient Descent Demo"
output: html_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
setwd("[your working directory]")
data = read.csv("mpg.csv")
require(plotly)
```
## Our Dataset
Let's take a look at some sample data. It shows attributes of several old cars and their fuel economy measured in miles per gallon.
```{r c1}
head(data)
```
We'll try to predict a given car's mpg using only its weight and year.
```{r c2}
data <- data[,c("mpg","weight","year")]
pairs(data)
```
## Create a Hypothesis
Our hypothesis will be that we can get an approximation of the mpg by multipling the car's weight by some number "wMult" and adding that to the car's year multiplied by some other number "yMult". Let's just pick some numbers to start.
```{r c3, include=FALSE}
mod1 <- lm(mpg~weight+year,data=data)
bias1 <- mod1$coefficients[1]
```
```{r}
wMult1 <- -.02
yMult1 <- -2
```
We can turn this into a prediction.
(Ignore the bias - I cheated and did some behind-the-scenes pre-work.)
```{r c4}
data$mpgPred1 <- wMult1*data$weight + yMult1*data$year + bias1
head(data)
```
Ok so we have predictions. They're clearly pretty bad since they're negative, and most cars don't get negative miles per gallon. But can we measure how bad they are?
## Evaluate the Hypothesis
We need some measure of how good (or bad) our prediction is. We'll use the Mean Absolute Error ("MAE"). As the name suggests, this is calculated finding the average of the absolute difference between each predicted value and actual value.
```{r c5}
MAE1 <- mean(abs(data$mpgPred1-data$mpg))
MAE1
```
Ok so on average we're only off by about 250 mpg. Surely we can do better.
## Adjust the Hypothesis
What to use for our next hypothesis? Well we assign new wMult and yMult values and see how we do.
```{R c6}
wMult2 <- wMult1 + .03
yMult2 <- wMult2 - 1.2
data$mpgPred2 <- wMult2*data$weight + yMult2*data$year + bias1
head(data)
```
Our predictions look better (At least they're positive!), but they're still pretty far off. Let's see how much better or worse they are.
## Evaluate the Hypothesis - Round 2
```{R c7}
MAE2 <- mean(abs(data$mpgPred2-data$mpg))
MAE1
MAE2
```
Now we're only off by 50 on average. Still pretty terrible, but better than before.
## Adjust the Hypothesis - There has to be a better way.
Ok so instead of just continuing to make random guesses, let's develop a way to intelligently update our hypothesis.
Thankfully, since we're only using two variables for our analysis, we can pretty easily visualize the effect of every reasonable combination of wMult and yMult.
```{R c8, include=FALSE}
plotdata <- data.frame(wCoef=double(),yCoef=double(),MAE=double())
wRange <- seq(mod1$coefficients[2]-300*summary(mod1)$coefficients["weight","Std. Error"],mod1$coefficients[2]+300*summary(mod1)$coefficients["weight","Std. Error"],length.out=201)
yRange <- seq(mod1$coefficients[3]-300*summary(mod1)$coefficients["year","Std. Error"],mod1$coefficients[3]+300*summary(mod1)$coefficients["year","Std. Error"],length.out=201)
for(i in wRange)
{for(j in yRange)
{
preds <- (i*data$weight) + (j*data$year) + bias1
resid <- preds-data$mpg
MAE = mean(abs(resid))
newRec <- data.frame(wCoef=i,yCoef=j,MAE=MAE)
plotdata <- rbind(plotdata,newRec)
}
}
z <- matrix(plotdata$MAE,nrow=201,ncol=201)
```
```{R c9}
p1 <- plot_ly() %>% add_surface(z=z,x=wRange,y=yRange) %>% layout(showlegend=FALSE,scene=list(xaxis=list(title="wMult"),yaxis=list(title="yMult"),zaxis=list(title="MAE")))
p1
```
Great - we can visibly explore this graph and see what some good weights might be. The best one is the one that minimizes the MAE. That's the center spot at the middle of the valley, where the crease seems to dip slightly.
Let's add our first hypothesis to this chart to see where it falls.
```{R c10,warning=F}
p2 <- p1 %>% add_markers(z=MAE1,x=wMult1,y=yMult1) %>% layout(showlegend=FALSE)
p2
```
And let's add our second one
```{R c11}
p3 <- p2 %>% add_markers(z=MAE2,x=wMult2,y=yMult2) %>% layout(showlegend=FALSE)
p3
```
Ok so it turns out our second guess actually overshot. This means that if we kept updating our hypothesis in the same manner, we'd actually get worse with each new step.
## Letting the machine do it
As I mentioned before, this approach works because we only have 2 variables we're working with. But if we had more, we'd be dealing with spaces greater than 3 dimensions. This gets hard to visualize.
Thankfully there's a way for the machine to navigate those higher dimensional spaces. We'll continue to use this two dimensional approach for now to help illustrate the approach.
