A Tensor is the fondamental data type in torch, (similar to numpy for tensorflow), it's a potentially multi-dimensional matrix.

See doc: https://github.com/torch/torch7/blob/master/doc/tensor.md

basic ops

• Indicate shape in constructor:

  th> x = torch.Tensor(3,4) [0.0000s] th> x 3.7366e ...

Intro

ML lang family

statically strongly typed languages

• fisrt-class functions
• type inference
• pattern matching

highlights of ocaml

• safty: static typing, pattern matching
• efficiency: high performance

• expressiveness: functional+type inference+polymorphism

• package manager: opam

• debugger
• profiler
• REPL: "toplevel"
• bytecode compiler: ccamlc
• native compiler: ocamlopt

programming environment fully online: https://try.ocamlpro ...

Recap: Functions and Pattern Matching

case classes

ex: json json objects can be seq, num, str, bool,...

⇒ represented as abstract class and case classes.

pattern matching

→ question: what is the type of the {case(key, value)=>"..."} clause?

it is (JBinding => String) type, which is a shorthand for Function1[JBinding, String ...

6.1 - Other Collections

so far: only seen List. → more (immutable) collections.

vector

List: is linear -- access to head is faster than middle or end element. Vector: better rand access performance.

represented as very shallow trees(32-split at each node)

Vector support similar operations as List (head, tail,map, fold ...

5.1 - More Functions on Lists

already known methods:

xs.head
xs.tail

sublist and ele access:

• xs.length
• xs.last
• xs.init: all elementh except last element
• xs.take(n): sublist of first n elements
• xs.drop(n): the rest of list after taking first n elements
• xs(n ...

R里面的统计函数有很多, 这里只用线性模型lm以及(一维)非参估计最常用的三个smoother: Nadaraya-Watson kernel(NW, ksmooth), Local Polynomial(LP, loess), Smoothing Spline(SS, smooth.spline). 用这三个smoother作为例子, 介绍R里面统计回归的一些用法.

数据的形式是:　

目标是估计函数m(). 例子使用R自带的cars数据集, 它包含两列: 汽车速度speed和刹车距离dist.

> data(cars)
> summary(cars)
     speed           dist       
 Min.   : 4.0   Min.   :  2.00  
 1st Qu.:12.0   1st Qu.: 26.00  
 Median :15 ...

R关于绘图应该可以写很多, 不过这里只列举在compstat这门课里最经常用的几个函数. 关于R的绘图, 详细了解可以运行 demo(graphics)或者 example("plot").

R里面的绘图命令分为两类: 一类是"high-level"的"创建新图片"命令, 运行以后会新画一个图; 另一类则是"low-level"的命令, 不会创建新图片, 而只会在当前图片中修改添加(例如添加线条, 添加点等). 下面分别简单介绍, 最后再介绍其他一些绘图配置的命令.

configurations/parameters

介绍一下常用的参数意义, 以及画图的配置. 详细文档见?par. 这些参数可以放在绘图命令中.

• par(mfrow=c(1,2)): 这个命令是设定画图的布局, 把放置图片的区域分为一行两列, 第一个plot的图片在左边, 第二个在右边.
• col: 设定画图(线段/点)的颜色, 可以用数字(col=1, 2 ...

首先, R似乎默认所有的变量都为向量vector, 即使一个单独的数字也是长度为1的, 所以1等价于c(1).

> a <- 1
> a
[1] 1
> length(a)
[1] 1
> a[1]
[1] 1
> typeof(a)
[1] "double" # means "double vector" (I think)
> 1 == c(1)
[1] TRUE

fancy indexing

R的vector/list/matrix支持类似numpy(稍有不同)的fancy indexing, 以下是例子:

> v <- 1:10
> v[1:3 ...

这个"从入门到放弃"系列是为了应付eth的computational statistics这门课... 对R无爱...

terminology

首先在stat里面有一些叫法和以前不太一样:

• predictor variable: 就是机器学习里面说的feature (Xi)
• design points: 是机器学习里的训练数据(X1...Xn)
• response variable: 要预测的变量(y)

Rstudio

这个是用R编程的标配, 确实很方便, 不用可惜. 另外R markdown也不错, 可以边写markdown边运行代码, 建议编辑器窗口里新建rmd文件.

• 默认有四个窗口: 编辑器, 变量, 命令行, 画图/帮助.

快捷键

一些常用的快捷键:

• alt+-: 用于输入赋值符号<-
• (编辑器窗口中) ctrl+enter: (在console里)执行光标所在的行, 等同于按钮"run"
• (r markdown编辑器窗口中) ctrl ...

4.1 - Objects Everywhere

scala is pure OO: every value is an obj, every operation is a method of obj.

scala.Int scala.Boolean maps to JVM standard primitive types.

Implement Boolean withous primitive type in scala:

Then defin false and true as objects, give implementation for ifThenElse() funciton:

object ...