Module is an abstract class which defines fundamental methods necessary for a Layer.

doc: https://github.com/torch/nn/blob/master/doc/module.md

Module class

variables in Module:

• output: Tensor, the ouput computed from last call of forward(input)
• gradInput: Tensor, gradient wrt input of module, computed from last …

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+193 …

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 …

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 …

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 …

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 …