没有合适的资源?快使用搜索试试~ 我知道了~
资源推荐
资源详情
资源评论
Areas of Mathematics Essential to
Machine Learning
• Machine learning is part of both statistics and
computer science
• Probability
• Statistical inference
• Validation
• Estimates of error,confidence intervals
• Linear Algebra
• Hugelyuseful for compact representation of linear
transformations on data
• Dimensionally reductiontechniques
• Optimization theory
Notations
•
•
•
•
•
•
•
•
set membership:ais member of setA
cardinality: number of items in set B
norm: length of vector v
summation
integral
vector(bold, lower case)
matrix (bold, upper case)
function: assigns unique value in range of y
toeachvalueindomainofx
function on multiple variables
•
Probability Spaces
• A probability space models a random process or
experiment with three components:
• Ω, the set of possible outcomes O
• number of possible outcomes = |Ω|
• Discrete space
• Continuous space
|Ω| is finite
|Ω| is infinite
• F, the set of possible events E
• number of possible events = |F|
• P, the probability distribution
• functionmapping each outcome and event to real number
between 0 and 1 (the probability ofO or E)
• probability of an event is sum of probabilities of possible
outcomes in event
AxiomsofProbability
• Non‐negativity:
• for any event
• All possible outcomes:
• p(Ω)=1
• Additivity of disjoint events:
• For all events where ,
ExampleofDiscrete ProbabilitySpace
• Three consecutive flips of a coin
• 8 possible outcomes: O=HHH, HHT, HTH,HTT,THH, THT,
TTH, TTT
• 2
8
=256 possibleevents
• example: E = ( O∈ {HHT,HTH,THH } ),i.e. exactlytwo
flipsareheads
• example: E = ( O∈ { THT,TTT} ), i.e. the first and third
flipsaretails
• If coin is fair,then probabilities of outcomes are equal
• p( HHH ) =p( HHT ) = p(HTH)=p(HTT)=p(THH)=p(THT)
=p(TTH)=p( TTT) =1/8
• example: probability of event E = ( exactly two heads ) is
p( HHT ) + p(HTH)+p(THH)= 3/8
剩余39页未读,继续阅读
资源评论
石悦
- 粉丝: 11
- 资源: 285
上传资源 快速赚钱
- 我的内容管理 展开
- 我的资源 快来上传第一个资源
- 我的收益 登录查看自己的收益
- 我的积分 登录查看自己的积分
- 我的C币 登录后查看C币余额
- 我的收藏
- 我的下载
- 下载帮助
安全验证
文档复制为VIP权益,开通VIP直接复制
信息提交成功