2022年1月21日星期五

機率

Random variable

A discrete random variable X is a quantity that can assume any value x from a discrete list of values with a certain probability.
The probability that the random variable X assumes the particular value x is denoted by Pr(X = x). This collection of probabilities, along with all possible values x, is the probability distribution of the random variable X.

Ex. Sum of two dices

X=4 ==> (1,3), (2,2) (3,1)

Discrete Probability Rules
Probabilities are numbers between 0 and 1: 0 ≤ Pr(X = xk) ≤ 1 for all k The sum of all probabilities for a given experiment (random variable) is equal to one: $\text{[math]}$ The probability of an event is 1 minus the probability that any other event occurs: $\text{[math]}$

Ex. Sum of two dices

Pr(X=3) = 2/36 , Pr(X=4) = 3/36

Cumulative Distribution Function of a Discrete Random Variable
The cumulative distribution function (CDF) of a random variable X is denoted by F(x), and is defined as F(x) = Pr(X ≤ x). Using our identity for the probability of disjoint events, if X is a discrete random variable, we can write $\text{[math]}$ where xn is the largest possible value of X that is less than or equal to x

Cumulative Distribution Function of a Discrete Random Variable

The cumulative distribution function (CDF) of a random variable X is denoted by F(x), and is defined as F(x) = Pr(X ≤ x).

Using our identity for the probability of disjoint events, if X is a discrete random variable, we can write

$\text{[math]}$

where xn is the largest possible value of X that is less than or equal to x

Binomial PDF
If X is a binomial random variable associated to n independent trials, each with a success probability p, then the probability density function of X is: $\text{[math]}$ where k is any integer from 0 to n. Recall that the factorial notation n! denotes the product of the first n positive integers: n! = 1·2·3···(n-1)·n, and that we observe the convention 0! = 1.

Binomial PDF

If X is a binomial random variable associated to n independent trials, each with a success probability p, then the probability density function of X is:

$\text{[math]}$

where k is any integer from 0 to n. Recall that the factorial notation n! denotes the product of the first n positive integers: n! = 1·2·3···(n-1)·n, and that we observe the convention 0! = 1.

Definition: Expected Value of a Discrete Random Variable
The expected value, $\text{[math]}$ , of a random variable X is weighted average of the possible values of X, weight by their corresponding probabilities: $\text{[math]}$ where N is the number of possible values of X.

Definition: Expected Value of a Discrete Random Variable

The expected value,

\text{[math]}

, of a random variable X is weighted average of the possible values of X, weight by their corresponding probabilities:

$\text{[math]}$

where N is the number of possible values of X.

References:

[1] https://blogs.ubc.ca/math105/

2021年12月13日星期一

[Linux 核心] Linux 核心功能的配置選單

開啓Linux 核心功能的配置選單,

Step1: 得先安裝ncurses 套件, 才能產生選單畫面

>> sudo apt-get install libncurses5-dev libncursesw5-dev

若以上無法成功安裝, 則先下這個指令後再安裝套件, 應該就能順利安裝 >> sudo apt-get update --allow-releaseinfo-change

Step2: 進入到核心原始碼的資料匣, 執行 make menuconfig

>> cd linux-raspberrypi-kernel_1.20190401-1/

>> make menuconfig

2021年12月10日星期五

為什麼Z-Score標準化後, 會得到平均數為0, 標準差為1

1.) How can I choose between normalization and standardization in different situations?

資料並無特別遵從常態分佈, 則使用 Normalization , 如圖片的像素常用 Normalization 將像素值壓在0~1 之間。若資料遵從常態分佈 (很多時候會假設資料是常態分佈), 則使用Standardization (z-score)

2.) 證明: 為什麼Z-Score標準化後, 會得到平均數為0, 標準差為1

[1] 什麼是機器學習 ?

[2] 回歸模型的效能評估: R平方(R squared)

[3] 為什麼Z-Score標準化後, 會得到平均數為0, 標準差為1

[4] 關於Log-loss: binary_cross_entropy

[5] Understanding ROC and AUC

[6] iPAS 機器學習工程師參考樣題解說

[7] Model Quantization

[9] Adaboost Algorithm 演算法

[10] Adaboost Algorithm 演算法實作解說

2021年11月10日星期三

How to save and load fine-tuned model?

如何儲存Fine-tune BERT model 的網路權重及架構?

Custom mask layers require a config and must override get_config ...........

1. ) 若pre-trained bert model 只是用來作為sentence embedding 的話,. 那就只儲存後面自己接的網路架構..不用整個儲存(即不必含BERT model), 因此可忽略載入pre-trained bert model . 那就回到原本傳統的model.save() , load_models('xxxx.h5')

2.) pre-trained bert model 串接自己網路架構, 一起訓練, 如果是這種的, 就用方法2

只存weight (model.save_weights), 用原本model 架構去產生一個空的new_model, 然後new_model.load_weights

model.save_weights('my_model_weights.h5')
...
new_model = <build your model with your model building code>
new_model.load_weights('my_model_weights.h5')