Machine Learning/

Data Science

motivations!

motivations!

  • “大数据技术与应用”专业
  • Digital Media Technology / Network Engineering  
  • NLP
  • MCM

Symbolism
Statistical
Connectionism

History of ML

Structure of modeling

  • fetch data
  • explore
  • preprocessing
  • models
  • techniques

fetch data

you already knew this

explore data

Preprocessing

Subtitle

preprocessing

  • categorical features
  • scale
  • lost data

model selecting

No free lunch theorem

model selecting

Error = Bias(h(\theta))^2 + Var(h(\theta)) +\epsilon^2
Error=Bias(h(θ))2+Var(h(θ))+ϵ2Error = Bias(h(\theta))^2 + Var(h(\theta)) +\epsilon^2

model selecting

Interpretability

Flexibility

SKLEARN

estimator.fit(Xtrain, ytrain)

estimator.predict(Xtrain, ytrain)

estimator = #@$%&(*param)

https://arxiv.org/pdf/1309.0238v1.pdf

what are we doing?

R_{D}(h(x)) = \frac{1}{N} \sum_{y_i \in D} (y_i - h(x_i))^2
RD(h(x))=1N∑yi∈D(yi−h(xi))2R_{D}(h(x)) = \frac{1}{N} \sum_{y_i \in D} (y_i - h(x_i))^2
g(x) = \arg\min_{h(x) \in H} R_{D}(h(x))
g(x)=argminh(x)∈HRD(h(x))g(x) = \arg\min_{h(x) \in H} R_{D}(h(x))

estimation risk

linear regression

Y = \beta_0 + \beta_1 X + \epsilon
Y=β0+β1X+ϵY = \beta_0 + \beta_1 X + \epsilon
Y = \beta_0 + \beta_1 X_1 + \ldots + \beta_p X_p + \epsilon
Y=β0+β1X1+…+βpXp+ϵY = \beta_0 + \beta_1 X_1 + \ldots + \beta_p X_p + \epsilon
\hat\beta = (X^T X)^{-1}X^T Y
β^=(XTX)−1XTY\hat\beta = (X^T X)^{-1}X^T Y
R = \sum_{i=1}^N r_i = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2
R=∑i=1Nri=∑i=1N(yi−(β0+β1xi))2 R = \sum_{i=1}^N r_i = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2

Ridge regression

 

LASSO

R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \sum_{i=0}^j \beta_i^2.
R(hj)=∑i=1N(yi−(β0+β1xi))2+α∑i=0jβi2.R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \sum_{i=0}^j \beta_i^2.
R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \sum_{i=0}^j ||\beta_i||
R(hj)=∑i=1N(yi−(β0+β1xi))2+α∑i=0j∣∣βi∣∣R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \sum_{i=0}^j ||\beta_i||

Regularization

Elastic Net

R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \lambda \sum_{i=0}^j ||\beta_i|| +\alpha (1 - \lambda) \sum_{i=0}^j \beta_i^2/2
R(hj)=∑i=1N(yi−(β0+β1xi))2+αλ∑i=0j∣∣βi∣∣+α(1−λ)∑i=0jβi2/2R(h_j) = \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha \lambda \sum_{i=0}^j ||\beta_i|| +\alpha (1 - \lambda) \sum_{i=0}^j \beta_i^2/2

Regularization

= \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha (\lambda \sum_{i=0}^j ||\beta_i|| + (1 - \lambda) \sum_{i=0}^j \beta_i^2/2)
=∑i=1N(yi−(β0+β1xi))2+α(λ∑i=0j∣∣βi∣∣+(1−λ)∑i=0jβi2/2)= \sum_{i=1}^N (y_i - (\beta_0 + \beta_1 x_i))^2 +\alpha (\lambda \sum_{i=0}^j ||\beta_i|| + (1 - \lambda) \sum_{i=0}^j \beta_i^2/2)

Logistic regression

h(z) = \frac{1}{1 + e^{-z}}.
h(z)=11+e−z.h(z) = \frac{1}{1 + e^{-z}}.

knn

SVM

\mathbf{w}^Tx + b =0
wTx+b=0\mathbf{w}^Tx + b =0

SVM

\min_{\mathbf{w}} \frac{1}{2}\|\mathbf{w}\|^2 +C \sum_{i=1}^N \xi_i
minw12∥w∥2+C∑i=1Nξi\min_{\mathbf{w}} \frac{1}{2}\|\mathbf{w}\|^2 +C \sum_{i=1}^N \xi_i

SVM

SVM

Bayes

p(h|D) = \frac{p(D|h)\,p(h)}{p(D)}
p(h∣D)=p(D∣h)p(h)p(D)p(h|D) = \frac{p(D|h)\,p(h)}{p(D)}
P(y = c_1 | X) =
P(y=c1∣X)=P(y = c_1 | X) =
\frac{P(x_1|c_1) P(x_2 | c_1)... P(y=c_1)}{P(x_1|c_1) P(x_2 | c_1)... P(y=c_1) + P(x_1|c_0) P(x_2 | c_0)... P(y=c_0)}
P(x1∣c1)P(x2∣c1)...P(y=c1)P(x1∣c1)P(x2∣c1)...P(y=c1)+P(x1∣c0)P(x2∣c0)...P(y=c0)\frac{P(x_1|c_1) P(x_2 | c_1)... P(y=c_1)}{P(x_1|c_1) P(x_2 | c_1)... P(y=c_1) + P(x_1|c_0) P(x_2 | c_0)... P(y=c_0)}

decision tree

decision tree

Ensemble method

Bagging

RandomForest

bootstrap

Ensemble method

Bagging

Ensemble method

RandomForest

• Builds upon the idea of bagging
• Each tree build from bootstrap sample
• Node splits calculated from random feature subsets 

Ensemble method

RandomForest

• All trees are fully grown
• No pruning
• Two parameters
           – Number of trees
           – Number of features 

Ensemble

Boosting

• Also ensemble method like Bagging
• But:
          – weak learners evolve over time
          – votes are weighted
• Better than Bagging for many applications 

Boosting

Boosting

• number of trees
• number of splits in each tree (often stumps
work well)
• parameters controlling how weights evolve 

How to choose?

knn

SVM

RF

deep learning

features

samples

How to choose?

Clustering

k-means

Clustering

mean-shift

http://www.youtube.com/watch?v=kmaQAsotT9s

1. Put a window around each point
2. Compute mean of points in the frame.
3. Shift the window to the mean
4. Repeat until convergence 

– single-linkage

 

– complete-linkage


– average linkage

Clustering

Hierarchical Clustering 

http://scikit-learn.org/stable/auto_examples/cluster/plot_cluster_comparison.html

techniques

Subtitle

Principal Component Analysis

Principal Component Analysis

Latent Dirichlet Allocation 

Cross Validation

decision risk

what else except accuracy/R^2 ?

Regression

MSE/MAE etc.

Cross Validation

Classification

ROC P-R etc.

ROC

P-R

Cross Validation

TPR = Recall = \frac{TP}{TP+FN}
TPR=Recall=TPTP+FNTPR = Recall = \frac{TP}{TP+FN}
FPR = \frac{FP}{FP+TN}
FPR=FPFP+TNFPR = \frac{FP}{FP+TN}
Precision = \frac{TP}{TP+FP}
Precision=TPTP+FPPrecision = \frac{TP}{TP+FP}
F1 = \frac{2*Recall*Precision}{Recall + Precision}
F1=2∗Recall∗PrecisionRecall+PrecisionF1 = \frac{2*Recall*Precision}{Recall + Precision}
F\beta = \frac{(1 + \beta)*Recall*Precision}{\beta^2 * Recall + Precision}
Fβ=(1+β)∗Recall∗Precisionβ2∗Recall+PrecisionF\beta = \frac{(1 + \beta)*Recall*Precision}{\beta^2 * Recall + Precision}

Cross Validation

           predict
fact                  
1
0
1 cost 1 cost 2
0 cost 3 cost 4

cost matrix

MDS

MDS

MDS

SVD

prerequisites

prerequisits

  • LA
  • calculus
  • statistic
  • probability
  • english

Big Picture

終わり

ML an overview

By orashi

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ML an overview

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