Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to...
Transcript of Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to...
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Welcome to Machine Learning
Konstantin Tretyakovhttp://kt.era.ee
AACIMP Summer
School 2015
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Data mining,
Data analysis, Statistical analysis,
Pattern discovery, Statistical learning,
Machine learning, Predictive analytics,
Business intelligence, Data-driven methods,
Inductive reasoning, Pattern analysis,
Knowledge discovery from databases,
Neural networks,
…
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A
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“Unformalizable” problems
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“Unformalizable” problems
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“Unformalizable” problems
А
A
A
B
B
B
B
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General rule:
IF (Х is made of plastic), THEN (Х is not edible)
Application in the particular case:Х = Rubic’s cube
⇒Rubic’s cube is not edible
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General rule:
is_solution(x) = function { … }
Application in the particular case:is_solution(?) = true
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General rule:
add(x, y) = function { … }
Application in the particular case:add(2,4) D
ed
ucti
on
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General rule:
add(x, y) = function {
???
}
Particular cases:add(2,4) = 6
add(5,3) = 8
add(1,2) = 3
…
Ind
uc
tio
n
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Deduction and Induction
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Deduction
Given a general rule, make a decision in a particular case
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Induction
Given particular cases, find a general rule
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Machine learning =
A set of techniques for dealing
with inductive problems.
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Classification
by analogy
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MNIST dataset
http://yann.lecun.com/exdb/mnist/
Handwritten digits, 28 х 28
…
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MNIST dataset
images = load_images()
labels = load_labels()
# Let us just use 1000 images
training_set = images[0:1000]
training_labels = labels[0:1000]
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MNIST dataset
> training_set[0]
array([ 0, 0, 0, ...,
254, 241, 198, ...])
> training_labels[0]
‘7’
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Nearest neighbor method
Training set
?4
7
9
7
4
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Nearest neighbor method
Training set
4
4
7
9
7
4
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
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Nearest neighbor method
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
def similarity(img1, img2):
return -sum(abs(img1 - img2))
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Testing the algorithm
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Testing the algorithm
test_set = images[1000:2000]
test_labels = labels[1000:2000]
predicted_class = [classify(p) for p in test_set]
n_successes =
sum(array(predicted_class) ==
array(test_labels))
=> 843/1000
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9 or 4?
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from sklearn.neighbors import
KNeighborsClassifier
clf = KNeighborsClassifier(n_neighbors=1)
clf.fit(training_set, training_labels)
predicted_class = clf.predict(test_set)
=> 855/1000
Scikit-learnhttp://scikit-learn.org/
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Voronoi diagram
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… not the only way
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How can we modify the method?
Training set
4
4
7
9
7
4
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Some samples may be thrown away
Training set
4
4
7
9
7
4
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…or we can add “weights”
Training set
4
4
7
9
7
4
0.0
1.0
1.0
1.0
0.0
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…or we can add “weights”
Training set
4
4
7
9
7
4
0.0
0.9
1.1
2.0
0.0
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.. or we can SUM instead of MAX
Training set
4
4
7
9
7
4
0.0
0.9
1.1
2.0
0.0
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.. or we can SUM instead of MAX
Training set
4
7
9
7
4
0.0
0.9
1.1
2.0
0.0
evidence(img, 4) =
0.9 * similarity(img, tr[1])
+
0.0 * similarity(img, tr[4])
= 34.0
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.. or we can SUM instead of MAX
Training set
4
7
9
7
4
0.0
0.9
1.1
2.0
0.0
evidence(img, 7) =
0.0 * similarity(img, tr[0])
+
2.0 * similarity(img, tr[3])
= 20.0
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Formally…
𝐾(𝒙1, 𝒛)
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Formally…
𝐾 𝒙1, 𝒛 , 𝐾(𝒙2, 𝒛), 𝐾 𝒙3, 𝒛 , …
𝐾 𝒙101, 𝒛 , 𝐾(𝒙212, 𝒛), …
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Formally…
𝑤1𝐾 𝒙1, 𝒛 + 𝑤2𝐾 𝒙2, 𝒛 + 𝑤3𝐾 𝒙3, 𝒛 , …
𝑤101𝐾 𝒙101, 𝒛 + 𝑤212𝐾 𝒙212, 𝒛 …
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Formally…
𝑖
𝑤𝑖𝐾(𝒙𝑖 , 𝒛)
𝑗
𝑤𝑗𝐾(𝒙𝑗 , 𝒛)
![Page 57: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/57.jpg)
Formally…
𝑖
𝑤𝑖𝐾(𝒙𝑖 , 𝒛)
−
𝑗
𝑤𝑗𝐾(𝒙𝑗 , 𝒛)
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Formally…
𝑖
𝑤𝑖𝑦𝑖𝐾(𝒙𝑖 , 𝒛)
+
𝑗
𝑤𝑗𝑦𝑗𝐾(𝒙𝑗 , 𝒛)
![Page 59: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/59.jpg)
Kernel-based classifier
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 60: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/60.jpg)
How to find the weights?
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 61: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/61.jpg)
How to find the weights?
Find weights, such that the
misclassification error rate on the training set
is the smallest.
w = argminw ErrorRate (fw, Data)
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 62: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/62.jpg)
How to find the weights?
Find weights, such that the
approximation to misclassification error on
the training set is the smallest.
w = argminw Error (fw, Data)
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 63: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/63.jpg)
How to find the weights?
Find weights, such that the
error rate on the training set is the smallest +
there are many zero weights.
w = argminw Error (fw, Data) + Complexity (w)
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 64: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/64.jpg)
Support Vector Machine
from sklearn.svm import SVC
clf = SVC(kernel=‘linear’)
clf.fit(training_set, training_labels)
predicted_class = clf.predict(test_set)
=> 865/1000
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Classification by
analogy:k-NN
SVM
RBF
![Page 67: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/67.jpg)
Search for the nearest neighbor
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
![Page 68: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/68.jpg)
Search for the nearest neighbor
def classify(img):
similarities =
[similarity(img, p) for p in training_set]
i = similarities.index(max(similarities))
return training_labels[i]
Inefficient
![Page 69: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/69.jpg)
Search for the nearest neighbor
def classify(img):
nearest_neighbour =
training_set.find_nearest_neighbour(img)
return nearest_neighbour.label
Indexing!
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find_nearest_neighbour
if pixel[10,13] > 4:
if pixel[3,24] < 0:
nearest_neighbour = A
else:
nearest_neighbour = B
else:
nearest_neighbour = C
![Page 76: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/76.jpg)
Classification Tree
if pixel[10,13] > 4:
if pixel[3,24] < 0:
class = ‘1’
else:
class = ‘2’
else:
class = ‘3’
![Page 77: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/77.jpg)
Classification Tree
![Page 78: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/78.jpg)
Classification Tree
![Page 79: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/79.jpg)
Classification Tree
Orangehttp://orange.biolab.si/
![Page 80: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/80.jpg)
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Trees
ID3
C4.5
RegTree
![Page 82: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/82.jpg)
Search for optimal model
parameters
General form of a model
𝑓𝒘 𝒛 =
𝑖
𝑤𝑖𝑦𝑖 𝐾(𝒙𝑖 , 𝒛)
![Page 83: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/83.jpg)
Search for the optimal
tree
General form of a model
![Page 84: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/84.jpg)
Search for the optimal
separation line
General form of a model
![Page 85: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/85.jpg)
Optimization
Modeling
![Page 86: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/86.jpg)
Optimization
Modeling
“Learning”
“Training”
“Estimation”
![Page 87: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/87.jpg)
Linear model
f(image) =
pixel1*w1 + pixel2*w2 + … + pixel784*w784
![Page 88: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/88.jpg)
Linear Classification
from sklearn.linear_model import
LinearRegression,
LogisticRegression,
RidgeClassifier,
LARS,
ElasticNet,
SGDClassifier,
...
=> 809/1000
![Page 89: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/89.jpg)
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Modeling
![Page 91: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/91.jpg)
Linear model
f(image) =
pixel1*w1 + pixel2*w2 + … + pixel784*w784
![Page 92: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/92.jpg)
f(image) =
pixel1*w1 + pixel2*w2 + … + pixel784*w784
…
pixel1
pixel2
pixel3
pixel4
pixel784
∑
w1w2
w3
w4
w784
f(image)
![Page 93: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/93.jpg)
Neural network
![Page 94: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/94.jpg)
Modeling
![Page 95: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/95.jpg)
Why should a model,
trained on one set of data,
work well on future data?
When is it not the case?
![Page 96: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/96.jpg)
How to formalize a new model?
How to find parameters?
![Page 97: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/97.jpg)
How to create efficient learning algorithms?
![Page 98: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/98.jpg)
How to handle structured data?
![Page 99: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/99.jpg)
Unsupervised learning
Semi-supervised learning
On-line learning
Active learning
Multi-instance learning
Reinforcement learning
![Page 100: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/100.jpg)
Probabilistic models
Graphical models
Ensemble learners
Data fusion
HPC
![Page 101: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/101.jpg)
Tools:R, Weka, RapidMiner,
Orange, scikits-learn,
MLPy, MDP, PyBrain,
Theano,Torch,Caffe,
Matlab…
![Page 102: Welcome to Machine Learning - kt.era.eekt.era.ee/lectures/aacimp2015/1-intro.pdf · Welcome to Machine Learning ... Neural networks, ... Quiz The machine learning algorithms mentioned](https://reader030.fdocuments.in/reader030/viewer/2022032712/5b2e1a7c7f8b9a594c8d1d1a/html5/thumbnails/102.jpg)
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“Unformalizable” problems
Model-based Instance-based
Deduction and Induction
Theory and
Practice
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Quiz
The OCR problem is unusual in that it is ____.
The two important perspectives on machine
learning are ______-based and _____-based.
The “soul” of machine learning is the
minimization task
argmin𝒘 ________ + 𝜆 _________
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Quiz
The visualization of a decision rule inferred by
a single-nearest-neighbor algorithm is called
_____________________
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Quiz
Two important components of machine
learning:
?
?
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Quiz
The machine learning algorithms mentioned in
this lecture were:
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Quiz
The machine learning algorithms mentioned in
this lecture were:
K-nearest neighbor classifier
SVM
Classification trees
Linear models
Neural networks
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Questions?
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“Unformalizable” problems
Model-based Instance-based
Deduction and Induction
Theory and
Practice