Machine learning

MachineLearning

Andrea Iacono https://github.com/andreaiacono/MachineLearning

Machine Learning: Intro

[Wikipedia]: a branch of artificial intelligence that allows the construction and the study of

systems that can learn from data

What is Machine Learning?

- Regression analysis- Similarity and metric learning- Decision tree learning- Association rule learning- Artificial neural networks- Genetic programming- Support vector machines (classification and regression analysis)- Clustering- Bayesian networks


Some approaches:


Supervised learningvs

Unsupervised learning

Machine learningvs

Data mining

Machine Learning: Regression analysis

Regression Analysis

A statistical technique for estimating the relationships among a dependent variable and independent variables


Prediction of house pricesSize (x) Price (y)

0.80 70

0.90 83

1.00 74

1.10 93

1.40 89

1.40 58

1.50 85

1.60 114

1.80 95

2.00 100

2.40 138

2.50 111

2.70 124

3.20 172

3.50 172


Prediction of house prices

Hypothesis:

hθ(x )=θ0+θ1 x



Hypothesis:

hθ(x )=θ0+θ1 x J (θ0,θ1)=12m

∑i=1

m

(hθ(x(i))− y(i ))2

Cost function for linear regression:



Hypothesis:

hθ(x )=θ0+θ1 x J (θ0,θ1)=12m

∑i=1

m

(hθ(x(i))− y(i ))2

Gradient Descent

repeat until convergence :

θ0=θ0−α1m∑i=1

m

(hθ( x(i ))− y(i )

)

θ1=θ1−α1m∑

i=1

m

[ (hθ(x(i))− y(i )) x(i) ]

Cost function for linear regression:



Iterative minimization of cost function with gradient descent


Hands on


Regression analysis

- one / multiple variables - linear / higher order curves

- several optimization algorithms - linear regression - logistic regression - simulated annealing - ...


Overfitting vs underfitting

Machine Learning: Similarity and metric learning

Similarity and metric learning

- concept of distance

Euclidean distance

euclidean distance (p , q )=√∑i =1

n

(p i −q i )2


manhattan distance (p , q )=∑i=1

n

∣(p i−q i )∣


Manhattan distance

Pearson ' s correlation (p , q )=∑i =1

n

(p i q i )−∑i =1

n

p i ∑i =1

n

q i

n

√(∑i =1

n

p i2−

(∑i =1

n

pi )2

n)(∑

i =1

n

q i2−

(∑i =1

n

q i )2

n)


Pearson's correlation

Searches a large group of users for finding a small subset that have tastes like yours. Based on what this subset likes or dislikes the system can recommend you other items.

Two main approaches: - User based filtering - Item based filtering


Collaborative filtering


User based filtering

- based on ratings given to the items, we can measure the distance among users

- we can recommend to the user the items that have the highest ratings among the closest users

Hands on



Is user based filtering good for- scalability?

- sparse data?- quickly changing data?


Is user based filtering good for- scalability?

- sparse data?- quickly changing data?

No, it's better to use item based filtering


Euclidean distance for item based filtering:nothing has changed!

- based on ratings got from the users, we can measure the distance among items

- we can recommend an item to a user, getting the items that are closer to the highest rated by the user

Hands on


P (A∣B )=P (B∣A)P (A)

P (B )

Machine Learning: Bayes' classifier

Example: given a company where 70% of developers use Java and 30% use C++, and knowing that half of the Java developers always use enhanced for loop, if you look at the snippet:

which is the probability that the developer who wrote it uses Java?

for (int j=0; j<100; j++) {t = tests[j];

}

P (A∣B )=P (B∣A)P (A)

P (B )

Bayes' theorem

P (A∣B )=P (B∣A)P (A)

P (B )





}

P (A∣B )=P (B∣A)P (A)

P (B )

Bayes' theorem

Hint:A = developer uses JavaB = developer writes old for loops

P (A∣B )=P (B∣A)P (A)

P (B )





}

P (A∣B )=P (B∣A)P (A)

P (B )

Bayes' theorem

Solution:A = developer uses JavaB = developer writes old for loops

P (A∣B )=P (B∣A)P (A)

P (B )=

0.5⋅0.70.65

=0.54

P(A) = prob. that a developer uses Java = 0.7P(B) = prob. that any developer uses old for loop = 0.3 + 0.7*0.5 = 0.65P(B|A) = prob. that a Java developer uses old for loop = 0.5


Naive Bayes' classifier

- supervised learning- trained on a set of known classes- computes probabilities of elements to be in a class- smoothing required

P c (w 1 , .... , w n)=∏i =1

n

P (c∣w i )

∏i =1

n

P (c∣w i )+∏i=1

n

(1−P (c∣w i ))


Naive Bayes' classifier

Example

- we want a classifier for Twitter messages- define a set of classes: {art, tech, home, events,.. }- trains the classifier with a set of alreay classified tweets- when a new tweet arrives, the classifier will (hopefully) tell us which class it belongs to


Hands on


Sentiment analysis

- define two classes: { +, - }- define a set of words: { like, enjoy, hate, bore, fun, …}- train a NBC with a set of known +/- comments - let NBC classify any new comment to know if +/-

- performance is related to quality of training set

Machine Learning: Clustering

- Unsupervised learning- Different algorithms: - Hierarchical clustering - K-Means clustering - ...

Clustering

Common use cases: - navigation habits - online commerce - social/political attitudes - ...


K-Means aims at identifying cluster centroids, such that an item belonging to a cluster X, is closer to the centroid of cluster X than to the centroid of any other cluster.

K-Means clustering


The algorithm requires a number of clusters to start, in this case 3. The centroids are placed in the item space, typically in random locations.

K-Means clustering


The algorithm will then assign to each centroid all items that are closer to it than to any other centroid.

K-Means clustering


The centroids are then moved to the center of mass of the items in the clusters.

K-Means clustering


A new iteration occurs, taking into account the new centroid positions.

K-Means clustering


The centroids are again moved to the center of mass of the items in the clusters.

K-Means clustering


Another iteration occurs, taking into account the new centroid positions.

K-Means clustering


The centroids are again moved to the center of mass of the items in the clusters.

K-Means clustering


Another iteration occurs, taking into account the new centroid positions. Note that this time the cluster membership did not change. The cluster centers will not move anymore.

K-Means clustering


The solution is found.

K-Means clustering


Hands on

Machine Learning: Neural networks

A logical calculus of the ideas immanent in nervous activity

by McCulloch and Pitts in 1943

Neural networks


Neural networks

Feedforward Perceptron


Neural networks

Logic operators with neural networks:

Threshold = 0

X0 X1 X2 Σ Result

-10 0 0 -10 0

-10 0 20 10 1

-10 20 0 10 1

-10 20 20 30 1

OR operator


Neural networks

Threshold = 0

X0 X1 X2 Σ Result

-30 0 0

-30 0 20

-30 20 0

-30 20 20

which operator?



Neural networks

Threshold = 0

X0 X1 X2 Σ Result

-30 0 0 -30 0

-30 0 20 -10 0

-30 20 0 -10 0

-30 20 20 10 1

AND operator



Hands on


Neural networks

Backpropagation

Phase 1: Propagation - Forward propagation of a training pattern's input through the neural network in order to generate the propagation's output activations - Backward propagation of the propagation's output activations through the neural network using the training pattern target in order to generate the deltas of all output and hidden neurons

Phase 2: Weight update - Multiply its output delta and input activation to get the gradient of the weight - Bring the weight in the opposite direction of the gradient by subtracting a ratio of it from the weight


Neural networks

Multilayer perceptrons


Hands on

Machine Learning: Genetic algorithms

Genetic algorithms

GA is a programming technique that mimics biological evolution as a problem-solving strategy

Steps- maps the variables of the problem into a sequence of bits, a chromosome

Chromosome

- creates a random population of chromosomes- let evolve the population using evolution laws: - the higher the fitness, the higher the chance of breeding - crossover of chromosomes - mutation in chromosomes- if otpimal solution is found or after n steps the process is stopped


Genetic algorithms

Mutation

Crossover

Hands on


Thanks!

Machine Learning

The code is available on:https://github.com/andreaiacono/MachineLearning

Machine learning

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