Week 1.pdf

Introduction to Machine Learning
Sudeshna Sarkar
IIT Kharagpur
Module 1: Introduction
Part A: Introduction

Overview of Course
1. Introduction
2. Linear Regression and Decision Trees
3. Instance based learning
Feature Selection
4. Probability and Bayes Learning
5. Support Vector Machines
6. Neural Network
7. Introduction to Computational Learning Theory
8. Clustering

Module 1
1. Introduction
a) Introduction
b) Different types of learning
c) Hypothesis space, Inductive Bias
d) Evaluation, Training and test set, cross-validation
Feature Selection
6. Neural Network
8. Clustering

Machine Learning History
• 1950s:
– Samuel's checker-playing program
• 1960s:
– Neural network: Rosenblatt's perceptron
– Minsky & Papert prove limitations of Perceptron
• 1970s:
– Symbolic concept induction
– Expert systems and knowledge acquisition bottleneck
– Qui la ’s ID3
– Natural language processing (symbolic)

• 1980s:
– Advanced decision tree and rule learning
– Learning and planning and problem solving
– Resurgence of neural network
– Valia t’s PAC learning theory
– Focus on experimental methodology
• 90's ML and Statistics
– Data Mining
– Adaptive agents and web applications
– Text learning
– Reinforcement learning
– Ensembles
– Bayes Net learning
• 1994: Self-driving car
road test
• 1997: Deep Blue
beats Gary Kasparov

• Popularity of this field in
recent time and the reasons
behind that
– New software/ algorithms
• Neural networks
• Deep learning
– New hardware
• GPU’s
– Cloud Enabled
– Availability of Big Data
• 2009: Google builds self
driving car
• 2011: Watson wins
Jeopardy
• 2014: Human vision
surpassed by ML systems

Programs vs learning algorithms
Algorithmic solution Machine learning solution
Computer
Data Program
Output
Computer
Data Output
Program

Machine Learning : Definition
• Learning is the ability to improve one's behaviour based on
experience.
• Build computer systems that automatically improve with
experience
• What are the fundamental laws that govern all learning
processes?
• Machine Learning explores algorithms that can
– learn from data / build a model from data
– use the model for prediction, decision making or solving
some tasks

Machine Learning : Definition
• A computer program is said to learn from
experience E with respect to some class of
tasks T and performance measure P, if its
performance at tasks in T, as measured by P,
improves with experience E.
[Mitchell]

Components of a learning problem
• Task: The behaviour or task being improved.
– For example: classification, acting in an
environment
• Data: The experiences that are being used to
improve performance in the task.
• Measure of improvement :
– For example: increasing accuracy in prediction,
acquiring new, improved speed and efficiency

Black-box Learner
Experiences
Data
Background knowledge/
Bias
Problem/
Task
Answer/
Performance

Learner
Experiences
Data
Background knowledge/
Bias
Problem/
Task
Answer/
Performance
Learner Reasoner
Models

Many domains and applications
Medicine:
• Diagnose a disease
– Input: symptoms, lab measurements, test results,
DNA tests,
– Output: o e of set of possi le diseases, or o e
of the a o e
• Data: historical medical records
• Learn: which future patients will respond best to
which treatments

Vision:
• say what objects appear in an image
• convert hand-written digits to characters 0..9
• detect where objects appear in an image

Robot control:
• Design autonomous mobile robots that learn
from experience to
– Play soccer
– Navigate from their own experience

NLP:
• detect where entities are mentioned in NL
• detect what facts are expressed in NL
• detect if a product/movie review is positive,
negative, or neutral
Speech recognition
Machine translation

Financial:
• predict if a stock will rise or fall
• predict if a user will click on an ad or not

Application in Business Intelligence
• Forecasting product sales quantities taking
seasonality and trend into account.
• Identifying cross selling promotional opportunities
for consumer goods.
• …

Some other applications
• Fraud detection : Credit card Providers
• determine whether or not someone will
default on a home mortgage.
• Understand consumer sentiment based off of
unstructured text data.
• Fore asti g o e ’s o i tio rates ased
off external macroeconomic factors.

Design a Learner
Experiences
Data
Background
knowledge/
Bias
Problem/
Task
Answer/
Performance
Learn
er
Reaso
ner
Models
1. Choose the training
experience
2. Choose the target
function (that is to be
learned)
3. Choose how to
represent the target
function
4. Choose a learning
algorithm to infer the
target function

Choosing a Model Representation
• The richer the representation, the more useful
it is for subsequent problem solving.
• The richer the representation, the more
difficult it is to learn.
• Components of Representation
– Features
– Function class / hypothesis language

Foundations of Machine Learning
Sudeshna Sarkar
IIT Kharagpur
Part B: Different types of learning

Module 1
1. Introduction
a) Introduction
b) Different types of learning
c) Hypothesis space, Inductive Bias
d) Evaluation, Training and test set, cross-validation
Feature Selection
5. Neural Network
8. Clustering

Broad types of machine learning
• Supervised Learning
– X,y (pre-classified training examples)
– Given an observation x, what is the best label for y?
• Unsupervised learning
– X
– Give a set of ’s, cluster or su arize the
• Semi-supervised Learning
• Reinforcement Learning
– Determine what to do based on rewards and punishments.

Supervised Learning
Learning
Algorithm
Model
New Input x
Output y
Input1 Output1
Input2 Output2
Input3 Output3
Input-n Output-n
X y

Unsupervised Learning
Learning
Algorithm
Clusters
Input1
Input2
Input3
Input-n
X

Reinforcement Learning
Agent Environment
Action at
State st
Reward rt
St+1
rt+1

Reinforcement Learning
RLearner Environment
Action at
State st
Reward rt
St+1
rt+1
User Environment
Action at
State st
Reward rt
St+1
rt+1
Policy
state
Best
action
State,
update
Q-values

Supervised Learning
Given:
– a set of input features 1, … , 𝑛
– A target feature
– a set of training examples where the values for the input
features and the target features are given for each
example
– a new example, where only the values for the input
features are given
Predict the values for the target features for the new
example.
– classification when Y is discrete
– regression when Y is continuous

Classification
Example: Credit scoring
Differentiating between
low-risk and high-risk
customers from their
income and savings

Regression
Example: Price of a
used car
x : car attributes
y : price
y = g (x, θ )
g ( ) model,
𝜃 parameters
y = wx+w0
x: mileage
y:
price

Features
• Often, the individual observations are analyzed
into a set of quantifiable properties which are
called features. May be
– categorical (e.g. "A", "B", "AB" or "O", for blood type)
– ordinal (e.g. "large", "medium" or "small")
– integer-valued (e.g. the number of words in a text)
– real-valued (e.g. height)

Example Data
Action Author Thread Length Where
e1 skips known new long Home
e2 reads unknown new short Work
e3 skips unknown old long Work
e4 skips known old long home
e5 reads known new short home
e6 skips known old long work
e7 ??? known new short work
e8 ??? unknown new short work
Training Examples:
New Examples:

Testing
Training
Set
Learning
Algorithm
Hypothesis Predicted
y
X
Training

Training phase
Label machine
learning
algorithm
Input
feature
extractor
features
Testing Phase
Input
features
classifier
model
Label
feature
extractor

Classification learning
• Task T:
– input:
– output:
• Performance metric P:
• Experience E:

• Task T:
– input: a set of instances d1,…,dn
• an instance has a set of features
• we can represent an instance as a vector d=<x1,…,xn>
– output: a set of predictions
• one of a fixed set of constant values:
– {+1,-1} or {cancer, healthy}, or {rose, hi is us, jas i e, …}, or …
• Experience E:
ŷ1,..., ŷn

Classification Learning
Task Instance Labels
medical
diagnosis
patient record:
blood pressure diastolic, blood
pressure systolic,
age, sex (0 or 1), BMI,
cholesterol
{-1,+1} = low, high risk
of heart disease
finding entity
names in text
a word in context: capitalized
(0,1), word-after-this-equals-
Inc, bigram-before-this-equals-
acquired-by, …
{first,later,outside} =
first word in name,
second or later word
in name, not in a
name
image
recognition
image:
1920*1080 pixels, each with a
code for color
{0,1} = no house,
house

• Task T:
– input: a set of instances d1,…,dn
– output: a set of predictions
– Prob (wrong prediction)
• Experience E:
– a set of labeled examples (x,y) where y is the true
label for x
– ideally, examples should be sampled from some fixed
distribution D
ŷ1,..., ŷn
on examples from D
we care about performance on the
distribution, not the training data

Classification Learning
Task Instance Labels Getting data
medical
diagnosis
patient record:
lab readings
risk of heart
disease
wait and look
for heart
disease
finding entity
names in text
a word in context:
capitalized,
nearby words, ...
{first,later,outside} text with
manually
annotated
entities
image
recognition
image:
pixels
no house, house hand-labeled
images

Representations
1. Decision Tree
2. Linear function
Weekend
EatOut Late
EatOut Home
Yes
Yes
No
No

Representations
3. Multivariate linear
function
4. Single layer perceptron

Representations
5. Multi-layer neural
network

Hypothesis Space
• One way to think about a supervised learning
machine is as a device that explores a
h pothesis space .
– Each setting of the parameters in the machine is a
different hypothesis about the function that maps
input vectors to output vectors.

Terminology
• Features: The number of features or distinct
traits that can be used to describe each item
in a quantitative manner.
• Feature vector: n-dimensional vector of
numerical features that represent some object
• Instance Space X: Set of all possible objects
describable by features.
• Example (x,y): Instance x with label y=f(x).

Terminology
• Concept c: Subset of objects from X (c is
unknown).
• Target Function f: Maps each instance x ∈ X to
target label y ∈ Y
• Example (x,y): Instance x with label y=f(x).
• Training Data S: Collection of examples observed
by learning algorithm.
Used to discover potentially predictive relationships

Sudeshna Sarkar
IIT Kharagpur
Part c: Hypothesis Space and Inductive Bias

Inductive Learning or Prediction
• Given examples of a function (X, F(X))
– Predict function F(X) for new examples X
• Classification
F(X) = Discrete
• Regression
F(X) = Continuous
• Probability estimation
F(X) = Probability(X):

Features
• Features: Properties that describe each
instance in a quantitative manner.
• Feature vector: n-dimensional vector of
features that represent some object

Feature Space
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Example:
<0.5,2.8,+>
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Slide by Jesse Davis: University of Washington

Terminology
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Hypothesis:
Function for labeling examples
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Terminology
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Hypothesis Space:
Set of legal hypotheses
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Representations
3. Multivariate linear
function
4. Single layer perceptron
5. Multi-layer neural
networks

Hypothesis Space
• The space of all hypotheses that can, in
principle, be output by a learning algorithm.
• We can think about a supervised learning
machine as a device that explores a
h pothesis space .
– Each setting of the parameters in the machine is a
different hypothesis about the function that maps
input vectors to output vectors.

Terminology
• Example (x,y): Instance x with label y.
• Training Data S: Collection of examples observed by
learning algorithm.
• Instance Space X: Set of all possible objects
describable by features.
• Concept c: Subset of objects from X (c is unknown).
• Target Function f: Maps each instance x ∈ X to target
label y ∈ Y

Classifier
• Hypothesis h: Function that approximates f.
• Hypothesis Space ℋ : Set of functions we allow for
approximating f.
• The set of hypotheses that can be produced, can be
restricted further by specifying a language bias.
• Input: Training set 𝒮 ⊆
• Output: A hypothesis ℎ ∈ ℋ

Hypothesis Spaces
• If there are 4 (N) input features, there are
2 6
2
𝑁
possible Boolean functions.
• We cannot figure out which one is correct
unless we see every possible input-output pair
24
(2𝑁
)

Example
Hypothesis language
1. may contain representations of all polynomial
functions from X to Y if X = ℛ𝑛 and Y = ℛ,
2. may be able to represent all conjunctive
concepts over X when = 𝐵𝑛
and = 𝐵 (with
B the set of booleans).
• Hypothesis language reflects an inductive bias
that the learner has

Inductive Bias
• Need to make assumptions
– E perie ce alo e does ’t allow us to ake
conclusions about unseen data instances
• Two types of bias:
– Restriction: Limit the hypothesis space
(e.g., look at rules)
– Preference: Impose ordering on hypothesis space
(e.g., more general, consistent with data)

Inductive learning
• Inductive learning: Inducing a general function
from training examples
– Construct hypothesis h to agree with c on the training
examples.
– A hypothesis is consistent if it agrees with all training
examples.
– A hypothesis said to generalize well if it correctly
predicts the value of y for novel example.
• Inductive Learning is an Ill Posed Problem:
Unless we see all possible examples the data is not sufficient
for an inductive learning algorithm to find a unique solution.

Inductive Learning Hypothesis
• Any hypothesis h found to approximate the
target function c well over a sufficiently large
set of training examples D will also
approximate the target function well over
other unobserved examples.

Learning as Refining the Hypothesis
Space
• Concept learning is a task of searching an hypotheses
space of possible representations looking for the
representation(s) that best fits the data, given the
bias.
• The tendency to prefer one hypothesis over another
is called a bias.
• Given a representation, data, and a bias, the problem
of learning can be reduced to one of search.

Occam's Razor
⁻ A classical example of Inductive Bias
• the simplest consistent hypothesis about the
target function is actually the best

Some more Types of Inductive Bias
• Minimum description length: when forming a
hypothesis, attempt to minimize the length of the
description of the hypothesis.
• Maximum margin: when drawing a boundary
between two classes, attempt to maximize the width
of the boundary (SVM)

Important issues in Machine Learning
• What are good hypothesis spaces?
• Algorithms that work with the hypothesis spaces
• How to optimize accuracy over future data points
(overfitting)
• How can we have confidence in the result? (How
much training data – statistical qs)
• Are some learning problems computationally
intractable?

Generalization
• Components of generalization error
– Bias: how much the average model over all
training sets differ from the true model?
• Error due to inaccurate assumptions/simplifications
made by the model
– Variance: how much models estimated from
different training sets differ from each other

Underfitting and Overfitting
• Underfitting: odel is too si ple to represe t all
the relevant class characteristics
– High bias and low variance
– High training error and high test error
• Overfitting: odel is too co ple a d fits
irrelevant characteristics (noise) in the data
– Low bias and high variance
– Low training error and high test error

Sudeshna Sarkar
IIT Kharagpur
Part D: Evaluation and Cross validation

Experimental Evaluation of Learning
Algorithms
• Evaluating the performance of learning systems is
important because:
– Learning systems are usually designed to predict the
lass of future unla eled data points.
• Typical choices for Performance Evaluation:
– Error
– Accuracy
– Precision/Recall
• Typical choices for Sampling Methods:
– Train/Test Sets
– K-Fold Cross-validation

Evaluating predictions
• Suppose we want to make a prediction of a
value for a target feature on example x:
– y is the observed value of target feature on
example x.
– is the predicted value of target feature on
example x.
– How is the error measured?

Measures of error
• Absolute error:
𝑛
|𝑓 − |
• Sum of squares error:
𝑛
𝑓 −
𝑛
𝑖=
• Number of misclassifications:
𝑛
𝛿 𝑓 ,
𝑛
𝑖=
• 𝛿 𝑓 , is 1 if f(x)  y, and 0, otherwise.

Confusion Matrix
• Accuracy =
(TP+TN)/(P+N)
• Precision =
TP/(TP+FP)
• Recall/TP rate =
TP/P
• FP Rate = FP/N
True class 
Hypothesized
class
Pos Neg
Yes TP FP
No FN TN
P=TP+FN N=FP+TN

Sample Error and True Error
• The sample error of hypothesis f with respect to
target function c and data sample S is:
errors(f)= 1/n xS(f(x),c(x))
• The true error (denoted errorD(f)) of hypothesis f
with respect to target function c and distribution D,
is the probability that h will misclassify an instance
drawn at random according to D.
errorD(f)= PrxD[f(x)  c(x)]

Why Errors
• Errors in learning are caused by:
– Limited representation (representation bias)
– Limited search (search bias)
– Limited data (variance)
– Limited features (noise)

Difficulties in evaluating hypotheses
with limited data
• Bias in the estimate: The sample error is a poor
estimator of true error
– ==> test the hypothesis on an independent test set
• We divide the examples into:
– Training examples that are used to train the learner
– Test examples that are used to evaluate the learner
• Variance in the estimate: The smaller the test set,
the greater the expected variance.

Validation set
Validation fails to use all the available data

k-fold cross-validation
1. Split the data into k equal subsets
2. Perform k rounds of learning; on each round
– 1/k of the data is held out as a test set and
– the remaining examples are used as training data.
3. Compute the average test set score of the k rounds

Trade-off
• In machine learning, there is always a trade-
off between
– complex hypotheses that fit the training data well
– simpler hypotheses that may generalise better.
• As the amount of training data increases, the
generalization error decreases.

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