CS代考 Ve492: Introduction to Artificial Intelligence

Ve492: Introduction to Artificial Intelligence
Introduction to Machine Learning
UM-SJTU Joint Institute
Some slides adapted from http://ai.berkeley.edu, CMU

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Learning Objectives
❖ What is machine learning?
❖ What are the different tasks in machine learning?
❖ What is a generative model?
❖ How to perform classification with a generative model?
❖ What are the common issues encountered in machine learning?

❖ Overview of Machine Learning ❖ Classification
❖ Model-based Classification based on Naïve Bayes
❖ Training a Machine Learning Model

Machine Learning
❖ Techniques that give a computer system the ability to learn to perform a given task
❖ Learn = improve itself as it sees more data, observations, interactions ❖ Programming with data
❖ Computational Statistics
❖ Data science, big data, data mining, pattern recognition

Machine Learning
❖ Up until now: how use a model to make optimal decisions ❖ Except reinforcement learning
❖ Machine learning: how to acquire a model from data/experience
❖ Learning parameters (e.g., probabilities)
❖ Learning structure (e.g., BN graphs)
❖ Learning hidden concepts (e.g., clustering)

What do we learn from?
Supervised
Reinforcement learning Online learning
Unsupervised
x, 𝑦 Reward
𝑥”, 𝑎”, 𝑟”, 𝑠”#$
No feedback
Classifier Regressor Structured predictor
Latent structure Hidden concept

Typical Supervised ML Pipeline
Data acquisition
Data collection, aggregation, consolidation
Data preprocessing
Data cleaning, missing data imputation,
normalization
Feature engineering
Feature construction, selection
Model building, training, selection
Training on training dataset, hyperparameter tuning on validation dataset, model selection on validation dataset, cross-validation,
evaluation on test dataset
Model deployment
❖ Batch vs online settings

Classification
Introduction

Example: Spam Filter
❖ Input: an email
❖ Output: spam/ham
❖ Get a large collection of example emails, each
labeled “spam” or “ham”
❖ Note: someone has to hand label all this data!
❖ Want to learn to predict labels of new, future emails
❖ Features: The attributes used to make the ham / spam decision
❖ Words: FREE!
❖ Text Patterns: $dd, CAPS
❖ Non-text: SenderInContacts ❖…
First, I must solicit your confidence in this transaction, this is by virture of its nature as being utterly confidencial and top secret. …
TO BE REMOVED FROM FUTURE MAILINGS, SIMPLY REPLY TO THIS MESSAGE AND PUT “REMOVE” IN THE SUBJECT.
99 MILLION EMAIL ADDRESSES FOR ONLY $99
Ok, Iknow this is blatantly OT but I’m beginning to go insane. Had an old Dell Dimension XPS sitting in the corner and decided to put it to use, I know it was working pre being stuck in the corner, but when I plugged it in, hit the power nothing happened.

Example: Digit Recognition
❖ Input: images / pixel grids
❖ Output: a digit 0-9
❖ Get a large collection of example images, each
labeled with a digit
❖ Note: someone has to hand label all this data!
❖ Want to learn to predict labels of new, future digit images
❖ Features: The attributes used to make the digit decision
❖ Pixels: (6,8)=ON
❖ Shape Patterns: NumComponents, AspectRatio,
NumLoops ❖…

Other Classification Tasks
❖ Classification: given inputs x, predict labels (classes) y
❖ Examples:
❖ Spam detection (input: document,
classes: spam / ham)
❖ OCR (input: images, classes: characters)
❖ Medical diagnosis (input: symptoms,
classes: diseases)
❖ Automatic essay grading (input: document,
classes: grades)
❖ Fraud detection (input: account activity,
classes: fraud / no fraud)
❖ Customer service email routing
❖ … many more
❖ Classification is an important commercial technology!

Classification Task
❖ How to solve a classification task?
❖ Given x, predict y ∈ C, finite set of possible classes
❖ Generative model
❖ Learns probabilistic model describing P(X, Y)
❖ Compute P(Y | X)
❖ Discriminative model
❖ Learns directly to predict y given x (often P(Y | X))

Model-Based Classification

Model-Based Classification
❖ Model-based approach
❖ Buildamodel(e.g.,Bayes’net) where both the label and features are random variables
❖ Instantiateanyobservedfeatures
❖ Queryforthedistributionofthe
label conditioned on the features
❖ Challenges
❖ WhatstructureshouldtheBNhave?
❖ Howshouldwelearnits parameters?

Naïve Bayes for Digits
❖ Naïve Bayes: Assume all features are independent effects of the label
❖ Simple digit recognition version:
❖ One feature (variable) Fij for each grid position
❖ Feature values are on / off, based on whether intensity
is more or less than 0.5 in underlying image
❖ Each input maps to a feature vector, e.g.
❖ Here: lots of features, each is binary valued
❖ Naïve Bayes model:
❖ What do we need to learn?

General Naïve Bayes
❖ A general Naive Bayes model: |Y|
|Y| x |F|n values
parameters
n x |F| x |Y| parameters
❖ We only have to specify how each feature depends on the class
❖ Total number of parameters is linear in n
❖ Model is very simplistic, but often works anyway

Inference for Naïve Bayes
❖ Goal: compute posterior distribution over label variable Y ❖ Step 1: get joint probability of label and evidence for each label
❖ Step 2: sum to get probability of evidence
❖ Step 3: normalize by dividing Step 1 by Step 2

General Naïve Bayes
❖ What do we need in order to use Naïve Bayes?
❖ Inference method (we just saw this part)
❖ Start with a bunch of probabilities: P(Y) and the P(Fi|Y) tables
❖ UsestandardinferencetocomputeP(Y|F1…Fn)
❖ Nothingnewhere
❖ Estimates of local (conditional) probability tables
❖ P(Y), the prior over labels
❖ P(Fi|Y)foreachfeature(evidencevariable)
❖ Theseprobabilitiesarecollectivelycalledtheparametersofthe model and denoted by q
❖ Up until now, we assumed these were given, but…
❖ …they typically come from training data counts: we’ll look at this soon

Example: Conditional Probabilities

Example: Spam Filter
❖ Naïve Bayes spam filter
❖ Collection of emails, labeled spam or ham
❖ Note: someone has to hand label all this data!
❖ Split into training, validation, test sets
❖ Classifiers
❖ Learn on the training set
❖ (Tune it on a validation set)
❖ Test it on new emails
First, I must solicit your confidence in this transaction, this is by virture of its nature as being utterly confidencial and top secret. …
TO BE REMOVED FROM FUTURE MAILINGS, SIMPLY REPLY TO THIS MESSAGE AND PUT “REMOVE” IN THE SUBJECT.
99 MILLION EMAIL ADDRESSES FOR ONLY $99
Ok, Iknow this is blatantly OT but I’m beginning to go insane. Had an old Dell Dimension XPS sitting in the corner and decided to put it to use, I know it was working pre being stuck in the corner, but when I plugged it in, hit the power nothing happened.

Naïve Bayes for Text
❖ Bag-of-words Naïve Bayes:
❖ Features: Wi is the word at position i
how many variables are there? how many values?
❖ As before: predict label conditioned on feature variables (spam vs. ham)
❖ As before: assume features are conditionally independent given label
❖ New: each Wi is identically distributed
❖ Generative model:
❖ “Tied” distributions and bag-of-words
Word at position i, not ith word in the dictionary!
❖ Usually, each variable gets its own conditional probability distribution P(F|Y)
❖ In a bag-of-words model
❖ Each position is identically distributed
❖ All positions share the same conditional probs P(W|Y)
❖ Why make this assumption?
❖ Called “bag-of-words” because model is insensitive to word order or reordering
i Wn h i s e n l e t c h t e u r l e e c l e t u c r t e u r i e s n o e v x e t r , o r v e e m r e p me r b s e o r n t o r e w m a e k m e b u e p r t r h o e o m persiottninsgittihnegtnhextthteotyootuo iunpthweaklecwtuhrenroyomu .

Example: Spam Filtering
❖ What are the parameters?
the : 0.0156
to : 0.0153
and : 0.0115
of : 0.0095
you : 0.0093
a : 0.0086
with: 0.0080
from: 0.0075
the : 0.0210
to : 0.0133
of : 0.0119
2002: 0.0110
with: 0.0108
from: 0.0107
and : 0.0105
a : 0.0100
ham : 0.66
spam: 0.33
❖ Where do these tables come from?

Spam Example
Word P(w|spam) P(w|ham) Tot Spam Tot Ham
(prior) 0.33333 0.66666 -1.1 -0.4
Gary 0.00002 0.00021 -11.8 -8.9
would 0.00069 0.00084 -19.1 -16.0
you 0.00881 0.00304 -23.8 like 0.00086 0.00083 -30.9 to 0.01517 0.01339 -35.1 lose 0.00008 0.00002 -44.5
-21.8 -28.9 -33.2 -44.0 -55.0 -63.2 -69.0
0.00016 0.00002 -53.3
0.00027 0.00027 -61.5
you 0.00881 0.00304 -66.2
sleep 0.00006 0.00001 -76.0 -80.5
P(spam | w) = 0.989

Training and Testing

Important Concepts
❖ Data: labeled instances, e.g., emails marked spam/ham
❖ Training set
❖ Validation set
❖ Test set
❖ Features: attribute-value pairs which characterize each x
❖ Experimentation cycle
❖ Learn parameters (e.g., model probabilities) on training set
❖ (Tune hyperparameters on validation set)
❖ Compute accuracy of test set
❖ Very important: never “peek” at the test set!
❖ Evaluation
❖ Accuracy: fraction of instances predicted correctly
❖ Overfitting and generalization
❖ Want a classifier which does well on test data
❖ Overfitting: fitting the training data very closely, but not generalizing well
❖ Underfitting: fits the training set poorly
Training Data
Validation Data

Parameter Estimation

Parameter Estimation
❖ Estimating the distribution of a random variable
❖ Elicitation: ask a human (why is this hard?)
❖ Empirically: use training data (learning!)
❖ E.g.: for each outcome x, look at the empirical rate of that
❖ This is the estimate that maximizes the likelihood of the data
brbb brrb brb b r b b

Maximum Likelihood Estimation
❖ Data: Observed set D of aH Head and aT Tail
❖ Hypothesis space: Binomial distributions Bin(q, aH+aT)
❖ Learning: finding q is an optimization problem
❖ What’s the objective function?
❖ MLE: Choose q to maximize probability of D

Maximum Likelihood Estimation
❖ Set derivative to zero, and solve!

Underfitting and
30 25 20 15 10
Degree 15 polynomial
0 2 4 6 8 10 12 14 16 18 20

Example: Overfitting

Example: Overfitting
❖ Posteriors determined by relative probabilities (odds ratios):
south-west : inf
seriously : inf
screens : inf
minute : inf
guaranteed : inf
$205.00 : inf
delivery : inf
signature : inf
What went wrong here?

Generalization and Overfitting
❖ Relative frequency parameters will overfit the training data!
❖ Just because we never saw a 3 with pixel (15,15) on during training doesn’t mean we
won’t see it at test time
❖ Unlikely that every occurrence of “minute” is 100% spam
❖ Unlikely that every occurrence of “seriously” is 100% ham
❖ What about all the words that don’t occur in the training set at all?
❖ In general, we can’t go around giving unseen events zero probability
❖ As an extreme case, imagine using the entire email as the only feature
❖ Would get the training data perfect (if deterministic labeling)
❖ Wouldn’t generalize at all
❖ Just making the bag-of-words assumption gives us some generalization, but isn’t enough
❖ To generalize better: we need to smooth or regularize the estimates

Maximum Likelihood?
❖ Relative frequencies are the maximum likelihood estimates
❖ Another option is to consider the most likely parameter value given the data

Laplace Smoothing
❖ Laplace’s estimate:
❖ Pretend you saw every outcome once
more than you actually did
❖ Can derive this estimate with Dirichlet Priors

Laplace Smoothing
❖ Laplace’s estimate (extended):
❖ Pretend you saw every outcome k extra times
❖ What’s Laplace with k = 0?
❖ k is the strength of the prior
❖ Laplace for conditionals:
❖ Smooth each condition independently:

Smoothing in Real Naïve Bayes
❖ For real classification problems, smoothing is critical
❖ New odds ratios:
helvetica : 11.4
seems group
: 10.8 : 10.2
: 8.4 : 8.3
verdana : 28.8
Credit : 28.4
ORDER : 27.2
: 26.9
money : 26.5
Do these make more sense?