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When Can Machine Learning Be Useful for Communication Systems? Osvaldo Simeone King’s College London Osvaldo Simeone ML for Comm 1 / 184

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Page 1: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When Can Machine Learning Be Useful forCommunication Systems?

Osvaldo Simeone

King’s College London

Osvaldo Simeone ML for Comm 1 / 184

Page 2: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Goals and Learning Outcomes

Goals:I Provide an introduction to main areas in machine learningI Offer pointers to specific applications for telecom

Learning outcomes:I Recognize scenarios in which machine learning can and cannot be usefulI Identify specific classes of machine learning methods that apply to a

given problem

Osvaldo Simeone ML for Comm 2 / 184

Page 3: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

Osvaldo Simeone ML for Comm 3 / 184

Page 4: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

Osvaldo Simeone ML for Comm 4 / 184

Page 5: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Traditional engineering (model-based) approach:

I Acquisition of domain knowledge...

Osvaldo Simeone ML for Comm 5 / 184

Page 6: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Traditional engineering (model-based) approach:

I ... mathematical (physics-based) modelling...

Osvaldo Simeone ML for Comm 6 / 184

Page 7: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Traditional engineering (model-based) approach:

I ... and optimized algorithm design with performance guarantees (underthe given model)

Osvaldo Simeone ML for Comm 7 / 184

Page 8: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?

Engineering design flow

acquisition of domain knowledge

algorithm development

physics-based mathematical model

algorithm with performance guarantees

acquisition of data

learning

training set

black-boxmachine

hypothesis class

(b)Osvaldo Simeone ML for Comm 8 / 184

Page 9: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Machine learning approach:

I Selection of a general-purpose model (hypothesis class)

Osvaldo Simeone ML for Comm 9 / 184

Page 10: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Machine learning approach:

I Selection of a general-purpose model (hypothesis class), objectivefunction, and a learning algorithm...

Osvaldo Simeone ML for Comm 10 / 184

Page 11: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Machine learning approach:

I ... learning based on data (examples)

Osvaldo Simeone ML for Comm 11 / 184

Page 12: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?Machine learning approach:

I ... and use of the trained (black-box) machine for inference

Osvaldo Simeone ML for Comm 12 / 184

Page 13: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?

Machine learning or data-driven approach

acquisition of domain knowledge

algorithm development

physics-based mathematical model

algorithm with performance guarantees

acquisition of data

learning

training set

black-boxmachine

hypothesis class

(a)

Osvaldo Simeone ML for Comm 13 / 184

Page 14: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

What is Machine Learning?

Integrating domain knowledge into a machine learning approachI Choose hypothesis class and learning algorithm based on knowledge of

the problem

acquisition of domain knowledge

acquisition of data

learning

training set

black-boxmachine

hypothesis class

Osvaldo Simeone ML for Comm 14 / 184

Page 15: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Taxonomy of Machine Learning Methods

Supervised learning

Unsupervised learning

Reinforcement learning

Osvaldo Simeone ML for Comm 15 / 184

Page 16: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Taxonomy of Machine Learning Methods

Supervised vs unsupervised learning

Osvaldo Simeone ML for Comm 16 / 184

Page 17: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Taxonomy of Machine Learning Methods

Reinforcement learning: feedback-based sequential decision making

[@ D. Silver]

st at

rt

Osvaldo Simeone ML for Comm 17 / 184

Page 18: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Potential advantages:I lower cost and faster development

F if collecting data is less expensive/ quicker than acquiring aphysics-based model or an optimal algorithm

I reduced implementation complexityF if hypothesis class contains low-complexity machines

Potential disadvantagesI suboptimal performance and limited performance guaranteesI limited interpretability

Osvaldo Simeone ML for Comm 18 / 184

Page 19: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Potential advantages:I lower cost and faster development

F if collecting data is less expensive/ quicker than acquiring aphysics-based model or an optimal algorithm

I reduced implementation complexityF if hypothesis class contains low-complexity machines

Potential disadvantagesI suboptimal performance and limited performance guaranteesI limited interpretability

Osvaldo Simeone ML for Comm 18 / 184

Page 20: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Potential advantages:I lower cost and faster development

F if collecting data is less expensive/ quicker than acquiring aphysics-based model or an optimal algorithm

I reduced implementation complexityF if hypothesis class contains low-complexity machines

Potential disadvantagesI suboptimal performance and limited performance guaranteesI limited interpretability

Osvaldo Simeone ML for Comm 18 / 184

Page 21: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate:

F model deficit: a physics-based model is not availableF algorithm deficit: a model is available, but optimal or near-optimal

algorithms are not known or too complex to implement

Osvaldo Simeone ML for Comm 19 / 184

Page 22: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit

I large data sets exist or can be created

I the task requires does not require detailed explanations for how thedecision was made

I the task does not have stringent optimality requirementsF Monte Carlo for algorithm deficit and generalization bounds for model

deficit

I the phenomenon or function being learned should not change rapidly

Osvaldo Simeone ML for Comm 20 / 184

Page 23: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit

I large data sets exist or can be created

I the task requires does not require detailed explanations for how thedecision was made

I the task does not have stringent optimality requirementsF Monte Carlo for algorithm deficit and generalization bounds for model

deficit

I the phenomenon or function being learned should not change rapidly

Osvaldo Simeone ML for Comm 20 / 184

Page 24: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit

I large data sets exist or can be created

I the task requires does not require detailed explanations for how thedecision was made

I the task does not have stringent optimality requirementsF Monte Carlo for algorithm deficit and generalization bounds for model

deficit

I the phenomenon or function being learned should not change rapidly

Osvaldo Simeone ML for Comm 20 / 184

Page 25: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit

I large data sets exist or can be created

I the task requires does not require detailed explanations for how thedecision was made

I the task does not have stringent optimality requirementsF Monte Carlo for algorithm deficit and generalization bounds for model

deficit

I the phenomenon or function being learned should not change rapidly

Osvaldo Simeone ML for Comm 20 / 184

Page 26: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When to Use Machine Learning?

Criteria inspired by [Brynjolfsson and Mitchell ’17]:I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit

I large data sets exist or can be created

I the task requires does not require detailed explanations for how thedecision was made

I the task does not have stringent optimality requirementsF Monte Carlo for algorithm deficit and generalization bounds for model

deficit

I the phenomenon or function being learned should not change rapidly

Osvaldo Simeone ML for Comm 20 / 184

Page 27: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

Osvaldo Simeone ML for Comm 21 / 184

Page 28: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Data in Communication Networks

Fog network architecture [5GPPP]

Osvaldo Simeone ML for Comm 22 / 184

Page 29: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Data in Communication Networks

Fog network architecture [5GPPP]

Data collection and processing can take place at the edge and/or atthe cloud.

Osvaldo Simeone ML for Comm 23 / 184

Page 30: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Data in Communication Networks

Data at the edge:I PHY: Baseband signals, (multi-RAT) channel qualityI MAC/ Link: Throughput, FER, random access load and latencyI Network: Location, traffic loads across services, users’ device types,

battery levelsI Application: Users’ preferences, content demands, computing loads,

QoS metrics

Osvaldo Simeone ML for Comm 24 / 184

Page 31: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Data in Communication Networks

Data at the cloud:I Network: Mobility patterns, network-wide traffic statistics, outage ratesI Application: User’s behavior patterns, subscription information, service

usage statistics, TCP/IP traffic statistics

Osvaldo Simeone ML for Comm 25 / 184

Page 32: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Machine Learning in Communication Networks

Which tasks?I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit (depends)I large data sets exist or can be created XI the task requires does not require detailed explanations for how the

decision was made XI the task does not have stringent optimality requirements (depends)I the phenomenon or function being learned should not change rapidly

(depends)

Osvaldo Simeone ML for Comm 26 / 184

Page 33: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Machine Learning in Communication Networks

Osvaldo Simeone ML for Comm 27 / 184

Page 34: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Machine Learning in Communication Networks3GPP has introduced Network Data Analytics to enable access todata from the network functions and services in the core networkETSI has proposed use cases for Experiential Network Intelligence(ENI) based on such data

[China Mobile] [ETSI]Osvaldo Simeone ML for Comm 28 / 184

Page 35: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Machine Learning for Communication vs Communicationfor Machine Learning

This presentation will discuss machine learning for communicationCommunication plays a key role in distributed learning systems,including edge and federated learning

[Park et al '19]

Osvaldo Simeone ML for Comm 29 / 184

Page 36: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

Osvaldo Simeone ML for Comm 30 / 184

Page 37: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning

Supervised learning:I regression: continuous labelsI classification: discrete labels

Osvaldo Simeone ML for Comm 31 / 184

Page 38: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning: Regression

0 0.2 0.4 0.6 0.8 1-1.5

-1

-0.5

0

0.5

1

1.5

?

Training set D: N training points (xn, tn), n = 1, ...,Nxn = covariates, domain points, or explanatory variablestn = dependent variables, labels, or responses (continuous)Goal: Predict the label t for a new, that is, as of yet unobserved,domain point x

Osvaldo Simeone ML for Comm 32 / 184

Page 39: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning: Classification

4 5 6 7 8 90.5

1

1.5

2

2.5

3

3.5

4

4.5

?

Training set D: N training points (xn, tn), n = 1, ...,Nxn = covariates, domain points, or explanatory variablestn = dependent variables, labels, or responses (discrete)Goal: Predict the label (class) t for a new, that is, as of yetunobserved, domain point x

Osvaldo Simeone ML for Comm 33 / 184

Page 40: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning

Impossible task without assuming a model (inductive bias) by the nofree lunch theorem

Memorizing vs. learning: Retrieval of a value tn corresponding to analready observed pair (xn, tn) ∈ D vs. predict the value t for anunseen x

Osvaldo Simeone ML for Comm 34 / 184

Page 41: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning

Impossible task without assuming a model (inductive bias) by the nofree lunch theorem

Memorizing vs. learning: Retrieval of a value tn corresponding to analready observed pair (xn, tn) ∈ D vs. predict the value t for anunseen x

Osvaldo Simeone ML for Comm 34 / 184

Page 42: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Defining Supervised Learning

Training set D:

(xn, tn) ∼i.i.d.

p(x , t), n = 1, ...,N

Based on the training set D, we derive a predictor t(x).

Test pair:(x, t) ∼

indep. of Dp(x , t)

Quality of the prediction t(x) for a pair (x , t)

`(t, t(x))

for some loss function `(t, t), e.g., `(t, t) = (t − t)2 (quadratic) or`(t, t) = 1(t 6= t) (probability of error)

Osvaldo Simeone ML for Comm 35 / 184

Page 43: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Defining Supervised Learning

Training set D:

(xn, tn) ∼i.i.d.

p(x , t), n = 1, ...,N

Based on the training set D, we derive a predictor t(x).

Test pair:(x, t) ∼

indep. of Dp(x , t)

Quality of the prediction t(x) for a pair (x , t)

`(t, t(x))

for some loss function `(t, t), e.g., `(t, t) = (t − t)2 (quadratic) or`(t, t) = 1(t 6= t) (probability of error)

Osvaldo Simeone ML for Comm 35 / 184

Page 44: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Defining Supervised Learning

Training set D:

(xn, tn) ∼i.i.d.

p(x , t), n = 1, ...,N

Based on the training set D, we derive a predictor t(x).

Test pair:(x, t) ∼

indep. of Dp(x , t)

Quality of the prediction t(x) for a pair (x , t)

`(t, t(x))

for some loss function `(t, t), e.g., `(t, t) = (t − t)2 (quadratic) or`(t, t) = 1(t 6= t) (probability of error)

Osvaldo Simeone ML for Comm 35 / 184

Page 45: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Defining Supervised Learning

Goal: minimize average loss on the test pair (generalization loss)

Lp(t) = E(x,t)∼pxt [`(t, t(x))]

Alternative viewpoints to frequentist framework: Bayesian andMinimum Description Length (MDL)

Osvaldo Simeone ML for Comm 36 / 184

Page 46: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Defining Supervised Learning

Goal: minimize average loss on the test pair (generalization loss)

Lp(t) = E(x,t)∼pxt [`(t, t(x))]

Alternative viewpoints to frequentist framework: Bayesian andMinimum Description Length (MDL)

Osvaldo Simeone ML for Comm 36 / 184

Page 47: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the True Distribution p(x , t) is Known...

... we don’t need data D

... and we have a standard inference problem, i.e., estimation(regression) or detection (classification).

The solution can be directly computed from the posterior orpredictive distribution

p(t|x) =p(x , t)

p(x)

as

t∗(x) = argmint

Et∼pt|x [`(t, t)|x ]

Osvaldo Simeone ML for Comm 37 / 184

Page 48: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the True Distribution p(x , t) is Known...

... we don’t need data D

... and we have a standard inference problem, i.e., estimation(regression) or detection (classification).

The solution can be directly computed from the posterior orpredictive distribution

p(t|x) =p(x , t)

p(x)

as

t∗(x) = argmint

Et∼pt|x [`(t, t)|x ]

Osvaldo Simeone ML for Comm 37 / 184

Page 49: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the Model p(x , t) is Known...

With quadratic loss, conditional mean: t∗(x) = Et∼pt|x [t|x ]

With probability of error, maximum a posteriori (MAP):t∗(x) = argmaxt p(t|x)

Example: with joint distribution

x\t 0 1

0 0.05 0.45

1 0.4 0.1

, we have

p(t = 1|x = 0) = 0.9

and

t∗(x = 0) = 0.9× 1 + 0.1× 0 = 0.9 for quadratic loss,

t∗(x = 0) = 1 for probability of error (MAP)

.

Osvaldo Simeone ML for Comm 38 / 184

Page 50: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the Model p(x , t) is Known...

With quadratic loss, conditional mean: t∗(x) = Et∼pt|x [t|x ]

With probability of error, maximum a posteriori (MAP):t∗(x) = argmaxt p(t|x)

Example: with joint distribution

x\t 0 1

0 0.05 0.45

1 0.4 0.1

, we have

p(t = 1|x = 0) = 0.9

and

t∗(x = 0) = 0.9× 1 + 0.1× 0 = 0.9 for quadratic loss,

t∗(x = 0) = 1 for probability of error (MAP)

.

Osvaldo Simeone ML for Comm 38 / 184

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When the True Distribution p(x , t) is Not Known...

... we need data D

... and we have a learning problem

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

Osvaldo Simeone ML for Comm 39 / 184

Page 52: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the True Distribution p(x , t) is Not Known...

... we need data D

... and we have a learning problem

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

Osvaldo Simeone ML for Comm 39 / 184

Page 53: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

When the True Distribution p(x , t) is Not Known...

... we need data D

... and we have a learning problem

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

Osvaldo Simeone ML for Comm 39 / 184

Page 54: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Logistic Regression

Example: Binary classification (t ∈ {0, 1})1. Model selection (inductive bias): logistic regression(discriminative model)

φ(x) = [φ1(x) · · ·φD′(x)]T is a vector of features (e.g., bag-of-wordsmodel for a text).

Osvaldo Simeone ML for Comm 40 / 184

Page 55: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Logistic Regression

Parametric probabilistic model:

p(t = 1|x ,w) = σ(wTφ(x))

where σ(a) = (1 + exp(−a))−1 is the sigmoid function.

Osvaldo Simeone ML for Comm 41 / 184

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Logistic Regression2. Learning: To be discussed3. Inference: With probability of error loss, MAP classification

wTφ(x)︸ ︷︷ ︸logit or LLR

t=1≷t=0

0

Osvaldo Simeone ML for Comm 42 / 184

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Multi-Layer Neural Networks

1. Model selection (inductive bias): multi-layer neural network(discriminative model)

Multiple layers of learnable weights enable feature learning.

Osvaldo Simeone ML for Comm 43 / 184

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Supervised Learning

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

Osvaldo Simeone ML for Comm 44 / 184

Page 59: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Supervised Learning

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

Osvaldo Simeone ML for Comm 45 / 184

Page 60: When Can Machine Learning Be Useful for Communication … · Goals and Learning Outcomes Goals: I Provide an introduction to main areas in machine learning I O er pointers to speci

Learning: Maximum Likelihood

ML selects a value of θ that is the most likely to have generated theobserved training set D:

maximize p(D|θ)

⇐⇒maximize ln p(D|θ) (log-likelihood, or LL)

⇐⇒minimize − ln p(D|θ) (negative log-likelihood, or NLL)

Also known as log-loss, or cross-entropy for discriminative models

Requires sum over training points, e.g., for discriminative models:

minimize − ln p(tD|xD, θ) = −N∑

n=1

ln p(tn|xn, θ)

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Learning: Maximum Likelihood

ML selects a value of θ that is the most likely to have generated theobserved training set D:

maximize p(D|θ)

⇐⇒maximize ln p(D|θ) (log-likelihood, or LL)

⇐⇒minimize − ln p(D|θ) (negative log-likelihood, or NLL)

Also known as log-loss, or cross-entropy for discriminative models

Requires sum over training points, e.g., for discriminative models:

minimize − ln p(tD|xD, θ) = −N∑

n=1

ln p(tn|xn, θ)

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Learning: Maximum LikelihoodThe problem rarely has analytical solutions and is typically addressedby Stochastic Gradient Descent (SGD).For discriminative models, we have

θnew ← θold + γ∇θ ln p(tn|xn, θ)|θ=θold

γ is the learning rate.With multi-layer neural networks, this approach yields thebackpropagation algorithm.

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Learning: Maximum Likelihood

Maximum likelihood is only concerned with the performance on thetraining set.

To improve generalization (performance outside the training set),regularization is typically used.

Regularization can be generally interpreted as imposing some priorknowledge on the model parameters θ.

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Supervised Learning

1. Model selection (inductive bias): Define a parametric model

p(x , t|θ)︸ ︷︷ ︸generative model

or p(t|x , θ)︸ ︷︷ ︸discriminative model

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Inference: Use model to obtain the predictor t(x) (to be testedon new data)

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Model Selection

How to select a model (inductive bias)?

Use domain knowledge if available, e.g., to select features

Focus here on model order selection, i.e., selection of the capacity ofthe model

Ex.: For logistic regression,I Model order M: Number of features

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Model Selection

How to select a model (inductive bias)?

Use domain knowledge if available, e.g., to select features

Focus here on model order selection, i.e., selection of the capacity ofthe model

Ex.: For logistic regression,I Model order M: Number of features

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Model Selection

Example: Regression using a discriminative model p(t|x ,w)

M∑m=0

wmxm

︸ ︷︷ ︸t(x): polynomial of order M

+N (0, 1)

0 0.2 0.4 0.6 0.8 1-1.5

-1

-0.5

0

0.5

1

1.5

?

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Model Selection

With M = 1, using ML learning of the coefficients –

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3

M= 1

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Model Selection: Underfitting...

With M = 1, the ML predictor t(x) underfits the data:I the model is not rich enough to capture the variations present in the

data;I large training loss

LD(θ) =1

N

N∑n=1

(tn − t(xn))2

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Model Selection

With M = 9, using ML learning of the coefficients –

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3

= 9M

M= 1

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Model Selection: ... vs Overfitting

With M = 9, the ML predictor overfits the data:I the model is too rich and, in order to account for the observations in

the training set, it appears to yield inaccurate predictions outside it;I presumably we have a large generalization loss

Lp(t) = E(x,t)∼pxt [(t− t(x))2]

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Model Selection

M = 3 seems to be a resonable choice...

... but how do we know given that we have no data outside of thetraining set?

0 0.2 0.4 0.6 0.8 1-3

-2

-1

0

1

2

3

= 9M

M= 1

M= 3

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Model Selection: ValidationKeep some data (validation set) to estimate the generalization errorfor different values of M(See cross-validation for a more efficient way to use the data)

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Model Selection: ValidationValidation allows model order selection.

1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

root

ave

rage

squ

ared

loss

training

generalization (via validation)

overfittingunderfitting

Validation can also be used more generally to select otherhyperparameters (e.g., learning rate).

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Model Selection: ValidationValidation allows model order selection.

1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

root

ave

rage

squ

ared

loss

training

generalization (via validation)

overfittingunderfitting

Validation can also be used more generally to select otherhyperparameters (e.g., learning rate).

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Model Selection: ValidationModel order selection should depend on the amount of data...It is a problem of bias (asymptotic error) versus generalization gap.

0 10 20 30 40 50 60 700

0.2

0.4

0.6

0.8

1ro

ot a

vera

ge q

uadr

atic

loss

M

M

= 1

= 7

generalization (via validation)

training

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Application to Communication Networks

Fog network architecture [5GPPP]

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At the Edge: PHYChannel detection and decoding – classification

[Cammerer et al '17]

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Machine Learning in Communication Networks

Which tasks?I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit (depends)I large data sets exist or can be created XI the task requires does not require detailed explanations for how the

decision was made XI the task does not have stringent optimality requirements (depends)I the phenomenon or function being learned should not change rapidly

(depends)

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At the Edge: PHYChannel detection and decoding – classificationModel deficit

[Farsad and Goldsmith '18]

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At the Edge: PHYChannel equalization in the presence of non-linearities, e.g., foroptical links – regressionAlgorithm deficit

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At the Edge: PHY

Channel equalization in the presence of non-linearities, e.g., forsatellite links with non-linear ampliers – regression

Algorithm deficit

[Bouchired HW�DO�¶��@

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At the Edge: PHY

Channel decoding for modulation schemes with complex optimaldecoders, e.g., continuous phase modulation – classification

Algorithm deficit

[De Veciana and Zakhor '92]

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Machine Learning in Communication Networks

Which tasks?I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit (depends)I large data sets exist or can be created XI the task requires does not require detailed explanations for how the

decision was made XI the task does not have stringent optimality requirements (depends)I the phenomenon or function being learned should not change rapidly

(depends)

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At the Edge: PHY

Channel decoding – classification

Leverage domain knowledge to choose the hypothesis class

[1DFKPDQL�HW�DO�µ��@

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At the Edge: PHYChannel equalization to compensate for hardware impairments –regressionLeverage domain knowledge to select blocks to be designed using amodel-based or a data-based approach

[Schibisch HW�DO�µ��@

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At the Edge: PHYModulation recognition – classificationAlgorithm deficit

[Agirman-Tosun et al '11]

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At the Edge: PHYLocalization – regressionModel deficit

(coordinates)

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At the Edge: PHYPrecoding and power allocation: Use known optimization algorithmto generate data set – regressionAlgorithm deficit

>6XQ�HW�DO�¶��@

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At the Edge: PHY

Approximate model and known optimization algorithm can be alsoused to generate data set for an initial training phase

Algorithm deficit

[Zappone al µ��@

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At the Edge: PHYInterference cancellation – regressionModel deficit

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At the Edge: PHYFDD massive MIMO via channel prediction from uplink training (seealso [Huang et al ’19])Model deficit

[Arnold et al ’19]

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At the Edge: MAC/ LinkSpectrum sensing – classificationModel deficit

[Tumuluru et al '10]

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At the Edge: Network and ApplicationContent prediction for proactive caching – classificationModel deficit

[Chen et al '17]

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At the Cloud: Network

Link prediction for wireless routing – classification/ regression

Model deficit

[Wang et al 06]

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At the Cloud: NetworkLink prediction for optical routing – classification/ regressionModel deficit

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At the Cloud: Network

Congestion prediction for smart routing – classification

Model deficit

[Tang et al µ17]

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At the Cloud: Network and ApplicationTraffic classification – classificationModel deficit

[Nguyen et al '08]

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Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

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Unsupervised Learning

Unsupervised learning tasks operate over unlabelled data sets.

General goal: discover properties of the data, e.g., for compressedrepresentation

“Some of us see unsupervised learning as the key towards machineswith common sense.” (Y. LeCun)

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Unsupervised Learning

Unsupervised learning tasks operate over unlabelled data sets.

General goal: discover properties of the data, e.g., for compressedrepresentation

“Some of us see unsupervised learning as the key towards machineswith common sense.” (Y. LeCun)

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“Defining” Unsupervised Learning

Training set D:xn ∼

i.i.d.p(x), n = 1, ...,N

Goal: Learn some useful properties of the distribution p(x)

Alternative viewpoints to frequentist framework: Bayesian and MDL

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“Defining” Unsupervised Learning

Training set D:xn ∼

i.i.d.p(x), n = 1, ...,N

Goal: Learn some useful properties of the distribution p(x)

Alternative viewpoints to frequentist framework: Bayesian and MDL

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Unsupervised Learning Tasks

Density estimation: estimate p(x), e.g., for use in plug-in estimators,compression algorithms, to detect outliers

Clustering: partition all points in D in groups of similar objects (e.g.,document clustering)

Dimensionality reduction, representation and feature extraction:represent each data points xn in a space of lower dimensionality, e.g.,to highlight independent explanatory factors, and/or to easevisualization, interpretation, or successive tasks

Generation of new samples: learn a machine that produces samplesapproximately distributed according to p(x), e.g., to produce artificialscenes based for games or films

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Unsupervised Learning Tasks

Density estimation: estimate p(x), e.g., for use in plug-in estimators,compression algorithms, to detect outliers

Clustering: partition all points in D in groups of similar objects (e.g.,document clustering)

Dimensionality reduction, representation and feature extraction:represent each data points xn in a space of lower dimensionality, e.g.,to highlight independent explanatory factors, and/or to easevisualization, interpretation, or successive tasks

Generation of new samples: learn a machine that produces samplesapproximately distributed according to p(x), e.g., to produce artificialscenes based for games or films

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Unsupervised Learning Tasks

Density estimation: estimate p(x), e.g., for use in plug-in estimators,compression algorithms, to detect outliers

Clustering: partition all points in D in groups of similar objects (e.g.,document clustering)

Dimensionality reduction, representation and feature extraction:represent each data points xn in a space of lower dimensionality, e.g.,to highlight independent explanatory factors, and/or to easevisualization, interpretation, or successive tasks

Generation of new samples: learn a machine that produces samplesapproximately distributed according to p(x), e.g., to produce artificialscenes based for games or films

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Unsupervised Learning Tasks

Density estimation: estimate p(x), e.g., for use in plug-in estimators,compression algorithms, to detect outliers

Clustering: partition all points in D in groups of similar objects (e.g.,document clustering)

Dimensionality reduction, representation and feature extraction:represent each data points xn in a space of lower dimensionality, e.g.,to highlight independent explanatory factors, and/or to easevisualization, interpretation, or successive tasks

Generation of new samples: learn a machine that produces samplesapproximately distributed according to p(x), e.g., to produce artificialscenes based for games or films

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Unsupervised Learning

1. Model selection (inductive bias): Define a parametric modelp(x |θ)

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Clustering, feature extraction, sample generation...

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Unsupervised Learning

1. Model selection (inductive bias): Define a parametric modelp(x |θ)

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Clustering, feature extraction, sample generation...

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Models

Unsupervised learning models typically involve hidden or latentvariables.

zn = hidden, or latent, variables for each data point xn

Ex.: zn = cluster index of xn

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Models

Unsupervised learning models typically involve hidden or latentvariables.

zn = hidden, or latent, variables for each data point xn

Ex.: zn = cluster index of xn

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(a) Directed Generative Models

Model data x as being caused by z :

p(x |θ) =∑z

p(z |θ)p(x |z , θ)

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(a) Directed Generative Models

Ex.: Document clusteringI x is a document, and z is (interpreted as) topicI p(z |θ) = distribution of topicsI p(x |z , θ) = distribution of words in document given topic

Basic representatives:I Mixture of GaussiansI Likelihood-free models

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(a) Directed Generative Models

Ex.: Document clusteringI x is a document, and z is (interpreted as) topicI p(z |θ) = distribution of topicsI p(x |z , θ) = distribution of words in document given topic

Basic representatives:I Mixture of GaussiansI Likelihood-free models

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(d) Autoencoders

Model encoding from data to hidden variables, as well as decodingfrom hidden variables back to data:

p(z |x , θ) and p(x |z , θ)

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(d) Autoencoders

Ex.: CompressionI x is an image and z is (interpreted as) a compressed (e.g., sparse)

representationI p(z |x , θ) = compression of image to representationI p(x |z , θ) = decompression of representation into an image

Basic representative: Principal Component Analysis (PCA), dictionarylearning, neural network-based autoencoders

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(d) Autoencoders

Ex.: CompressionI x is an image and z is (interpreted as) a compressed (e.g., sparse)

representationI p(z |x , θ) = compression of image to representationI p(x |z , θ) = decompression of representation into an image

Basic representative: Principal Component Analysis (PCA), dictionarylearning, neural network-based autoencoders

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Unsupervised Learning

1. Model selection (inductive bias): Define a parametric modelp(x |θ)

2. Learning: Given data D, optimize a learning criterion to obtainthe parameter vector θ

3. Clustering, feature extraction, sample generation...

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Learning: Maximum Likelihood

Focus on directed generative models (a)

To simplify the notation, consider a single data point x (sum overdata set D to generalize).

ML problem:

maxθ

ln p(x |θ) = ln

(∑z

p(x , z |θ)

)= ln

(Ez∼p(z|θ)[p(z|x , θ)]

)Key issue: Need to marginalize over latent variables, whosedistribution is to be learned, in order to evaluate LL.

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Learning: Maximum Likelihood

Focus on directed generative models (a)

To simplify the notation, consider a single data point x (sum overdata set D to generalize).

ML problem:

maxθ

ln p(x |θ) = ln

(∑z

p(x , z |θ)

)= ln

(Ez∼p(z|θ)[p(z|x , θ)]

)Key issue: Need to marginalize over latent variables, whosedistribution is to be learned, in order to evaluate LL.

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ELBO

To tackle this issue, a standard approach is the introduction of avariational distribution (or encoder) q(z |x) that provides aprobabilistic estimate of z given x.

For any distribution q(z |x), the Evidence Lower BOund (ELBO) or(negative) free energy L(q, θ) is defined as

L(q, θ) =Ez∼q(z|x)[ln p(x , z|θ)− ln q(z|x)︸ ︷︷ ︸learning signal

]

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ELBO

To tackle this issue, a standard approach is the introduction of avariational distribution (or encoder) q(z |x) that provides aprobabilistic estimate of z given x.

For any distribution q(z |x), the Evidence Lower BOund (ELBO) or(negative) free energy L(q, θ) is defined as

L(q, θ) =Ez∼q(z|x)[ln p(x , z|θ)− ln q(z|x)︸ ︷︷ ︸learning signal

]

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ELBO

The ELBO is a global lower bound on the LL function

ln p(x |θ) ≥ L(q, θ),

Equality holds at a value θ0 if and only if the distribution q(z |x) isthe posterior of z given x (i.e., optimal Bayesian estimate)

q(z |x) = p(z |x , θ0).

LL

0

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Expectation-Maximization (EM) Algorithm

...

LL

newold

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Expectation-Maximization (EM) Algorithm

Initialize parameter vector θold.

For each iterationI E step: For fixed parameter vector θold,

maxqL(q, θold)→ qnew(z |x) = p(z |x , θold).

Estimate of the latent variables

I M step: For fixed variational distribution qnew(z |x),

maxθL(qnew, θ)→ max

θEz∼qnew(z|x) [ln p(x , z|θ)]

Solve a supervised learning problem

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Expectation-Maximization (EM) Algorithm

EM guarantees decreasing objective values, which ensuresconvergence to a local optimum of the original problem.

...

LL

newold

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Expectation-Maximization (EM) Algorithm

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Example: Mixture of Gaussians

Directed generative model:

z ∼ Bern(π)

x|z =k ∼ N(µk ,Σk)

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Example: Mixture of Gaussians

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Example: Mixture of Gaussians

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Example: Mixture of Gaussians

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Example: Mixture of Gaussians

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Example: Mixture of Gaussians

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Example: Mixture of Gaussians

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Scaling EM

EM algorithm may be impractical for large scale problems: need tocompute posterior in E step and to average over z in the M step.

Solutions:I E step: Parametrize the variational distribution q(z |x , ϕ) and maximize

ELBO over ϕ (variational autoencoder)I M step: Approximate Ez∼qnew(z|x) [ln p(x , z|θ)] via Monte CarloI Use gradient descent for E and/or M steps

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Scaling EM

EM algorithm may be impractical for large scale problems: need tocompute posterior in E step and to average over z in the M step.

Solutions:I E step: Parametrize the variational distribution q(z |x , ϕ) and maximize

ELBO over ϕ (variational autoencoder)I M step: Approximate Ez∼qnew(z|x) [ln p(x , z|θ)] via Monte CarloI Use gradient descent for E and/or M steps

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Learning: Beyond Maximum Likelihood

ML tends to provide inclusive and “blurry” estimates of thedistribution of the data distribution.

-5 0 50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

This can be a problem for tasks such as data generation.

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Learning: Beyond Maximum Likelihood

ML can be proven to minimize the KL divergence

KL(pD(x)||p(x |θ)) = Ez∼pD(x)

[ln

pD(x)

p(x |θ)

]betwen the empirical distribution

pD(x) =N[x ]

N(with counts N[x ] = |{n : xn = x}|)

and the model.

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Learning: Beyond Maximum LikelihoodThe KL divergence is part of the larger class of f -divergences betweentwo distributions p(x) and q(x):

Df (p||q) = maxT (x)

Ex∼p[T (x)]− Ex∼q[g(T (x))],

for some concave increasing function g(·).

6:T;

T1L:T;

T1M:T;

L T �� 6 T �����

discriminator

M T �� 6 T �����

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Learning: Generative Adversarial Networks (GANs)

Generalizing the ML problem, GANs attempt to solve the problem

minθ

maxϕ

Ex∼pD [Tϕ(x)]− Ex∼p(x |θ)[g(Tϕ(x))]

for some differentiable function Tϕ(x) of the parameter vector ϕ.

Choice of the divergence (via the discriminator) is tailored to data.

Can be applied to likelihood-free models.

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Learning: Generative Adversarial Networks (GANs)

84 [NVIDIA]

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Applications to Communication Networks

Fog network architecture [5GPPP]

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At the Edge: PHYEnd-to-end encoding/decoding for wireless channels – autoencoders

[2¶6KHD�DQG�Hoydis ¶��@

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Machine Learning in Communication Networks

Which tasks?I traditional engineering flow not applicable or inadequate: model deficit

or algorithm deficit (depends)I large data sets exist or can be created XI the task requires does not require detailed explanations for how the

decision was made XI the task does not have stringent optimality requirements (depends)I the phenomenon or function being learned should not change rapidly

(depends)

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At the Edge: PHYEnd-to-end encoding/decoding for optical channels – autoencodersAlgorithm deficit

[Karanov HW�DO�o18]

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At the Edge: PHYEnd-to-end encoding/decoding for Gaussian channels with feedback –autoencoders based on Recurrent Neural Network (RNN)Algorithm deficit

>.LP�HW�DO�µ��@

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At the Edge: PHYJoint source-channel coding for image transmissionAlgorithm deficit

[Bourtsoulatze et al ’18]

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At the Edge: PHYChannel State Information (CSI) compression and feedback –autoencodersModel deficitRelated work: quantization of log-likelihoods [Arvinte et al ’19]

>:HQ�HW�DO�µ��@

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At the Edge: PHYFingerprinting for localization – autoencodersModel deficit

[Xiao et al '17]Osvaldo Simeone ML for Comm 122 / 184

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At the Edge: PHYMimicking a propagation channel - GAN (see also [Ye et al ’18])Model deficit

[2¶6KHD�HW�DO�µ18]

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At the Edge: PHY

Mimicking and identifying a propagation channel (e.g., satellite) -generative models

Leveraging domain knowledge improves the learned model.

104 [Ibnkahla µ��@

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At the Edge: MAC/ LinkResource allocation – clusteringAlgorithm deficit

[Abdelnasser et al '14]

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At the Cloud: NetworkSelf-organizing multi-hop networks – clusteringAlgorithm deficit

[Abbassi and Younis '07]

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At the Cloud: NetworkAnomaly detection – density estimationModel deficit

[Musumeci HW�DO�¶��@

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Overview

What is Machine Learning and When to Use It

Data and Machine Learning in Communication Systems

Supervised Learning and Applications

Unsupervised Learning and Applications

Reinforcement Learning and Applications

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Reinforcement Learning

Feedback-based sequential decision making

[@ D. Silver]

st at

rt

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Reinforcement Learning

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Reinforcement Learning

Data collected while acting

Given an observation of the world (input) st at time t, the agenttakes an action (output) at ...

Ex.: st=current image; at ∈ {up,down,stay}

[Karpathy µ��@

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Reinforcement Learning

... and receives a reward signal (feedback) rt

Ex.: rt = 1 if ball goes past opponent; rt = −1 if misses ball; rt = 0otherwise

Current actions generally affect future states and rewards

[Karpathy µ��@

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Reinforcement Learning

... and receives a reward signal (feedback) rt

Ex.: rt = 1 if ball goes past opponent; rt = −1 if misses ball; rt = 0otherwise

Current actions generally affect future states and rewards

[Karpathy µ��@

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Defining Reinforcement Learning

Nç1 L:N�Oá=;

Oç>51 L Oñ Oá =

Oç>5

=ç1è: �Oç;

Oç>6

=ç>5 «

«

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Defining Reinforcement Learning

Goal: optimize policy π(a|s) = Pr[a = a|s = s] by maximizing theexpected return Eπ [Gt |st = s] with

Gt =∞∑τ=0

γτ rt+τ = rt + γrt+1 + γ2rt+2 + ...

Discount factor 0 < γ ≤ 1: preference for immediate reward if γ < 1

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Defining Reinforcement Learning

Problem defined by two “true” distributions:I Reward distribution given state and action: p(r |s, a)I State transition probability: p(s ′|s, a)

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Defining Reinforcement Learning

Nç1 L:N�Oá=;

Oç>51 L Oñ Oá =

Oç>5

=ç1è: �Oç;

Oç>6

=ç>5 «

«

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Defining Reinforcement Learning

When the true distributions are known, we have a Markov DecisionProcess (MDP)

When it is not, we have a reinforcement learning problem

Reinforcement learning:I Model-based: Learn a model (p(r |s, a, θ), p(s ′|s, a, θ)) and then solve

as MDPI Model-free: Learn directly the policy, i.e., how to act

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Defining Reinforcement Learning

When the true distributions are known, we have a Markov DecisionProcess (MDP)

When it is not, we have a reinforcement learning problem

Reinforcement learning:I Model-based: Learn a model (p(r |s, a, θ), p(s ′|s, a, θ)) and then solve

as MDPI Model-free: Learn directly the policy, i.e., how to act

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Methodology: Generalized Policy Iteration

Solution methods for both MDP and model-free reinforcementlearning generally alternate between two steps:

I Policy evaluation: Estimate the performance of the either the currentpolicy (on-policy learning) or of the current optimal policy (off-policylearning)

I Control: Act and update the policy to increase the expected return

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Methodology: Generalized Policy Iteration

Solution methods for both MDP and model-free reinforcementlearning generally alternate between two steps:

I Policy evaluation: Estimate the performance of the either the currentpolicy (on-policy learning) or of the current optimal policy (off-policylearning)

I Control: Act and update the policy to increase the expected return

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Methodology: Policy Evaluation

Policy evaluation: Action-value functionQπ(s, a) = Eπ [Gt |st = s, at = a]...

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Methodology: Policy EvaluationPolicy evaluation: Action-value functionQπ(s, a) = Eπ [Gt |st = s, at = a]...

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Methodology: Policy EvaluationPolicy evaluation: ... and/or value functionVπ(s) = Eπ [Gt |st = s] = Eπ [Q(s, a)|st = s]...

Va

lue

(V

)

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Methodology: Policy EvaluationSpectrum of solutions for policy evaluation:

I breadth and depth of the exploration of the state-action tree

TD(�)Osvaldo Simeone ML for Comm 143 / 184

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Methodology: Policy EvaluationExploration in breadth generally requires the availability of a modelModel-free methods are based on Temporal-Difference (TD) and/orMonte Carlo

TD(λ)

model-based

model-free

(sample-based)

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Methodology: Policy Evaluation

Monte Carlo (offline): Q(st , at) ≈ rt + γrt+1 + γ2rt+2 + ...

TD (online): Q(st , at) ≈ rt + γQ(st+1, at+1)

These techniques are on-policy and there are off-policy variants

TD(�)

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Methodology: Policy Evaluation

Monte Carlo (offline): Q(st , at) ≈ rt + γrt+1 + γ2rt+2 + ...

TD (online): Q(st , at) ≈ rt + γQ(st+1, at+1)

These techniques are on-policy and there are off-policy variants

TD(�)

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Methodology: Policy Evaluation

Monte Carlo (offline): Q(st , at) ≈ rt + γrt+1 + γ2rt+2 + ...

TD (online): Q(st , at) ≈ rt + γQ(st+1, at+1)

These techniques are on-policy and there are off-policy variants

TD(�)

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Methodology: Generalized Policy Iteration

Solution methods for both MDP and model-free reinforcementlearning generally alternate between two steps:

I Policy evaluation: Estimate the performance of the either the currentpolicy (on-policy learning) or of the current optimal policy (off-policylearning)

I Control: Act and update the policy to increase the expected return

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Methodology: ControlHow to choose actions? Exploration vs exploitation

I Ex: Multi-armed banditI Exploration: choose a random action with probability ε; Gibbs random

policies

N51L:N�= L s; N61L:N�= L t; N71L:N�= L u;

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Methodology: ControlHow to choose actions? Exploration vs exploitation

I Ex: Multi-armed banditI Exploration: choose a random action with probability ε; Gibbs random

policies

N51L:N�= L s; N61L:N�= L t; N71L:N�= L u;

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Methodology: Control

How to improve a policy?I greedy: maxaQπ(s, a)I gradient-based: policy gradient

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Methodology

Value vs policy-based methods:I value-based: policy evaluation and control via action-value function

Q(s, a)I policy-based: update an explicit policy π(a|s)I actor-critic: policy evaluation via action-value function Q(s, a) and

control via policy π(a|s)

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Example: Deep Q LearningValue-based – action-value function Q(s, a) parameterized via aneural networkPolicy evaluation: Off-policy TDControl: ε−greedy

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Example: Advantage Actor CriticActor-critic – action-value function Q(s, a) and policy π(a|s)parameterized via neural networksPolicy evaluation: On/Off-policy TDControl: policy gradient

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Applications to Communication Networks

Fog network architecture [5GPPP]

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At the Edge: PHYEnd-to-end encoding/decoding training in the absence of a channelmodelModel deficit

[Aoudia and Hoydis µ��@

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At the Edge: PHYIteratively trains decoder using supervised learning and encoder usingreinforcement learning (policy gradient)Requires receiver-to-transmitter feedback – impact of noise [Goutayet al ’18]

[Aoudia and Hoydis µ��@

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At the Edge: PHYLearning to act and to communicate (binary signals on binarysymmetric channels) to carry out collaborative tasksAlgorithm deficitLearned communication carries out compression and unequal errorprotection

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At the Edge: MAC/LinkBeamforming-user assignment in mmWave communicationsModel deficitRequires feedback

[Klautau HW�DO�¶��@Osvaldo Simeone ML for Comm 156 / 184

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At the Edge: MAC/LinkAnti-jamming channel and base station selectionModel deficitRequires feedbackSimilar applications in cognitive radio networks [Li et al ’17]

>+DQ�HW�DO�¶��@

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At the Edge: MAC/LinkLearning how to allocate random access opportunitiesModel and algorithm deficit

[Jiang et al '18]

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At the Edge: MAC/LinkLearning to act and to schedule to carry out collaborative tasksAlgorithm deficit

[Kim et al '19]

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At the Edge: Network

Handover and base station selection for access

Model deficit

[Hasan et al ‘13]

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At the Edge: Network

On-off scheduling of base stations

Model deficit

[Xu et al '17]

on/off state

& users’ demands

tx, circuitry and

transition power

on/off scheduling

& beamforming

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At the Edge: Application

Caching on wireless devices based on channel conditions and contentlifetime

Model deficit

[Somuyiwa et al '18]

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At the Cloud: NetworkPacket routing in a dynamically changing networkModel deficit

[Boyan and Littman '94]

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Concluding Remarks

Machine learning tools can leverage the availability of data andcomputing resources in modern communication systems.

Supervised, unsupervised and reinforcement learning paradigms lendthemselves to different key communication (sub)tasks.

Not a universal solution – case by case analysis of advantages anddisadvantages.

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Concluding Remarks

Engineering the integration of traditional model-based techniques anddata-driven machine learning methods

>5HLFK�µ��@

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Concluding Remarks

Additional topics, e.g., adversarial (white-box) attacks

[Sadeghi and Larsson ’19]

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Concluding Remarks

Additional topics, e.g., meta-learning (learning the inductive bias fromother tasks)

[Park et al’19]

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Concluding Remarks

Additional topics, e.g., neuromorphic computing [Jang et al ’19]

[Rajendran '18]

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Concluding Remarks

How to integrate machine learning analytics and control with protocolstack?

[China Mobile]

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For More...

O. Simeone, “A Brief Introduction to Machine Learning forEngineers,” Foundations and Trends in Signal Processing, 2018.

O. Simeone, “A Very Brief Introduction to Machine Learning withApplications to Communication Systems,” IEEE Transactions onCognitive Communications and Networking, 2019.

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Acknowledgements

This work has received funding from the European Research Council(ERC) under the European Union’s Horizon 2020 research and innovation

programme (grant agreement No. 725731).

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