Privacy by Design in the machine learning pipeline
+
Workshop, University of Venice
+
+
+
+
+Zak Varty
+
+
+
+
+
2024-11-01
+
+
+
Hello! Who am I?
+
+
+
+
Statistician by training, got to where I am through medical, environmental and industrial applications.
+
Teaching Fellow at Imperial College London
+
+
Data Science, Data Ethics
+
+
Privacy, fairness and explainability in ML.
+
+
Capable enthusiast, realist / pessimist
+
+
+
Really it all comes down to doing good statistics well.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Why do we care about privacy?
+
+
+
Protecting Sensitive Data: ML models often train on personal or confidential data (health records, financial info), and safeguarding this data is essential to prevent misuse or unauthorized access.
+
Compliance with Regulations: Laws like GDPR require organisations to protect user privacy, impacting how data is collected, stored, and used in ML.
+
Preventing Data Leakage Models can unintentionally expose sensitive information from their training data, risking user privacy if someone exploits the model’s outputs.
+
Building Trust: Privacy-conscious ML practices foster trust among users, making them more willing to share data and participate in systems that use ML.
+
Avoiding Discrimination: Privacy techniques can reduce bias and discrimination risks, ensuring the ML model treats users fairly without targeting sensitive attributes.
+
+
+
+
+
“If you have nothing to hide, you have nothing to fear”
+
+
+
+
+
+
“The benefits outweight the costs”
+
+
+
+
Machine Learning Pipeline
+
+
+
+
Machine Learning Pipeline Life Cycle
+
+
+
Reality is much messier. See Gelman and Loken (2013) for a discussion of the implications.
+
+
+
+
+
This workshop
+
+
+
+
+
Work through the ML life cycle
+
How could and have things gone wrong
+
+
+
+
+
+
What tools do we have?
+
What are their limitations?
+
+
+
+
+
+
Interactive bits, every now and then
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
1. Data Collection
+
+
+
+
Collecting Appropriate Data - GDPR
+
+
+
+
Collect only necessary data, purpose clear at time of collection
+
Data subject has right to
+
+
access
+
rectify
+
erase
+
object
+
+
Consequences both financial and reputational
+
+
+
+
+
+
+
+
+
Collecting Data - Hard-to-Reach Groups
+
Standard ML assumes that data are cheap and easy to collect.
+
Assumption that data are cheap and easy to collect. Out of the box model fitting assumes we are working with big, representative and independent samples.
+
+
+
Applications of ML to social science to study hard-to-reach populations: persecuted groups, stigmatised behaviours.
+
Standard study designs and analysis techniques will fail.
+
+
+
+
+
Snowball Sampling - Hidden Network
+
+
+
+
Snowball Sampling - Initial Recruitment
+
+
+
+
Snowball Sampling - Referral Round 1
+
+
+
+
Snowball Sampling - Referral Round 2
+
+
+
+
Snowball Sampling - Referral Round 3
+
+
+
+
Snowball Sampling
+
+
+
By using subject-driven sampling design, we can better explore the hard to reach target population while preserving the privacy of data subjects who do not want to be included in the study.
+
+
+
Bonus: Also allows us to study community (network) structure if we are interested in that.
+
+
+
+
+
Drawbacks:
+
+
“isolated” nodes,
+
partitioned graphs,
+
adapting model fitting to non-uniform sampling.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Collecting Data - Asking Difficult Questions
+
Even if data subjects are easy to access and sample from, they may not wish to answer honestly.
+
Can you give me some examples?
+
+
+
+
cheated on an exam?
+
cheated on a romantic / sexual partner?
+
experienced suicidal ideation?
+
killed another person?
+
+
+
+
+
Dishonest answers will bias any subsequent analysis, leading us to underestimate the prevalence of an “undesirable outcome”.
+
+
+
(Interesting intersection with survey design and psychology. The order and way that you ask questions can influence responses but we will focus on a single question here.)
Our estimator worked “best” for central values of \(\theta\), unlikely for stigmatised events.
+
Add random element to survey to provide plausible deniability.
+
+
Flip a fair coin. If heads, switch your answer.
+
+
MoM estimation: Equate probabilities and proportions.
+
+
+
+
Estimation from Randomised Response Data
+
+
+
Consider using a weighted coin, probability \(p\) of telling truth. Derive an expression for the probability of answering “Yes”.
+
+
\[\begin{align*}
+\Pr(\text{Yes}) &= \theta p + (1 - \theta)(1 - p) \\
+& \approx \frac{\#\{yes\}}{\#\{subjects\}} \\
+&= \bar y
+\end{align*}\]
+
+
+
Rearrange this expression to get a formula for \(\hat \theta\).
+
+
+
\[\hat \theta = \frac{\bar y - 1 + p}{2p -1}.\]
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Randomised Response Activities
+
\[ \hat \theta = \frac{\bar y - 1 + p}{2p -1}.\]
+
+
Direct response is a special case of randomised response. How can we use that to check our working?
+
+
+
+
If our previous survey results came from this randomised response survey design with \(p = 0.25\), what is your best guess of the proportion of people who have been unfaithful?
+
+
+
+
+
Are you more or less confident in this estimate than previously, when we had the same data but from a direct response design?
+
+
+
+
+
What does your confidence depend on? And which of those factors do you have knowledge of / control over?
+
+
+
+
+
When would this estimation procedure break and why? How could we fix that?
+
+
+
+
+
Randomised Response - Privacy Schematic
+
+
+
+
Randomised Response
+
+
Approach to privacy for single, binary response.
+
Issues with applying to multiple questions, e.g. surveys with follow on questions.
+
Extensions to categorical and continuous responses and predictors
+
General principle of adding noise
+
+
Need to make observations indistinguishable
+
Need to preserve important aspects of “signal”
+
+
+
+
+
Data Collection Summary
+
+
Collect what you need and use that information only for its intended purpose.
+
Targeting hard-to-reach populations can be challenging but possible by combining survey design and specific learning approaches. Keeps statisticians in a job!
+
Asking difficult questions can lead to biased responses. Plausible deniability through randomised response designs can help.
+
+
+
+
+
2. Data Storage
+
+
+
+
Encryption
+
Once we have gone to the effort of collecting data we don’t want to just leave it lying around for anyone to access.
+
+
+
\[ \text{Plain text} \overset{f}{\rightarrow} \text{Cipher Text}\] \[ \text{Cipher text} \overset{f^{-1}}{\rightarrow} \text{Plain Text}\] \[ f(\text{data}, \text{key})\] Many encryption schemes depending on the data to be encrypted and how the key is to be distributed.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Caesar Cipher
+
+
+
Write your own short message and pass it to a friend to decode.
+
+
+
What are some benefits and drawbacks of this encryption scheme?
+
+
+
+
K-anonymity
+
What happens if someone gets access to the data?
+
+
+
\(k\)-anonymity is a measure of privacy within a dataset.
+
Given a set of predictor-outcome responses, each unique combination forms an equivalence class.
+
The smallest equivalence class of a \(k\)-anonymous dataset is of size \(k\).
+
Equivalently, each individual is indistinguishable from at least \(k-1\) others.
+
+
+
+
K-anonymity Example
+
+
+
+
K-anonymity Worked Example
+
+
+
+
K-anonymity Your Turn
+
I asked ChatGPT to generate 4-anonymous datasets but it hasn’t done a good job.
+
+
Establish the true value of k for your dataset.
+
Use pseudonymisation, aggregation, redaction and partial-redaction to make your dataset 4-anonymous.
+
+
+
+
K-anonymity Feedback
+
+
How did ChatGPT do?
+
How did you alter the anonymity level of your dataset?
+
What did you have to consider as you were doing this?
+
+
+
+
K-anonymity Drawbacks
+
What do you think some of the limitations of \(k\)-anonymity might be?
+
+
+
Knowing what is important before analysis.
+
Publishing multiple versions of the dataset.
+
Can be checked easily but not implemented algorithmically.
+
External data attacks; Jane Doe, Latanya Sweeney
+
+
+
+
+
Data Storage - Summary
+
+
Don’t leave important data lying around unprotected.
+
Choose a level of security appropriate to the sensitivity of the data.
+
Consider the consequences of someone gaining access to the data.
+
Remember that your data does not live in isolation.
+
K-anonymity not a good measure of privacy but an accessible starting point.
+
+
+
+
End of Part 1 Tomorrow: analyitcs, modelling and production.
attached base packages:stats, graphics, grDevices, utils, datasets, methods and base
+
loaded via a namespace (and not attached):compiler(v.4.3.3), fastmap(v.1.1.1), cli(v.3.6.3), tools(v.4.3.3), htmltools(v.0.5.8.1), rstudioapi(v.0.16.0), yaml(v.2.3.8), Rcpp(v.1.0.12), pander(v.0.6.5), rmarkdown(v.2.26), knitr(v.1.45), jsonlite(v.1.8.8), xfun(v.0.43), digest(v.0.6.35), rlang(v.1.1.4), png(v.0.1-8) and evaluate(v.0.23)
+
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+
+
References
+
+
+
+
+
+
+Gelman, Andrew, and Eric Loken. 2013. “The Garden of Forking Paths: Why Multiple Comparisons Can Be a Problem, Even When There Is No ‘Fishing Expedition’ or ‘p-Hacking’ and the Research Hypothesis Was Posited Ahead of Time.”Department of Statistics, Columbia University 348 (1-17): 3.
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+---
+title: "Privacy by Design in the machine learning pipeline"
+subtitle: " Workshop, University of Venice"
+author: Zak Varty
+date: "November, 2024"
+editor: source
+format:
+ revealjs:
+ theme: assets/zv-slides-theme.scss
+ logo: assets/zv-logo-192x192.png
+ bibliography: ../zv-talk-refs.bib
+ footer: "Privacy by Design - November 2024 - Zak Varty"
+ menu: true
+ slide-number: true
+ show-slide-number: all # (all / print / speaker)
+ self-contained: true # (set to true before publishing html to web)
+ width: 1600 # default is 1050
+ height: 900 # default is 850
+ incremental: false
+title-slide-attributes:
+ data-background-color: "#555555"
+---
+
+## Hello! Who am I?
+
+:::{.columns}
+:::{.column width="50%"}
+- Statistician by training, got to where I am through medical, environmental and industrial applications.
+
+- Teaching Fellow at Imperial College London
+ - Data Science, Data Ethics
+
+- Privacy, fairness and explainability in ML.
+ - Capable enthusiast, realist / pessimist
+
+Really it all comes down to doing good statistics well.
+:::
+:::{.column width="50%"}
+
+```{r who-am-i}
+#| echo: false
+#| fig-align: center
+#| out-width: 50%
+knitr::include_graphics("images/zv_c.jpg")
+```
+:::
+::::
+
+## Why do we care about privacy?
+
+. . .
+
+1. **Protecting Sensitive Data:** ML models often train on personal or confidential data (health records, financial info), and safeguarding this data is essential to prevent misuse or unauthorized access.
+
+2. **Compliance with Regulations:** Laws like GDPR require organisations to protect user privacy, impacting how data is collected, stored, and used in ML.
+
+3. **Preventing Data Leakage** Models can unintentionally expose sensitive information from their training data, risking user privacy if someone exploits the model’s outputs.
+
+4. **Building Trust:** Privacy-conscious ML practices foster trust among users, making them more willing to share data and participate in systems that use ML.
+
+5. **Avoiding Discrimination:** Privacy techniques can reduce bias and discrimination risks, ensuring the ML model treats users fairly without targeting sensitive attributes.
+
+
+# "If you have nothing to hide, you have nothing to fear"
+
+:::{.notes}
+- Assumes everyone has an equal tolerance for information exposure
+- Assumes that what needs to be private does not change over time or space
+:::
+
+# "The benefits outweight the costs"
+
+:::{.notes}
+- subjective decision
+- have to draw the line somewhere
+- how do we ensure that line is not crossed?
+- what can we do without crossing that line?
+:::
+
+## Machine Learning Pipeline
+
+```{r ml-pipeline}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/private-ml-piepline.png")
+```
+
+## Machine Learning ~~Pipeline~~ Life Cycle
+
+```{r ml-lifecycle}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/private-ml-cycle.png")
+```
+
+. . .
+
+Reality is much messier. See @gelman2013garden for a discussion of the implications.
+
+:::{.notes}
+- describe each stage
+- not recall linear, iterative process
+- reality much messier
+ - presents issues for valid inference
+ - see garden of forking paths for more
+:::
+
+## This workshop
+
+::::{.columns}
+:::{.column width="45%"}
+:::{.fragment}
+- Work through the ML life cycle
+- How could and have things gone wrong
+:::
+
+
+
+:::{.fragment}
+- What tools do we have?
+- What are their limitations?
+:::
+
+
+
+:::{.fragment}
+- Interactive bits, every now and then
+:::
+:::
+:::{.column width="10%"}
+:::
+:::{.column width="45%"}
+```{r ml-lifecycle-2}
+#| echo: false
+#| fig-align: center
+#| out-width: 75%
+knitr::include_graphics("images/private-ml-cycle.png")
+```
+:::
+::::
+
+# 1. Data Collection {background-color="#555555"}
+
+## Collecting Appropriate Data - GDPR
+
+::::{.columns}
+:::{.column width="60%"}
+- Collect only necessary data, purpose clear at time of collection
+- Data subject has right to
+ - access
+ - rectify
+ - erase
+ - object
+- Consequences both financial and reputational
+
+:::
+:::{.column width="40%"}
+```{r gdpr-screenshot}
+#| echo: false
+#| fig-align: center
+# knitr::include_graphics()
+# GDPR screenshot
+```
+:::
+::::
+
+:::{.notes}
+- Only collect necessary information
+- Purpose clear at time of collection
+ - hypothetical example: BMI study to H & M
+- Data subject has right to access, rectify erase and object
+- huge financial and reputational consequences
+ - recently LLM integration
+:::
+
+## Collecting Data - Hard-to-Reach Groups
+
+Standard ML assumes that data are cheap and easy to collect.
+
+Assumption that data are cheap and easy to collect. Out of the box model fitting
+assumes we are working with big, representative and independent samples.
+
+. . .
+
+- Applications of ML to social science to study hard-to-reach populations: persecuted groups, stigmatised behaviours.
+
+- Standard study designs and analysis techniques will fail.
+
+
+## Snowball Sampling - Hidden Network
+
+```{r snowball-1}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/snowball-1.png")
+```
+
+## Snowball Sampling - Initial Recruitment
+
+```{r snowball-2}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/snowball-2.png")
+```
+
+## Snowball Sampling - Referral Round 1
+
+```{r snowball-3}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/snowball-3.png")
+```
+
+## Snowball Sampling - Referral Round 2
+
+```{r snowball-4}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/snowball-4.png")
+```
+
+## Snowball Sampling - Referral Round 3
+
+```{r snowball-5}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/snowball-5.png")
+```
+
+## Snowball Sampling
+
+::::{.columns}
+
+:::{.column width="50%"}
+By using subject-driven sampling design, we can better explore the hard to reach target population while preserving the privacy of data subjects who _do not_ want to be included in the study.
+
+:::{.fragment}
+- Bonus: Also allows us to study community (network) structure if we are interested in that.
+:::
+
+:::{.fragment}
+- Drawbacks:
+ - "isolated" nodes,
+ - partitioned graphs,
+ - adapting model fitting to non-uniform sampling.
+:::
+:::
+:::{.column width="50%"}
+```{r snowball-final}
+#| echo: false
+#| fig-align: center
+#| out-width: "70%"
+knitr::include_graphics("images/snowball-5.png")
+```
+:::
+::::
+
+
+## Collecting Data - Asking Difficult Questions
+
+Even if data subjects are easy to access and sample from, they may not wish to answer honestly.
+
+_Can you give me some examples?_
+
+. . .
+
+:::{.incremental}
+- cheated on an exam?
+- cheated on a romantic / sexual partner?
+- experienced suicidal ideation?
+- killed another person?
+:::
+
+. . .
+
+Dishonest answers will _bias_ any subsequent analysis, leading us to underestimate the prevalence of an "undesirable outcome".
+
+. . .
+
+(Interesting intersection with survey design and psychology. The order and way that you ask questions can influence responses but we will focus on a single question here.)
+
+## Direct Response Survey
+
+$$\Pr(Y_i = 1) = \theta \quad \text{and} \quad \Pr(Y_i = 0) = 1 - \theta.$$
+Method of Moments Estimator: (General dataset)
+
+$$ \hat \Theta = \hat\Pr(Y_i = 1)$$
+
+. . .
+
+$$ \hat \Theta = \frac{1}{n}\sum_{i=1}^n \mathbb{I}(Y_i = 1) = \bar Y = \frac{\#\{yes\}}{\#\{subjects\}}.$$
+
+. . .
+
+Method of Moments Estimate: (Specific dataset)
+$$ \hat \theta = \frac{1}{n}\sum_{i=1}^n \mathbb{I}(y_i = 1) = \bar y.$$
+
+## MoM Example
+
+Suppose I ask 100 people whether they have ever been unfaithful in a romantic relationship and 24 people respond "Yes".
+
+
+
+What is your best guess of the proportion of all people who have been unfaithful?
+
+. . .
+
+$\hat\theta = \bar y = \frac{24}{100}$
+
+
+
+How confident are you about that guess?
+
+Would that change if I had 1 person responding "Yes"?
+
+Would that change if I had 99 people responding "Yes"?
+
+
+## MoM - Nice Properties
+
+Over lots of samples we get it right on average:
+
+$\mathbb{E}_Y[\hat\Theta] = \mathbb{E}_Y\left[\frac{1}{n}\sum_{i=1}^n \mathbb{I}(Y_i = 1)\right] = \frac{1}{n}\sum_{i=1}^n \mathbb{E}_Y\left[ \mathbb{I}(Y_i = 1)\right] = \frac{n \theta}{n} = \theta$
+
+. . .
+
+As the number of samples gets large, we get more confident and therefore recover the truth
+
+\begin{align*}
+\text{Var}_Y[\hat\Theta]
+&= \text{Var}_Y\left[\frac{1}{n}\sum_{i=1}^n \mathbb{I}(Y_i = 1)\right] \\
+&= \frac{1}{n^2}\sum_{i=1}^n\text{Var}_Y\left[\mathbb{I}(Y_i = 1)\right] \\
+&= \frac{1}{n^2}\sum_{i=1}^n p(1-p) \\
+&= \frac{n p (1-p)}{n^2} \\
+&= \frac{p (1-p)}{n} \rightarrow 0
+\end{align*}
+
+## Adding Privacy - Randomised Response
+
+- Mathematically nice but in reality people lie.
+
+- Our estimator worked "best" for central values of $\theta$, unlikely for stigmatised events.
+
+- Add random element to survey to provide plausible deniability.
+ - Flip a fair coin. If heads, switch your answer.
+
+- MoM estimation: Equate probabilities and proportions.
+
+## Estimation from Randomised Response Data
+
+::::{.columns}
+:::{.column width="50%"}
+
+Consider using a weighted coin, probability $p$ of telling truth. Derive an expression for the probability of answering "Yes".
+
+:::{.fragment}
+\begin{align*}
+\Pr(\text{Yes}) &= \theta p + (1 - \theta)(1 - p) \\
+& \approx \frac{\#\{yes\}}{\#\{subjects\}} \\
+&= \bar y
+\end{align*}
+:::
+:::{.fragment}
+Rearrange this expression to get a formula for $\hat \theta$.
+:::
+:::{.fragment}
+$$\hat \theta = \frac{\bar y - 1 + p}{2p -1}.$$
+:::
+:::
+:::{.column width="50%"}
+```{r randomised-response-tree}
+#| echo: false
+#| fig-align: center
+#| out-width: "60%"
+knitr::include_graphics("images/randomised-response-tree.png")
+```
+:::
+::::
+
+## Randomised Response Activities
+
+$$ \hat \theta = \frac{\bar y - 1 + p}{2p -1}.$$
+
+- Direct response is a special case of randomised response. How can we use that to check our working?
+
+. . .
+
+- If our previous survey results came from this randomised response survey design with $p = 0.25$, what is your best guess of the proportion of people who have been unfaithful?
+
+. . .
+
+- Are you more or less confident in this estimate than previously, when we had the same data but from a direct response design?
+
+. . .
+
+- What does your confidence depend on? And which of those factors do you have knowledge of / control over?
+
+. . .
+
+- When would this estimation procedure break and why? How could we fix that?
+
+## Randomised Response - Privacy Schematic
+
+```{r randomised-response-privacy}
+#| echo: false
+#| fig-align: center
+#| out-width: "100%"
+knitr::include_graphics("images/randomised-response-privacy.png")
+```
+
+## Randomised Response
+
+- Approach to privacy for single, binary response.
+
+- Issues with applying to multiple questions, e.g. surveys with follow on questions.
+
+- Extensions to categorical and continuous responses and predictors
+
+- General principle of adding noise
+ - Need to make observations indistinguishable
+ - Need to preserve important aspects of "signal"
+
+## Data Collection Summary
+
+- _Collect what you need_ and use that information only for its intended purpose.
+
+- _Targeting hard-to-reach populations can be challenging_ but possible by combining survey design and specific learning approaches. Keeps statisticians in a job!
+
+- _Asking difficult questions_ can lead to biased responses. Plausible deniability through randomised response designs can help.
+
+# 2. Data Storage {background-color="#555555"}
+
+## Encryption
+
+Once we have gone to the effort of collecting data we don't want to just leave it lying around for anyone to access.
+
+::::{.columns}
+:::{.column width="50%"}
+
+$$ \text{Plain text} \overset{f}{\rightarrow} \text{Cipher Text}$$
+
+$$ \text{Cipher text} \overset{f^{-1}}{\rightarrow} \text{Plain Text}$$
+
+$$ f(\text{data}, \text{key})$$
+Many encryption schemes depending on the data to be encrypted and how the key is to be distributed.
+:::
+:::{.column width="50%"}
+```{r encryption}
+#| echo: false
+#| fig-align: center
+#| out-width: "80%"
+knitr::include_graphics("images/encryption.png")
+```
+:::
+::::
+
+## Caesar Cipher
+
+```{r caesar}
+#| echo: false
+#| fig-align: center
+#| out-width: "80%"
+knitr::include_graphics("images/caesar-cipher-zak.png")
+```
+
+. . .
+
+Write your own short message and pass it to a friend to decode.
+
+. . .
+
+What are some benefits and drawbacks of this encryption scheme?
+
+
+## K-anonymity {.incremental}
+
+What happens if someone gets access to the data?
+
+
+
+- $k$-anonymity is a measure of privacy within a dataset.
+
+- Given a set of predictor-outcome responses, each unique combination forms an _equivalence class_.
+
+- The smallest equivalence class of a $k$-anonymous dataset is of size $k$.
+
+- Equivalently, each individual is indistinguishable from at least $k-1$ others.
+
+## K-anonymity Example
+
+```{r k-anon-survey}
+#| echo: false
+#| fig-align: center
+#| out-width: "100%"
+knitr::include_graphics("images/k-anon-survey.png")
+```
+
+## K-anonymity Worked Example
+
+```{r k-anon-example}
+#| echo: false
+#| fig-align: center
+knitr::include_graphics("images/k-anon-example.png")
+```
+
+## K-anonymity Your Turn
+
+I asked ChatGPT to generate 4-anonymous datasets but it hasn't done a good job.
+
+- Establish the true value of k for your dataset.
+
+- Use pseudonymisation, aggregation, redaction and partial-redaction to make your dataset 4-anonymous.
+
+## K-anonymity Feedback
+
+- How did ChatGPT do?
+- How did you alter the anonymity level of your dataset?
+- What did you have to consider as you were doing this?
+
+## K-anonymity Drawbacks
+
+What do you think some of the limitations of $k$-anonymity might be?
+
+. . .
+
+- Knowing what is important before analysis.
+- Publishing multiple versions of the dataset.
+- Can be checked easily but not implemented algorithmically.
+- External data attacks; Jane Doe, Latanya Sweeney
+
+## Data Storage - Summary
+
+- Don't leave important data lying around unprotected.
+- Choose a level of security appropriate to the sensitivity of the data.
+
+- Consider the consequences of someone gaining access to the data.
+- Remember that your data does not live in isolation.
+
+- K-anonymity not a good measure of privacy but an accessible starting point.
+
+# End of Part 1 Tomorrow: analyitcs, modelling and production.
+
+# 3. Data Analytics {background-color="#555555"}
+
+# 4. Modelling {background-color="#555555"}
+
+# 5. Going into Production {background-color="#555555"}
+
+## Build Information {.smaller}
+
+```{r}
+pander::pander(sessionInfo())
+```
+
+## References
diff --git a/2024-privacy-by-design/assets/refs.bib b/2024-privacy-by-design/assets/refs.bib
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