12 Metaphors, Analogies, and Similes
12.1 What are They?
In the literary sense, a metaphor is a figure of speech that equates two things: “Time is money” or “All the world is a stage”. When one of them is unfamiliar or unknown and the other is familiar and known, a metaphor allows us to understand by making connections. A “self-amplifying event” becomes a “chain reaction”, describing perfectly what is going on, a series of reactions connected to each other, with each link of the chain firing off another event.
An analogy is similar to a metaphor, it compares two things—the unfamiliar or unknown concept is like a familiar concept. Use this hint to remember the difference between metaphors and analogies: “an analogy is like a metaphor”. If you want to put a finer point on it, then analogies can be distinguished from similes. Both make comparisons via like or as. The goal of the analogy is to provide an explanation, whereas a simile simply says one thing is like another thing. “Life is like a box of chocolate” is a simile.
- Metaphor: Time is a thief
- Simile: Time is like a thief
- Analogy: Time is like a thief that steals moments of our lives.
We use metaphors in what follows as an umbrella term for all three, with apologies to linguists.
12.2 Why Use Them
Metaphors make your communication more interesting, fun, and relatable—thus memorable. They break down barriers and engage the audience. Which of the following two phrases is more engaging and memorable?
The analysis of unstructured data collected through social media suggests
significant customer interest in the update compared to the previous release.
A lot of online buzz suggests that customers love the update.
When communicating data science to decision makers, you might be running into some resistance. Not everyone has embraced data-based decisioning as the way forward. For many executives, this new way of thinking is an existential threat to the intuition-based decisioning that has led them to their prestigious role. Someone explained the tension around data science this way
Data-driven decisioning is considered a threat because based on data and technology you can now make ostensibly better decisions than the folks who have been honing their intuition for 25 years. This empowers a new and younger generation of decision makers to take a seat at the table; disrupting the established order.
In one of his blog posts Jason Parker lists these attitudes about predictive models as common challenges to overcome:
- “There’s nothing this can tell me that I don’t already know.”
- “There’s no way that a machine can replace people in making this kind of decision.”
- “We already do a great job with this, there’s no need to rock the boat.”
The metaphor he uses to connect with the audience is to compare using a predictive model in business with looking at Google Maps to plan a route home from work. We do it not because we are confused about where Home is, but because the predictive algorithm in Google Maps reliably predicts the shortest route given the current conditions—more so than we can.
Similarly, predictive models are not used to tell executives how to run the business, but help them to realize their business goals most efficiently. The analogy is
Using predictive models is like letting Google suggest a route to a known destination. It is the best way to get to where you want to go.
12.3 Careful with Established Metaphors
Some metaphors are well established in data science and have taken their place in the vocabulary:
- Data lake
- Data warehouse
- Data mining
- Data ingest
These terms have very precise meaning and they serve as metaphors. When using “data lake” in a presentation, what do you want to achieve? Are you referring to the particular data architecture in the organization as distinct from, say, a data warehouse, or do you want the audience to think of data as floating around in a lake?
In situations where metaphors are well established, make sure the audience knows whether you use a technical term or whether you want to draw on the metaphor.
Some metaphors have become so commonplace that they have devolved into boilerplate:
- Big data
- Data is the new oil (the new gold)
- Data tsunami
- Data deluge
- Data rush
- Raw data
Different audiences will relate and react to these metaphors differently. As Awati and Shum (2015) point out, a marketing professional might look at a tsunami of unstructured data as a valuable resource to be exploited for marketing purposes while the IT director is worried about being washed away by the tsunami of data stored on the company servers.
12.4 Dangerous Metaphors and Analogies
The desire to express complex and unfamiliar topics in familiar terms takes us too far when metaphors oversimplify or distort. There be dragons.
One of the most controversial analogies in recent data science history is that between neural networks and the brain. Now most of us do not understand how brains work but we are familiar with carrying one around. It is ironic to try and explain a complex and unfamiliar system—the neural network—with an analogy to another system whose functioning is not (well) understood—the human brain.
Some argue that it should be obvious that an artificial neural network (ANN) does not work like a brain. The numerous contributions that use the analogy to do away with an explanation of the technology by hand-waving suggest otherwise. By calling the units in the hidden layer of an ANN neurons and their connections synapses, comparisons with the brain are invited.
Ever since the analogy between ANN and brain was made, the field had to push back against it. A neural network is a piece of software that does not at all look, work, behave, like a wet-substrate organ. Unfortunately, because the connection was made, and because ANNs are foundational technology in AI applications, the hyperbole about the capabilities and effects of AI had free reign.
If the brain analogy of neural networks is out, then what other analogies can be used to relate such a complex and unfamiliar concept?
A neural network is like performing a complex task by enaging thousands or millions of partial experts, each solving a tiny subtask, in anticipation that their collective effort does the job.
A neural network is like weaving a garment where the threads are made from data. If the threads or the weaver are not very good you don’t want to wear the garment.
12.5 Analogies for Data Science Concepts
Behar, Grima, and Marco-Almagro (2013) list 25 analogies the authors use to teach statistical concepts. In this section we draw on some of their analogies, modify and expand on them, and add some of our own.
Sample Size
The appropriate size of a sample is not a function of the size of the population, rather it depends on the variability of the population and the desired accuracy or power of the statistical methods applied to the sample.
Imagine cooking a pot of soup and using a teaspoon to taste the soup. If you are expecting more dinner guests and cook a much bigger pot of soup you would not be tasting the soup with a bigger spoon–you would still use a teaspoon.
You can extend this analogy to explain selection bias.
Selection Bias
Sampling bias–also called selection bias—is a form of representation bias where the sampling method is defective and does not represent the target population. A random sample is always representative of the target population but there are many ways in which the selected data can deviate from the properties of a random sample:
Available data can misrepresent the target population, for example, if medical data is only available for individuals having a condition.
Random sampling that does not reflect the distribution of groups in the target population, for example, drawing random samples from lists of users (website, mobile phone, phone book, tax records) does not accurately represent the overall population (over-/under-coverage).
Missing values processes can be related to the objective of the study (non-response bias).
Participants who exercise control over their inclusion in a study can bias the data (self-selection bias).
Survivorship bias can occur when the sample focuses on those meeting a selection criterion. For example, studying current companies does not reflect companies that have previously failed.
Drop-out: when subjects drop out of a long-term study for reasons related to the objective of the study it can bias the results.
Suppose you are tasting soup from a pot that is not well stirred. You might be dipping the spoon into an area where salt or spices have accumulated, thus not getting a representative taste of the entire soup.
The problem is not addressed by tasting with a bigger spoon (taking a larger sample), but by making sure the pot is properly stirred prior to tasting.
Confidence Level
The confidence level is the probability associated with a confidence interval. A 95% confidence interval has confidence level 0.95 and it represents the interval that will contain the unknown value of the parameter in 95% of the conceptual repetitions of the experiment.
If you draw a (single) random sample and calculate the confidence level of a parameter based on it, then we do not know whether the parameter will actually be covered by the interval we computed. But we know, were we to repeat the sampling over and over again, that 95% of those intervals will cover the parameter.
A 95% confidence interval is like a person who tells the truth 95% of the time. We do not know whether a particular statement is true or not but in the long run, 95% of their statements will be true.
Sample (Study) Size and Treatment Effect
A treatment effect of a certain size is more likely detectable as sample size increases as this increases the power of the statistical comparison between the treatments. This can lead to situations where the sample size is so large that treatment differences are detected as significant even though the magnitude of those differences is practically irrelevant.
Suppose you are looking at two animals through a magnifying glass. At low magnification you might not be able to tell that one is a dog and one is a cat. As the magnification increases, differences between the animals become more apparent. If you look at them under a microscope you will detect minute dissimilarities and always declare them different individuals. If the question is “Are they both dogs?”, then you do not need a microscope.
Residuals
A residual is typically the difference between an observed value and a predicted value under a model; the raw difference is sometimes modified to imbue the residuals with particular properties that aid in the diagnostic of model assumptions. A residual should not exhibit systematic effects as the signal, the systematic part of the relationship between target and input, should have been removed by training a model to the data.
Many loss functions in statistical estimation are functions of residuals.
After reading the newspaper, the pages are thrown into the trash (or are recycled) when we have consumed all the necessary information from the paper. It should not contain any valuable information we overlooked to incorporate into our thinking.
Feature Selection
Models depend on features and we cannot include all possible features into a model. Doing so would make the model too large, unwieldy, impractical, and the model would not generalize well. So we use various techniques to choose subsets of the features (variable selection, Lasso) or use regularization techniques that dampen the negative effect of having too many features.
Selecting features in a statistical model is like choosing which consultants to hire in order to solve future business problems. (Bear with me here, I know that some will quip that the correct number of consultants to be hired is always zero.)
You cannot afford to hire all consultants, and they would likely trip all over each other anyway. So you choose to bring the best two or three you can afford. The first consultant you choose should be the one with the broadest knowledge base because you cannot know yet what future problems they will need to solve. Suppose that this consultant can handle 65% of all problems.
Which consultant should you hire next? The one with the second-most breadth in problem solving—say 45% or the one whose problem-solving ability covers the blind spots of the first (is orthogonal to the first consultant)? You are making the company most future-proof by hiring second the consultant who knows most about the problems the first consultant does not know anything about.
Type-I and Type-II Errors
Feinberg (1971) uses analogies with the judicial process to explain the concepts of the Type-I and Type-II errors.
We are testing a hypothesis, called the null hypothesis, by gathering data and examining how likely the outcome of the experiment is under the hypothesis (if the null hypothesis were true). If the outcome is very unlikely under this condition the null hypothesis is rejected—as the outcome should not have happened. A Type-I error is the mistake to reject a true hypothesis. A Type-II error is to fail to reject in the situation when the null hypothesis is not true.
Consider a trial before court. The hypothesis is that the accused is innocent of the charges—following the principle of presumption of innocence: in the absence of evidence against, we have to assume that the defendant is innocent.
- A Type-I error is to find a defendant guilty when in fact they are innocent.
- A Type-II error occurs if the court fails to declare the defendant guilty when they in fact broke the law.
The analogy can be continued to explain the significance level and the inverse relationship between the two error types.
Significance level
The decision about the validity of a null hypothesis based on statistical analysis rests on estimated quantities that have variability. We cannot say whether a hypothesis is true or false, we can only make statements about the probability of having observed the result we did (or a result more extreme) if the hypothesis were true. The probability threshold at which we we are confident to state that a result is unusual enough for the hypothesis to be a viable explanation is the significance level.
In order to convict someone, we need evidence beyond a reasonable doubt to reduce the chance to declare an innocent person guilty (a Type-I error). By raising the bar of reasonable doubt for a conviction, we make sure that it is unlikely to convict an innocent person. But at the same time we are increasing the chances that a guilty person will go free (a Type-II error). This happens when there is evidence against the guilty person but it does not rise to the level of beyond reasonable doubt required for a conviction.
Regularization
Regularization is a form of shrinkage estimation where a penalty term is added to an objective function. The regularization penalty has the effect of introducing bias while reducing variability at the same time, leading to smaller mean-squared errors compared to unbiased methods. The parameter estimates of regularized models are shrunk toward zero—sometimes made exactly zero—which reduces their variability.
Regularization is like a wise teacher. After you have read many books on a subject, the teacher can tell you which ones matter most and encourage you not to take any of the sources too serious.
Loss Function
A loss function measures the cost of committing an error in a supervised estimation method, in the sense that the observed and predicted values will disagree to some extent. The form of the loss function expresses how we measure and value these cost.
Loss functions are objective functions we try to minimize in statistical estimation.
A loss function is like a teacher comparing a student’s response to a question to the correct answer. The goal is not to get all questions correct by remembering the answers, but for the student to learn and gain knowledge that they can apply to find answers to new questions.
The loss function tells the teacher how far off an individual student is, how far off the entire class is, and whether further instruction is needed.
Bias-Variance Tradeoff
The contributions to the mean-squared error by a statistical estimator have two sources: the variability of the estimator itself, and its bias, the deviation between the mean of the estimator and the target of estimation. The mean-squared error is the sum of the variance and the squared bias.
An estimator can achieve a small mean-squared error by having small variance and/or having small bias. In constructing statistical models using supervised learning we balance bias and variance by making sure models do not overfit (low bias and high variance) or underfit (high bias and low variance) and by choosing appropriate model families and estimation principles.
Balancing bias and variance in data science models is like maximizing employee productivity by finding the balance between remote working and spending time in the office.
Ensemble Method
An ensemble is a collection of weak or strong learning models that produce a prediction or classification collectively, usually by some form of averaging or majority voting. The combination of base learners improves performance by reducing variability through averaging, or by sequentially improving on previous models.
An ensemble method is like estimating the number of marbles in a jar by relying on the wisdom of crowds. Any one person’s guess is unreliable, but when you average many person’s guesses you can estimate the number of marbles well.
No one person has to be an expert at marble guessing for the group to do well.
12.6 Terms with Established Meaning
Another issue to look out for in technical communication are terms that have established meaning in everyday language which can be different from their meaning in technical vernacular.
An error in everyday English refers to a mistake. In statistics, error has multiple meanings:
- the discrepancy between an observation and a model prediction (mean-squared error, classification error)
- the discrepancy between a true value and an observed value (measurement error)
- the amount of loss incurred
- a probable interval (margin of error)
- a measure of variability (standard error)
- an erroneous decision (Type-I error, Type-II error)
To statisticians it might be perfectly clear which type of error you are referring to. Given the many meanings of the term in statistics, that is not guaranteed. Imagine the confusion of a non-technical audience.
Significance in everyday English refers to something important, worthy of attention. Statistical significance is a threshold level of probability beyond which an assumption (the hypothesis) is deemed unlikely to be true. This threshold is not related to practical importance. Non-technical audiences are easily misled into thinking that findings matter if they have found to be statistically significant. Better words to use in technical writing are remarkable, important, and relevant.
Correlation in everyday English refers to the relationship or connection between things. In statistical terms, the correlation is a measure of a particular type of relationship between random variables, a linear relationship. Replacing the word correlation in technical writing with association or the generic relationship is a good idea.
Independence in everyday language is a state of freedom, being free of the control of others. In statistics and probability, independence is a property of the joint distribution of random variables. Two events are stochastically independent when the occurrence of one event does not affect the likelihood that the other event occurs. In modeling, the term independent variable is also common, as compared to the dependent variable. Independent variables are the explanatory variables (predictors, inputs) in a model. The dependent variable is the target. The use of the terms independent variables and dependent variable is particularly confusing to non-technical audiences.