You may think that engineering must follow science, but often it is the other way round. For instance, we learned how to build things before we learned the science behind it—we trialed-and-errored and overengineered our way to many still standing buildings while the scientific understanding slowly accumulated. Similarly, we were able to predict the seasons and the phases of the moon before learning how our solar system worked. Our ability to solve problems with machine learning is similarly ahead of our ability to put it on a firm scientific basis.

Often, we build something based on some vague intuition, find that it ‘works,’ and only over time, deepen our intuition about why (and when) it works. Take, for instance, Dropout. The original paper (released in 2012, published in 2014) had the following as motivation:

A motivation for Dropout comes from a theory of the role of sex in evolution (Livnat et al., 2010). Sexual reproduction involves taking half the genes of one parent and half of the other, adding a very small amount of random mutation, and combining them to produce an offspring. The asexual alternative is to create an offspring with a slightly mutated copy of the parent’s genes. It seems plausible that asexual reproduction should be a better way to optimize individual fitness because a good set of genes that have come to work well together can be passed on directly to the offspring. On the other hand, sexual reproduction is likely to break up these co-adapted sets of genes, especially if these sets are large and, intuitively, this should decrease the fitness of organisms that have already evolved complicated coadaptations. However, sexual reproduction is the way most advanced organisms evolved. …

Srivastava et al. 2014, JMLR

Moreover, the paper provided no proof and only some empirical results. It took until Gal and Ghahramani’s 2016 paper (released in 2015) to put the method on a firmer scientific footing.

Then there are cases where we have made ad hoc choices that ‘work’ and where no one will ever come up with a convincing theory. Instead, progress will mean replacing bad advice with good. Take, for instance, the recommended step of ‘normalizing’ variables before doing k-means clustering or before doing regularized regression. The idea of normalization is simple enough: put each variable on the same scale. But it is also completely weird. Why should we put each variable on the same scale? Some variables are plausibly more substantively important than others and we ideally want to prorate by that.

The first point is about teaching machine learning. Bricklaying is thought to be best taught via apprenticeship. And core scientific principles are thought to be best taught via books and lecturing. Machine learning is closer to the bricklaying end of the spectrum. First, there is a lot in machine learning that is ad hoc and beyond scientific or even good intuitive explanation and hence taught as something you do. Second, there is plausibly much to be learned in seeing how others trial-and-error and come up with kludges to fix the issues for which there is no guidance.

The second point is about the maturity of machine learning. Over the last few decades, we have been able to accomplish really cool things with machine learning. And these accomplishments detract us from how early we are. The fact is that we have been able to achieve cool things with very crude tools. For instance, OOS validation is a crude but very commonly used tool for preventing overfitting—we stop optimization when the OOS error starts increasing. As our scientific understanding deepens, we will likely invent better tools. The best of machine learning is a long way off. And that is exciting.

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- Because we often scavenge information, many of us are not well versed in the core principles of the discipline (and adjacent disciplines) we purport to specialize in or want to learn about.
- The core ideas, the big hits, etc., by their very nature, are important and illuminating.
- Many of these big ideas are accessible, partly because people have spent time thinking about ways to communicate the points. So you will find excellent distillations of the points, and you will find that many of these ideas are on your knowledge frontier (things you can learn immediately).

Or, if you are disciplined enough, focus relentlessly on finding new things in a narrow niche. Going from gambling to anything else is not easy. The highs won’t be as high. But the average high and ROI is a lot greater.

]]>One big reason why the FPR may vary across groups is that, given the data, some groups’ outcomes are less predictable than others. This may be because of the limitations of the data itself or because of the limitations of algorithms. For instance, Kearns and Roth in their book bring up the example of college admissions. The training data for college admissions is the decisions made by college counselors. College counselors may well be worse at predicting the success of minority students because they are less familiar with their schools, groups, etc., and this, in turn, may lead to algorithms performing worse on minority students. (Assume the algorithm to be human decision-makers and the point becomes immediately clear.)

One way to address worse performance may be to estimate the uncertainty of the prediction. This allows us to deal with people with wider confidence bounds separately from people with narrower confidence bounds. The optimal strategy for people with wider confidence bounds people may be to collect additional data to become more confident in those predictions. For instance, Komiyama and Noda propose something similar (pdf) to help overcome a lack of information during hiring. Or we may need to figure out a way to compensate people based on their uncertainty interval.

The average width of the uncertainty interval across groups may also serve as a reasonable way to diagnose this particular problem.

]]>What’s the least amount of data you need to collect to estimate the population mean with a particular standard error? For the simplest case—estimating the mean of a binomial variable using simple random sampling, a conservative estimate of the variance (p=.5), and a ±3 confidence interval—the answer (n∼1,000) is well known. The simplest case, however, assumes little to no information. Often, we know more. In opinion polling, we generally know sociodemographic strata in the population. And we have historical data on the variability in strata. Take, for instance, measuring support for Mr. Obama. A polling company like YouGov will usually have a long time series, including information about respondent characteristics. Using this data, the company could derive how variable the support for Mr. Obama is among different sociodemographic groups. With information about strata and strata variances, we can often poll fewer people (vis-a-vis random sampling) to estimate the population mean with a particular s.e. In a note (pdf), we show how.

In a realistic example, we find the benefit of using optimal allocation over simple random sampling is 6.5% (see the code block below).

Assuming two groups a and b, and using the notation in the note (see the pdf)—wa denotes the proportion of group a in the population, vara and varb denote the variances of group a and b respectively, and letting p denote sample mean, we find that if you use the simple random sampling formula, you will estimate that you need to sample 1095 people. If you optimally exploit the information about strata and strata variances, you will need to just sample 1024 people.

```
## The Benefit of Using Optimal Allocation Rules
## wa = .8
## vara = .25; pa = .5
## varb = .16; pb = .8
## SRS: pop_mean of .8*.5 + .2*.8 = .56
# sqrt(p(1 -p)/n) = .015
# n = p*(1- p)/.015^2 = 1095
# optimal_n_plus_allocation(.8, .25, .16, .015)
# n na nb
#1024 853 171
```

**Github Repo.**: https://github.com/soodoku/optimal_data_collection/

Often, product development starts with a business problem. And your first job is to understand the business problem as well as you can, familiarizing yourself with as much detail as possible.

Let’s say the problem is as follows: A company gets a lot of customer emails. All the emails go to a common inbox from which specialist customer agents fish out emails that are relevant to them. For instance, finance specialists fish out billing emails. And technical specialists fish out emails about technical errors. Fishing is time-consuming and chaotic.

Once you understand the precise problem—time taken to discover and assign emails—work on developing solutions for the problem. When developing solutions, the bias should be toward solving the problem the best way possible than injecting custom ML into whatever solution you propose. For instance, you could propose a solution that makes it easier to search (using no ML or off-the-shelf ML) and bulk assign to a new queue. But let’s say that after careful consideration of costs and benefits, a particularly appealing solution is a system that uses machine learning to automatically direct relevant emails to specialist inboxes, obviating the need to fish. That’s a start to a solution, not the end. You need to spend enough time thinking about the solution so that you have thought about how to handle edge cases, e.g., when there is a technical issue about billing, a misclassified email, etc., and any spillover issues, like the latency of such a system, how implementing such a system may break existing data pipelines that measure the total number of emails, etc.

Next, you need to define the KPIs. How much time will be saved? What is the total cost of the saved time? How many mistakes is the system making? What is the cost of handling mistakes?

Next, you need to turn the business problem into a precise machine learning problem. What labels would you predict? How would you collect the initial labels?

Once the outline of the solution has been agreed upon, you need to don your architect’s hat and outline a system diagram. Wearing the data engineer’s hat, figure out where the data needed for training and for live classification is stored, and how you would build a pipeline for training and serving the model. This is also the time to understand what guarantees, if any, exist on the data, and how you can test those guarantees.

Right next to the data engineer’s hat is the modeler’s hat. Wearing that, you must decide what algorithms you want to run, etc. how to version control your models, etc. The ML modeler’s hat also directs your attention to your plan for how to improve the model. Machine learning is an elaborate system to learn from your losses and you must design a system to continuously learn from your errors. More precisely, you must answer what is your system in place to improve your model? There is a pipeline for that: 1. Learn about your losses: from feedback, errors, etc. 2. Understand your losses: error analysis, etc., 3. Reducing your losses: new data collection, fixing old data, diff. models, objective functions, and 4. Testing: A/B testing, offline testing, etc.

Last, you must wear an operator’s hat. Wearing that you answer the operational nitty-gritty of how to introduce a new product. This is the time when you work with stakeholders to stand up dashboards to monitor the system, develop a rollout strategy, and a rollback strategy, a dashboard for monitoring A/B tests, etc.

The key to wearing an architect’s hat is to not only designing a system but also to make sure that enough logging is in place for different parts of the system for you to triage failures. So part of the dashboard would display logs from different parts of the system.

]]>**Net Harm Over Relative Harm**: Because of lower accuracy, the number of people from a minority group that are unfairly rejected (say for a loan application) may be a lot higher. (This is ignoring the harm done to other groups.)**Mismeasuring Harm?**Consider an algorithm used to approve or deny loans. Say we get the same FPR across groups but lower accuracy for loans with a fair algorithm. Using this algorithm, however, means that credit is more expensive for everyone. This, in turn, may cause fewer people of the vulnerable group to get loans as the bank factors in the cost of mistakes. Another way to think about the point is that using such an algorithm causes net interest paid per borrowed dollar to increase by some number. It seems this common scenario is not discussed in many of the papers on fair ML. One reason for that may be that people are fixated on who gets approved and not the interest rate or total approvals.

Let there be n families and let the stopping rule be that after the birth of a male child, the family stops procreating. Let p be the probability a male child is born and q=1−p

After 1 round:

\[\frac{pn}{n} = p\]

After 2 rounds:

\[ \frac{(pn + qpn)}{(n + qn)} = \frac{(p + pq)}{(1 + q)} = \frac{p(1 + q)}{(1 + q)} \]

After 3 rounds:

\[\frac{(pn + qpn + q^2pn)}{(n + qn + q^2n)}\\
= \frac{(p + pq + q^2p)}{(1 + q + q^2)}\]

After k rounds:

\[\frac{(pn + qpn + q^2pn + … + q^kpn)}{(n + qn + q^2n + \ldots q^kn)} \]

After infinite rounds:

Total male children:

\[= pn + qpn + q^2pn + \ldots\\
= pn (1 + q + q^2 + \ldots)\\
= \frac{np}{(1 – q)}\]

Total children:

\[= n + qn + q^2n + \ldots\\
= n (1 + q + q^2 + \ldots)\\
= \frac{n}{(1 – q)}\]

Prop. Male:

\[= \frac{np}{(1 – q)} * \frac{(1 – q)}{n}\\
= p\]

If it still seems like a counterintuitive result, here’s one way to think: In each round, we get pq^k successes, and the total number of kids increases by q^k. Yet another way to think is that for any child that is born, the data generating process is unchanged.

The male-child stopping rule may not affect the aggregate sex ratio. But it does cause changes in families. For instance, it causes a negative correlation between family size and the proportion of male children. For instance, if your first child is male, you stop. (For more results in this vein, see here.)

But why does this differ from our intuition that comes from early stopping in experiments? Easy. We define early stopping as when we stop data collection as soon as the results are significant. This causes a positive bias in the number of false-positive results (w.r.t. the canonical sample-fixed-in-advance rule). But early stopping leads to both kinds of false positives—mistakenly thinking that the proportion of females is greater than .5 and mistakenly thinking that the proportion of males is greater than .5. The rule is unbiased w.r.t. to the expected value of the proportion.

]]>With Atul Dhingra

For a broad class of machine learning problems, nitpicking over the neural net architecture is over (see, for instance, here). Instead, the focus has shifted to data. In the note below, we articulate some ways of thinking about what data to collect. In our discussion, we focus on supervised learning.

The answer to “What data to collect?” varies by where you are in the product life cycle. If you are building a new ML product and the aim is to deploy something (basic) that delivers value and then iterate on it, one answer to the question is to label easy-to-predict cases—cases that allow you to build models where the precision is high but the recall is low. The bar is whether the model can do as well as business as usual for a small set of cases. The good thing is that you can hurdle that bar another way—by coding a random sample, building a model, and choosing a threshold where the precision is greater than business as usual (read more here). For producing POCs, models built on cheap data, e.g., open-source data, which plausibly do not produce value, can also “work” though they need to be managed against the threat of poor performance reducing faith in the system.

The more conventional case is where you have a deployed model, and you want to improve its performance. There the answer to what data to collect is data that yields the highest ROI. (The answer to what data provides the highest ROI will vary over time, so we need a system that continuously answers it.) If we assume that the labeling costs for points are the same, the prioritization function reduces to ranking data by returns. To begin with, let’s assume that returns are measured by the function specified by the cost function. So, for instance, if we are looking for a model that lowers the RMSE, we would like to rank by how much reduction in RMSE we get from labeling an additional point. And naturally, we care about the test set RMSE. (You can generalize this intuition to any loss function.) So far, so good. The rub comes from the fact that there is no trivial answer to the problem.

One way to answer the question is to run experiments, sampling across Xs, or plausibly use bandits and navigate the explore-exploit tradeoff smartly. Rather than do experiments, you can also exploit the data you have to figure out the kinds of points that make the most impact on RMSE. One way to get at that is using influence functions. There are, however, a couple of challenges in using these methods. The first is that the covariate space is large and the marginal impact is small, and that means inference is noisy. The second is a more general problem. Say you find that X_1, X_2, X_3, … are the points that lead to the largest reduction in RMSE. But how do you use that knowledge to convert it into a data collection problem? Is it that we should collect replicas of X_1? Probably not. We need to generalize from these examples and come up with a statement about the “type of data” that needs to be collected, e.g., more images where the traffic sign is covered by trees. To come up with the ‘type’, we need to specify what the example is not—how does it differ from the rest of the data we have? There are a couple of ways to answer the question. The first is to use clustering (using embeddings) and then assigning someone to label the clusters. Another is to use supervised learning to classify the X_1, X_2, X_3 from the rest of the data and figure out the “important predictors.”

There are other answers to the question, “What data to collect?” For instance, we could look to label points where we are least certain or where we make the largest error. The intuition in the classification setting is that these points are closest to the hyperplane that separates the classes, and if you can learn to classify near the boundary, you are set. In using this method, you can also sometimes discover mislabeling. (The RMSE method we talk about above doesn’t interrogate the Y, taking the labels as given.)

Another way to answer the question is to use model interpretation tools to figure out “why” the models are making errors. For instance, you could find that the reason why the model is making errors is because of confounding. Famously, for instance, a cat vs. dog classifier can merely be an outdoor vs. indoor classifier. And if we see the model using confounding features like the background in consideration, we could a) better label the data to segment out dogs and cats from the background, b) introduce paired examples such that the only thing different between any two images is strictly presence or absence of a dog/cat.

]]>Sinn Féin and Fianna Fáil have said that activists posed as members of a polling company and went door-to-door to canvass the opinions of voters.

https://amp.rte.ie/amp/1227134/The rationale is simple. If you pose as an SF worker, you are likely to be met with shut doors or opinions in favor of SF got under slight duress. Is it a bridge too far or is it a harmless lie? More generally, do we use the same moral reasoning paradigm for violations by co-partisans and opposing partisans? My hunch is that for such kinds of violations we use a deontological framework for opposing partisans and a consequential one for co-partisans. The framework we use may switch depending on the circumstance. One way to test it would be to do a survey experiment with the above news article, switching parties. To get a better baseline, it may be useful to do three conditions: party_a, party_b, consumer_brand, e.g., Coke, etc.

]]>“To get roughly 70% of the planet’s population inoculated by April, the IMF calculates, would cost just $50bn. The cumulative economic benefit by 2025, in terms of increased global output, would be $9trn, to say nothing of the many lives that would be saved.”

https://www.economist.com/leaders/2021/06/09/the-west-is-passing-up-the-opportunity-of-the-centuryThe Economist frames this as an opportunity for G7. And it is. But it is also an opportunity for third-world countries, which plausibly can borrow $50bn given the return on investment. The fact that money hasn’t already been allocated poses a puzzle. Is it because governments think about borrowing decisions based on whether or not a policy is tax revenue positive (which a 180x return ought to be even with low tax collection and assessment rates)? Or is it because we don’t have a marketplace where we can transact on this information? If so, it seems like an important hole.

Here’s another way to look at this point. Among countries where the profits mostly go to a few, why do the people at the top not come to invest together so that they can harvest profits later? Brunei is probably an ok example.

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