# What’s the difference between statistics and machine learning?

I had an interesting discussion at work today (among people I think would all call themselves statisticians!) about the distinction(s) between statistics and machine learning. It is something I am still not very clear about myself, and have yet to find a satisfactory answer. It’s a topic that seems to get particularly some statisticians hot under the collar, when machine learning courses apparently claim that methods statisticians tend to think are part of statistics are in fact part of machine learning:

This post is certainly not going to tell you what the difference machine learning and statistics is. Rather I hope that it spurs readers of the post to help me understand their differences.

Historically I think it’s the case that machine learning algorithms were developed in computer science departments of universities, whereas statistics was developed within mathematics or statistics departments. But this is merely about the historical origins, rather than any fundamental distinction.

Machine learning (about which I know a lot less) tends I think to focus on algorithms, and a subset of these has as their objective to prediction some outcome based on a set of inputs (or predictors as we might call them in statistics). In contrast to parametric statistical models, these algorithms typically do not make rigid assumptions about the relationships between the inputs and the outcome, and therefore can perform well then the dependence of the outcome on the predictors is complex or non-linear. The potential to capture such complex relationships is however not unique to machine learning – within statistical models we have flexible parametric / semiparametric, and even non-parametric methods such as non-parametric regression.

The Wikipedia page on machine learning states:

Machine learning and statistics are closely related fields in terms of methods, but distinct in their principal goal: statistics draws population inferences from a sample, while machine learning finds generalizable predictive patterns.

So statistics is about using sample data to draw inferences or learn about a wider population from which the sample has been drawn, whereas machine learning finds patterns in the data that can be generalised. It’s not clear from this quote alone to what machine learning will generalise to, but the natural thing that comes to mind is some broader collection or population which is similar to the sample at hand. So this apparent distinction seems quite subtle. Indeed the Wikipedia page goes on to say:

A core objective of a learner is to generalize from its experience.[2][17] Generalization in this context is the ability of a learning machine to perform accurately on new, unseen examples/tasks after having experienced a learning data set. The training examples come from some generally unknown probability distribution (considered representative of the space of occurrences) and the learner has to build a general model about this space that enables it to produce sufficiently accurate predictions in new cases.

To me, when one starts saying that the training data is considered representative of the space of occurrences, this sounds remarkably similar to the notion of the training data being a sample from some larger population, as would often be assumed by statistical models.

An interesting short article in Nature Methods by Bzdok and colleagues considers the differences between machine learning and statistics. The key distinction they draw out is that statistics is about inference, whereas machine learning tends to focus on prediction. They acknowledge that statistical models can often be used both for inference and prediction, and that while some methods fall squarely in one of the two domains, some methods, such as bootstrapping, are used by both. They write:

ML makes minimal assumptions about the data-generating systems; they can be effective even when the data are gathered without a carefully controlled experimental design and in the presence of complicated nonlinear interactions. However, despite convincing prediction results, the lack of an explicit model can make ML solutions difficult to directly relate to existing biological knowledge.

The claim that ML methods can be effective even when the data are not collected through a carefully controlled experimental design is interesting. First it seems to imply that statistics is mainly useful only when the data are from an experiment, something which epidemiologists conducting observational studies or survey statisticians conducting national surveys would presumably take issue with. Second it seems to suggest that ML can give useful predictions for the future with minimal assumptions on how the training data arose. This seems problematic, and I cannot see why the importance of how the data arose should be different depending on whether you use a statistical method or a machine learning method. For example, if we collect data on the association between an exposure (e.g. alcohol consumption) and an outcome (e.g. blood pressure) from an observational (non-experimental) study, I cannot see how machine learning can without additional assumptions overcome the probable issue of confounding.

As I wrote earlier, I do not have a well formed view of the distinction between machine learning and statistics. My best attempt is the following: statistics starts with a model assumption, which could be more rigid (i.e. simple parametric models) or less so (i.e. semiparametric or nonparametric) which describes aspects of the data generating distribution in a way that answers a question of interest or could be used for prediction for the population from which the sample has been drawn. Uncertainty about parameters in the model or about predictions can be quantified. Machine learning doesn’t assume a model, but is a collection of algorithms for building prediction rules or finding clustering in data. The prediction rules should work well at prediction future data. Uncertainty about predictions or clustering is presumably not possible or harder, given the absence of a model.

Please add your views in a comment and help me understand the distinction(s).

I posted this to the website Hacker News last night, and it picked up some interest. As a consequence there are lots of interesting comments from people available on the its Hacker News thread.

### 9 thoughts on “What’s the difference between statistics and machine learning?”

1. Interesting points. I’ll think about this further, two things that come to mind:

1) “I think it’s the case that machine learning algorithms were developed in computer science”. I hear this a lot, but I’m not sure it is as generally true as it seems. For instance, someone recently pointed out to me that Leo Breiman (developer of methods such as random forest that are typically labeled as “machine learning”) was a trained mathematical statistician and, indeed, a professor of Statistics.

2) “The key distinction they draw out is that statistics is about inference, whereas machine learning tends to focus on prediction”, I think this thought echos the idea of the famous “two cultures” paper (by the same Breiman): http://www2.math.uu.se/~thulin/mm/breiman.pdf. I don’t think this idea aged very well. For instance, the field of clinical prediction has been dominated by statistical models (and machine learning is yet to prove itself here: https://www.sciencedirect.com/science/article/pii/S0895435618310813); on the other hand the “superlearners” (van der Laan and others) seem to become more popular among causal inference folks. It seems the superlearning is something that one could classify as machine learning technique.

The only real difference I can spot is with people calling themselves statisticians or machine learners. These groups, however, share many of their methods (so classifying a method a machine learning or statistical modeling easily triggers a fight) and often seem to share goals (understanding and prediction).

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2. ML is a collection of dubious statistical techniques

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3. In my opinion, Machine Learning is “applied statistics” in a business context. By operationalizing some data source(s) and applying a statistical model, we attempt to gain insights that will impact our future decisions & actions in order to make some money or provide another benefit.

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4. There is another offering by MIT/edx (https://micromasters.mit.edu/ds/) that takes a rigorous bottom-up approach by starting with fundamentals — a course on Probability taught by Prof. Tsitsikilis and a course on Statistics by Prof. Rigolette. These are grad level courses using serious multivariate calculus, definitely not for the weak-hearted. Building on these solid foundations it expands on to two more courses: one on Data Science for Social Scientists that uses R heavily, and another course on ML with Python: from Linear Models to Deep Learning. The DS for Social Scientists course could be structured better, but it is a course common to two programs and ultimately ends up opening one’s eyes to serious applications of stats and ML to social problems that actually improves people’s lives.

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5. Can we say that fitting the models to optimize a metric on a blind sample specific to machine learning?

In this case you design your procedure to ensure a level of generalization power in prediction.

The tools you use can be from the ‘statistics’ world or other algorithms and they are all judged based on this performance metric.

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6. It is very simple, and it’s more related to the amount of information the algorithm needs to make a prediction. Take for example Presidential elections. With a single dimension, just analyzing one value like voter polls, there is no doubt both are similar. But in my opinion, something that machine learning can do and statistics can’t, is considering many variables like, economy, what party was elected before, race, and more environmental variables you can add the better to detect patterns. Yes both use past behavior but statistics gets everything as a whole for a single dimension variable, meanwhile ML detect patterns in each individual case with many variables.

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7. @Kyle lahnakoski
“ML is a collection of dubious statistical techniques”
I’d rather say that your conclusion is a dubious one, since ML algorithms often perform much better in prediction than standard statistical models, in many problems.

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8. @Kyle lahnakoski
“ML is a collection of dubious statistical techniques”
That’s a dubious statement in itself, since ML often performs better in prediction than standard statistical models.

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9. Machine learning is statistics with an overzealous public relations manager.

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