## About this document

This document is intended to help students navigate the large amount of jargon, terminology, and acronyms encountered in the MDS program and beyond. There is also an accompanying blog post.

## Stat-ML dictionary

This section covers terms that have different meanings in different contexts, specifically statistics vs. machine learning (ML).

`regression`

- in ML,
`regression`

refers to predicting continuous outputs given input features, and classification refers to predicting categorical outputs given input features. - in statistics, both of the above tasks are referred to as
`regression`

. See also`supervised learning`

below.

`bias`

- even within statistics this word has a lot of meanings. See also bias of an estimator.
- in ML, when we have a trasformation of the form Wx+b (especially in linear models or neural networks) we refer to b as the “bias vector” or the elements of b as the biases. For example, see this Stack Overflow post. In statistics we would call this the “intercept”.
- in both fields, we talk about the bias-variance tradeoff, which is related to the tradeoff between overfitting and underfitting.

`parameter`

and `parametric`

- in statistics,
`parameter`

is used to describe probability distributions, like “the gamma distribution has a shape parameter and a scale parameter”. Thus, a`parametric model`

is a model using a parametric probability distribution. - in ML,
`parameter`

refers to the components (usually numbers) that are getting learned in a system. A`parametric model`

has a fixed number of parameters that is independent of the number of training examples, and typically doesn’t require the training examples to be stored in order to make predictions. An example would be linear regression, which involves one parameter per feature plus one more intercept parameter. On the other hand, k-nearest neighbours (KNN) would be an example of a nonparametric model as we don’t “distill” the training data into a fixed set of parameters. Another way to think about this is that, with KNN, the complexity of the model grows with the amount of training data. - the differences above can cause confusion. For example, a statistician might say a linear support vector machine (SVM) is not a parametric classifier because it is not based on an underlying probabilistic model. And yet, in ML, a linear SVM is parametric because we’re learning one parameter per dimension (in the primal formulation) to represent a linear boundary, and thus the number of parameters is fixed.

`early stopping`

- in ML, this refers to terminating an optimization routine before reaching convergence, which may mitigate overfitting (see here).
- in statistics, this sometimes refers to stopping an experiment early, particularly as in early stopping of clinical trials.

`hypothesis`

- in statistics, this word evokes hypothesis testing.
- in ML,
`hypothesis`

is sometimes used to refer to a particular model or decision boundary from the hypothesis space. E.g., we select a linear decision boundary from the hypothesis space of all possible hyperplanes; more complicated models have a larger hypothesis space.

`factor`

- in statistics,
`factor`

means categorical variable; factorial experiment means trying all possible combinations of two or more factors. - spanning both statistics and ML, we have factor analysis and factor graphs, which do not use
`factor`

in the sense described above (or in the same way as each other, even…). - (and in math, factor means one of several things being multiplied together.)

## Common acronyms

`FDR`

: False Discovery Rate`MC`

: Monte Carlo`MCMC`

: Markov chain Monte Carlo`OOP`

: object-oriented programming`IID`

: independent and identically distributed`RV`

: random variable`CDF`

: cumulative distribution function`ROC`

: receiver operating characteristic (curve) – sort of like precision/recall`MAP`

: maximum a posteriori (DSCI 553), not to be confused with`map`

of MapReduce (DSCI 513/525).`NLP`

: natural language processing`PCA`

: principal components analysis`EM`

: expectation maximization algorithm

### Acronyms that have more than one meaning

`S3`

: is an OOP paradigm in R (DSCI 524), and a storage service offered by Amazon (DSCI 525)`ML`

: Maximum Likelihood, Machine Learning`CI`

: Confidence Interval (DSCI 552), Continuous Integration (DSCI 524)`IP`

: Internet Protocol (as in IP address, DSCI 525), and Intellectual Property (as in software licenses, DSCI 524)`MDS`

: Master of Data Science, or Multi-Dimensional Scaling (DSCI 563).`PDF`

: Probability Density Function, or the file format, Portable Document Format. And at UBC it even has a third meaning: Post-Doctoral Fellow. So, at UBC, a PDF could save a plot of a PDF as a PDF!

## Compare and contrast

`discriminative`

vs. `generative`

A discriminative model directly models the probability of a given output given the inputs. On the other hand, with a generative model one starts from assumptions about how the data are generated (the “forward model”), and then performs inference about the model given the data (the “backward” step). The term `generative model`

itself has some ambiguity: in some contexts it includes the prior distribution (see below) and in other contexts it does not.

`Bayesian`

vs. `frequentist`

This represents a divide in the field of statistics and is related to, but not the same as, `discriminative`

vs. `generative`

above.
The Bayesian approach involves generative models and following Bayes’ Theorem. In this paradigm, one uses a generative model and attempts to compute a posterior distribution of the quantities of interest. See DSCI 553. The frequentist approach relates to hypothesis testing and does not involve prior distributions (which is both good and bad!). See DSCI 552.

`supervised`

vs. `unsupervised`

learning

In supervised learning you are given a set of input-output pairs and you try to model the relationship between them so that, given a new input, you can predict its output. In unsupervised learning there are no outputs. Your job is then to find some structure or pattern in the data. Sometimes it’s helpful to think of unsupervised learning as supervised learning except that you don’t know which features are the inputs and which are the output(s).

See also pattern recognition and semi-supervised learning.

`learning`

vs. `inference`

One (probably flawed) definition of `learning`

is updating your parameters given your data. The term `inference`

is perhaps slightly more specific, as it typically refers to inferring parameters of a model, either Bayesian or frequentist (see above). Here’s some more thoughts on this.

`mean`

vs. `expected value`

These are the same thing when referring to a random variable. However, `mean`

is sometimes used to refer to the sample mean. Therefore you can have the (sample) mean of the data you collected, but not the expected value. You can also discuss the mean of a bunch of numbers, like the mean (or average) of 1,2,3,4,5; but you wouldn’t say the expected value of these numbers.

## Definitions

### Error types

`Type I error`

: false positive, meaning it was actually negative but you said positive`Type II error`

: false negative, meaning it was actually positive but you said negative`sensitivity`

aka`recall`

: true positive rate. in math: 1 - (# of type II errors)/(# of true positives)`specificity`

: true negative rate. in math: 1 - (# of type I errors)/(# of true negatives)`precision`

aka`positive predictive value`

: 1 - (# of type I errors)/(# reported positives)

Note: `power`

and `sensitivity`

are highly related. But we tend to think of power as a conditional probability (a property of a statistical test) whereas we tend to think of sensitivity/recall as counts (a property of the predictions).

`lasso`

and `ridge`

regression

`Lasso regression`

means regression using L1 regularization.

`Ridge regression`

means regression using L2 regularization.

`shrinkage`

This can be thought of in terms of regularization. As an example, using L2 regularization in regression “shrinks” the coefficients. But it’s best not to interpret “shrink” as “make smaller in magnitude”. In Bayesian terms, a regularizer is viewed as a prior distribution. You could have a prior that believes the weights are near some non-zero value, and thus the prior “shrinks your beliefs to that value”. Thus, `shrinkage`

can be thought of as shrinking your uncertainty in the model parameters rather than literally making the weights smaller, although both become true when you are shrinking towards zero (which is almost always the case with regularization).

## Equivalence classes

In each equivalence class below, the terms tend to be used interchangeably (even if this isn’t a good idea!).

- regression coefficients = weights = parameters
- residual variance = noise variance
- inputs = predictors = features = explanatory variables = regressors = independent variables = covariates
- outputs = outcomes = targets = response variables = dependent variables. Also called a label if it’s categorical.
- Gaussian distribution = Normal distribution = bell curve
- sensitivity = recall (see Error types above)
- training = learning = fitting (sort of; depending on context)
- ordinary least squares (OLS) = linear least squares = least squares
- kriging = Gaussian process regression
- Bayesian network = Bayes net = directed graphical model = DAG graphical model
- Markov random field = Markov network = undirected graphical model

## Misc

This is not really a terminology issue, but note a connection between `collaborative filtering`

in recommender systems (ML) and `data imputation`

(statistics). Both are about estimating missing values. But imputation is more of a means to an end whereas in collaborative filtering finding those values is often the end itself.