Features, Targets, and Prediction Time

Definition The unit of observation is what one row of a learning table represents, the entity together with the prediction made about it, for example one parcel booking with one prediction at the moment the booking is accepted. It fixes the row key, the fields that identify a row, and it fixes what counts as one more observation. Rows are not automatically independent. Two rows can share a customer, an address, a route or a day, and then part of the information they carry is shared. The sampling frame, the set of cases from which the rows were drawn, limits the population that conclusions from the table can describe.

Definition A feature is an input variable of the model, a field defined for every observation whose value is available at the prediction time. With $n$ observations and $p$ features, $x_{ij}$ denotes the value of feature $j$ for observation $i$. The feature vector of observation $i$ is

with the features in a fixed order, and the design matrix, or feature matrix, $X$ is the $n \times p$ matrix whose row $i$ is $\mathbf{x}_i^{\top}$. Numerical features record quantities, such as a distance. Categorical features record membership in a category and enter $X$ through a numerical encoding. A field with two categories is often coded 0 and 1, a binary encoding, while fields with more categories need more care, since numbering them 1, 2, 3 would invent an order they may not have.

Definition The target is the quantity or category the model is meant to predict, fixed by a precise rule before any labels are made. A label is the value of the target recorded for one observation. The labels form the target vector $\mathbf{y} = (y_1, \dots, y_n)^{\top}$, and $y_i$ must belong to the same observation as row $i$ of $X$. For the lateness task, let $d_i$ be the original promised deadline of booking $i$ and $t_i$ its delivery time. For a booking with a trustworthy delivery record,

Reliable evidence that a parcel was not delivered by its deadline also gives $y_i = 1$. A booking with no delivery record while its deadline is still ahead, or with a missing delivery record after the deadline and no such evidence, is unresolved, and that state is kept apart from both 0 and 1.

Definition The prediction time of an observation is the moment at which its prediction must be made. A field may enter the features only if its value is available to the prediction system by that moment, which depends on when the value reaches the system and not only on when the underlying event happened. The prediction horizon is the length of time from the prediction time to the time the target refers to. In the lateness task the prediction time of booking $i$ is its acceptance time $b_i$ and the target refers to the deadline $d_i$, so the horizon is $d_i - b_i$, which can differ from booking to booking.

Definition Target leakage occurs when a feature carries information about the target that would not be available at prediction time, usually because it is recorded after the prediction time or is computed from the outcome itself. A model trained with such a feature can look accurate on historical data and then fail in use, because for a new case the feature is not yet known when the prediction is made. Target leakage is one form of data leakage, the wider problem of information that would not be available in use reaching a model or its evaluation, treated in Data Leakage and Honest Splitting.

Definition A data schema is a written description of every field in a learning table, stating its meaning, type, unit, allowed values, treatment of missing values and the time at which it becomes available. It also states the unit of observation and the row key, how duplicate records are handled, how outcomes are matched to bookings, and the exact rule that defines the target, including its edge cases.