metrax.DCGAtK

class metrax.DCGAtK(total: Array, count: Array)

Bases: Average

Computes Discounted Cumulative Gain at k metric.

DCG tells how good a list of search results or recommendations is, based on the relevance of the items and their positions in the list.

This implementation calculates \(DCG@k\) based on the following formula:

\[DCG@K(y, s) = \sum_{i=1}^{K} \text{gain}(y_i) \times \text{rank_discount}(\text{rank}(s_i))\]

where

• \(y_i\) is the relevance label from the labels,

• \(s_i\) is its score from the prediction,

• \(\text{rank}(s_i)\) is the 1-based rank of item \(i\).

• \(\text{gain}(y_i) = 2^{y_i} - 1\).

• \(\text{rank_discount}(\text{rank}(s_i)) = \frac{1}{\log_2(\text{rank}(s_i) + 1)}\).

We get the final formula:

\[DCG@K(y, s) = \sum_{i=1}^{K} \frac{2^{y_i} - 1}{\log_2(\text{rank}(s_i) + 1)}\]

__init__(total: Array, count: Array) → None

Methods

__init__(total, count)
compute()	Computes final metrics from intermediate values.
compute_value()	Wraps compute() and returns a values.Value.
empty()	Returns an empty instance (i.e. .merge(Metric.empty()) is a no-op).
from_fun(fun)	Calls cls.from_model_output with the return value from fun.
from_model_output(predictions, labels, ks)	Creates a DCGAtK metric instance from model output.
from_output(name)	Calls cls.from_model_output with model output named name.
merge(other)	Returns Metric that is the accumulation of self and other.
reduce()	Reduces the metric along it first axis by calling _reduce_merge().
replace(**updates)	Returns a new object replacing the specified fields with new values.

Attributes

total
count

classmethod from_model_output(predictions: Array, labels: Array, ks: Array) → DCGAtK

Creates a DCGAtK metric instance from model output.

__init__(total: Array, count: Array) → None

replace(**updates)

Returns a new object replacing the specified fields with new values.