NDCG#

class ignite.metrics.rec_sys.NDCG(top_k, ignore_zero_hits=True, relevance_threshold=1.0, gain_function='exp_rank', output_transform=<function NDCG.<lambda>>, device=device(type='cpu'), skip_unrolling=False)[source]#

Calculates the Normalized Discounted Cumulative Gain (NDCG) at k for Recommendation Systems.

For a step-by-step guide on how to use this metric, please refer to the NDCG Tutorial <https://github.com/pytorch-ignite/examples/tree/main/tutorials/intermediate/ndcg-metric-tutorial.ipynb>

NDCG measures the quality of ranking by considering both the relevance of items and their positions in the ranked list. It compares the achieved DCG against the ideal DCG (IDCG) obtained by sorting items by their true relevance.

\text{NDCG}@K = \frac{\text{DCG}@K}{\text{IDCG}@K}

where:

\text{DCG}@K = \sum_{i=1}^{K} \frac{2^{\text{rel}_i} - 1}{\log_2(i + 1)}

and $\text{rel}_i$ is the relevance score of the item at position $i$ in the ranked list (1-indexed).

update must receive output of the form (y_pred, y).
y_pred is expected to be raw logits or probability score for each item in the catalog.
y is expected to contain relevance scores (can be binary or graded).

Relevance Types: - Binary relevance: Labels are either 0 (not relevant) or 1 (relevant) - Graded relevance: Labels can have multiple levels (e.g., 0-4 scale)

Common graded scales: - 0: Not relevant - 1: Marginally relevant - 2: Relevant - 3: Highly relevant - 4: Perfectly relevant

The NDCG formula handles both types through the gain function: 2^relevance - 1. Higher relevance scores contribute more to the metric.
y_pred and y are only allowed shape $(batch, num\_items)$ .
returns a list of NDCG ordered by the sorted values of top_k.

Parameters:

top_k (list[int]) – a list of sorted positive integers that specifies k for calculating NDCG@top-k.
ignore_zero_hits (bool) – if True, users with no relevant items (ground truth tensor being all zeros) are ignored in computation of NDCG. If set False, such users are counted with NDCG of 0. By default, True.
relevance_threshold (float) – minimum label value to be considered relevant. Defaults to 1, which handles standard binary labels and graded relevance scales (e.g. TREC-style 0-4) by treating any label >= 1 as relevant. Items below this threshold contribute 0 to DCG/IDCG calculations.
gain_function (str) – Gain function for relevance scores. Options: - 'exp_rank': 2^relevance - 1 (emphasizes high relevance, default) - 'linear_rank': relevance (simpler, linear scale) Defaults to 'exp_rank'.
output_transform (Callable) – a callable that is used to transform the Engine’s process_function’s output into the form expected by the metric. The output is expected to be a tuple (prediction, target) where prediction and target are tensors of shape (batch, num_items).
device (str | device) – specifies which device updates are accumulated on. Setting the metric’s device to be the same as your update arguments ensures the update method is non-blocking. By default, CPU.
skip_unrolling (bool) – specifies whether input should be unrolled or not before being processed. Should be true for multi-output models..

Examples

To use with Engine and process_function, simply attach the metric instance to the engine. The output of the engine’s process_function needs to be in the format of (y_pred, y). If not, output_tranform can be added to the metric to transform the output into the form expected by the metric.

For more information on how metric works with Engine, visit Attach Engine API.

from collections import OrderedDict

import torch
from torch import nn, optim

from ignite.engine import *
from ignite.handlers import *
from ignite.metrics import *
from ignite.metrics.clustering import *
from ignite.metrics.fairness import *
from ignite.metrics.rec_sys import *
from ignite.metrics.regression import *
from ignite.utils import *

# create default evaluator for doctests

def eval_step(engine, batch):
    return batch

default_evaluator = Engine(eval_step)

# create default optimizer for doctests

param_tensor = torch.zeros([1], requires_grad=True)
default_optimizer = torch.optim.SGD([param_tensor], lr=0.1)

# create default trainer for doctests
# as handlers could be attached to the trainer,
# each test must define his own trainer using `.. testsetup:`

def get_default_trainer():

    def train_step(engine, batch):
        return batch

    return Engine(train_step)

# create default model for doctests

default_model = nn.Sequential(OrderedDict([
    ('base', nn.Linear(4, 2)),
    ('fc', nn.Linear(2, 1))
]))

manual_seed(666)

ignore_zero_hits=True case

metric = NDCG(top_k=[1, 2, 3, 4])
metric.attach(default_evaluator, "ndcg")
y_pred=torch.Tensor([
    [4.0, 2.0, 3.0, 1.0],
    [1.0, 2.0, 3.0, 4.0]
])
y_true=torch.Tensor([
    [0.0, 0.0, 1.0, 1.0],
    [0.0, 0.0, 0.0, 0.0]
])
state = default_evaluator.run([(y_pred, y_true)])
print(state.metrics["ndcg"])

[0.0, 0.38..., 0.38..., 0.65...]

ignore_zero_hits=False case

metric = NDCG(top_k=[1, 2, 3, 4], ignore_zero_hits=False)
metric.attach(default_evaluator, "ndcg")
y_pred=torch.Tensor([
    [4.0, 2.0, 3.0, 1.0],
    [1.0, 2.0, 3.0, 4.0]
])
y_true=torch.Tensor([
    [0.0, 0.0, 1.0, 1.0],
    [0.0, 0.0, 0.0, 0.0]
])
state = default_evaluator.run([(y_pred, y_true)])
print(state.metrics["ndcg"])

[0.0, 0.19..., 0.19..., 0.32...]

New in version 0.6.0.

Methods

`compute`	Computes the metric based on its accumulated state.
`reset`	Resets the metric to its initial state.
`update`	Updates the metric's state using the passed batch output.

compute()[source]#

Computes the metric based on its accumulated state.

By default, this is called at the end of each epoch.

Returns:

the actual quantity of interest. However, if a Mapping is returned, it will be (shallow) flattened into engine.state.metrics when completed() is called.

Return type:

Any

Raises:

NotComputableError – raised when the metric cannot be computed.

reset()[source]#

Resets the metric to its initial state.

By default, this is called at the start of each epoch.

Return type:: None

update(output)[source]#

Updates the metric’s state using the passed batch output.

By default, this is called once for each batch.

Parameters:: output (tuple[torch.Tensor, torch.Tensor]) – the is the output from the engine’s process function.
Return type:: None

NDCG#

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