[Enhancement] Native PyTorch Implementation for `SpearmanRankCorrelation`

Description

The current implementation of SpearmanRankCorrelation in ignite.metrics.regression is a wrapper around scipy.stats.spearmanr and inherits from EpochMetric. This introduces several limitations:

Hard Dependency:
It requires scipy to be installed. As shown in the reproduction below, the metric cannot even be initialized in a pure PyTorch environment.

Memory Inefficiency:
As an EpochMetric, it stores all predictions and targets in a list (O(n) memory complexity), which can lead to Out-Of-Memory (OOM) issues on large datasets.

Performance Bottleneck:
Data must be moved to the CPU and converted to NumPy/Scipy, preventing the metric from running natively on accelerators such as GPU/TPU.

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Steps to Reproduce (In Environment Without SciPy)

import torch
from ignite.metrics.regression import SpearmanRankCorrelation

# This raises ModuleNotFoundError immediately
metric = SpearmanRankCorrelation()

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Actual Output

ModuleNotFoundError: This module requires scipy to be installed.

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Proposed Improvement

I propose a Native PyTorch implementation of SpearmanRankCorrelation that:

Remove the SciPy Dependency

Use torch.argsort or a unique/cumsum-based ranking logic to compute ranks directly in PyTorch.

Use Streaming Accumulation

Instead of relying on EpochMetric, accumulate the necessary sums for the Pearson correlation of ranks incrementally.
This reduces memory complexity from:

O(n) → O(1)

(or O(batch) depending on the ranking approach).

Device Agnostic

Keep all computations on the original device (CPU/GPU) so the metric can run efficiently on accelerators.

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Hi @vfdev-5, I'd like to work on refactoring this as part of my GSoC contributions. I believe making this PyTorch-native will significantly improve the portability and performance of Ignite's regression suite. Waiting for your thoughts! 😊.

Start with SpearmanRankCorrelation in ignite.metrics.regression and inspect its current EpochMetric and scipy.stats.spearmanr usage. Review the ranking and accumulation requirements in the issue before deciding how ties and batches should be handled. Done means the metric works without SciPy, avoids storing the full epoch, and keeps computation on the input device.