Beyond torch.median: Alternative Approaches for Median Calculation in PyTorch

Purpose

• The median is the "middle" value when the data is sorted in ascending order.
• Calculates the median value(s) along a specified dimension of a PyTorch tensor.

Behavior

• Returns a namedtuple containing two elements:
  • values: A tensor containing the median value(s) for each row (along dim).
  • indices: A tensor containing the index(es) of the median element(s) for each row (along dim).
• Takes an optional dim argument (defaulting to 0) that specifies the dimension along which to compute the median.
• Operates on a single tensor input.

Example

import torch

# Create a sample tensor
data = torch.tensor([[1, 7, 3], [4, 5, 6], [2, 8, 9]])

# Calculate median along the first dimension (rows)
medians, indices = torch.median(data, dim=0)

print(medians)  # tensor([3., 6., 7.])
print(indices)  # tensor([1, 1, 0])

• indices contains the index of the median element in each row: [1, 1, 0]. For example, in the first row [1, 7, 3], the median is 3, which is at index 1.
• medians contains the median for each row: [3, 6, 7].

• torch.median is generally less performant than vectorized operations like sorting and slicing, especially for large tensors. Consider alternative approaches for performance-critical scenarios.
• If input contains NaN values (Not a Number), use torch.nanmedian instead, which excludes NaNs from the calculation.
• For tensors with an even number of elements along the specified dimension, torch.median returns the lower of the two middle values.

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Calculating Median of the Entire Tensor

import torch

# Create a sample tensor
data = torch.tensor([3, 1, 4, 1, 5])

# Calculate median without specifying a dimension (across all elements)
median = torch.median(data)

print(median)  # tensor(3.)

In this case, dim is omitted (or set to None), so the median is calculated across all elements, resulting in a single value (3).

Calculating Median Along Multiple Dimensions

import torch

# Create a 3D sample tensor
data = torch.arange(24).reshape(2, 3, 4)

# Calculate median along the second dimension (columns)
medians, indices = torch.median(data, dim=1)

print(medians.shape)  # torch.Size([2, 4])
print(indices.shape)   # torch.Size([2, 4])

# Now medians and indices contain values for each row (across columns)

This example calculates the median along columns (dimension 1). medians and indices will have the same shape ([2, 4]), with medians for each row (across columns) and corresponding indices.

import torch

data = torch.tensor([[1, 7, 3], [4, 5, 6]])

# Calculate median along the first dimension, keeping the dimension
medians, indices = torch.median(data, dim=0, keepdim=True)

print(medians.shape)  # torch.Size([1, 3])
print(indices.shape)   # torch.Size([1, 3])

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torch.quantile for Median with More Control

• You can specify the desired quantile (between 0 and 1) to calculate other percentiles as well.
• This offers more control over handling edge cases like even-numbered elements.
• Use torch.quantile with q=0.5 to calculate the median.

import torch

data = torch.tensor([1, 7, 3])

# Calculate median using quantile
median = torch.quantile(data, q=0.5)

print(median)  # tensor(3.)

Custom Median Function (For Specific Use Cases)

• This might be useful for handling specific edge cases or incorporating additional logic.
• If you need more customization or control over median calculation, consider writing a custom function.

Sorting and Slicing (Performance-Critical Scenarios)

• This can be more efficient than torch.median in some cases. However, it requires more manual steps.
• For very large tensors where performance is crucial, consider using vectorized operations like sorting and slicing.

import torch

data = torch.randn(10000)

# Calculate median using sorting and slicing (manual approach)
sorted_data, _ = torch.sort(data, dim=0)
median_index = sorted_data.shape[0] // 2
median = sorted_data[median_index]

# This approach might be faster for large tensors but requires more steps

• For very large tensors and performance-critical scenarios, explore vectorized operations like sorting and slicing, but be aware of the additional manual steps involved.
• Consider a custom function if you have specific requirements or logic to incorporate.
• Use torch.quantile if you need more control over handling even-numbered elements or want to calculate other percentiles.
• If you need basic median calculation and performance isn't a major concern, torch.median is a good choice.