Understanding NumPy’s np.mean() Function

Photo by Roman Synkevych on Unsplash

The reason I became curious about the np.mean() function is that I realized I could easily calculate ratios without directly dividing, thanks to this function. This discovery highlighted how useful it is for computing conditional probabilities without complex calculations. In data analysis tasks, especially where ratios are frequently handled, this can be extremely helpful.

Building on this, I wrote some code to calculate Conditional Entropy, as shown in the example below:

def compute_conditional_entropy(Xdata, ydata):
    """Return the conditional entropy H(Y|X) of ydata given the series (i.e. 'column') Xdata.    - Xdata is a series (e.g., a single column) from a pandas DataFrame, e.g. X['long petal']
    - ydata are the associated labels
    Returns the conditional entropy H(Y|X).
    """
    entropy = 0
    for v in Xdata.unique():
        px = np.mean(Xdata == v)  # Using np.mean to calculate the conditional probability px
        entropy += px * compute_entropy(ydata[Xdata == v])
    return entropy

In this code, np.mean() is used to compute the conditional probability in a straightforward manner. For each unique value in Xdata, I easily obtain the ratio of conditions being true using np.mean(), which is then used to calculate the entropy of ydata.

A similar approach can be taken :

def compute_conditional_entropy2(Xdata, ydata):
    entropy = 0
    for v in Xdata.unique():
        px = Xdata.value_counts()[v] / len(Xdata)  # Directly calculating the ratio
	entropy += px * compute_entropy(ydata[Xdata == v])
    return entropy

Both methods compute conditional entropy, but the first method utilizing np.mean() is more concise and intuitive.

Explanation of np.mean() Function

def mean(a, axis=None, dtype=None, out=None, keepdims=<no value>):
    arr = asanyarray(a)
    
    # Check for empty input
    if arr.size == 0:
        raise ValueError("Empty array passed")
    
    # Compute the sum of array elements over a given axis
    arr_sum = arr.sum(axis=axis, dtype=dtype, out=out, keepdims=keepdims)
    # Count the number of elements
    arr_count = _count_reduce_items(arr, axis)
    # Divide sum by the number of elements to get the mean
    return arr_sum / arr_count

Key Parameter Descriptions

1. a: The input array or data structure, which is the target for mean calculation.
2. axis: Specifies the axis along which to compute the mean. By default, it computes the mean of all elements, but a specific axis can be specified for axis-wise calculation.
3. dtype: Specifies the data type of the output. By default, it matches the input data type, but it can be changed to prevent overflow during calculations.
4. out: An array to store the result. If specified, the mean result will be stored in this array.
5. keepdims: Decides whether to retain the dimensions of the result when computing the mean along the specified axis.

Use Cases

• Data Analysis: Used to find a representative value for an entire dataset or to compute the mean for specific subsets of data that meet certain conditions.
• Conditional Frequency Calculation: By passing a logical array like np.mean(Xdata == value, you can easily compute the ratio of true values.
• Image and Signal Processing: Used to calculate the mean of pixel values or signals, aiding in smoothing data or understanding fundamental characteristics.