Where does pooling collide?

The act of combining separate results, each from its own sample or experiment, into a single summary estimate, usually as a weighted average that gives more weight to the more precise results. Cochran's 1937 Problems arising in the analysis of a series of similar experiments worked out how to combine findings from a run of comparable trials, and his 1954 The combination of estimates from different experiments set the weighting and heterogeneity ideas that later meta-analysis relies on. The referent here is a statistical average of numbers drawn from many studies, judged by its variance and by whether the studies agree, and it has nothing to do with sharing insurance risk or shrinking an image inside a neural network.[1][2]

Unit

One weighted summary estimate built from many study-level estimates

Recovery means

Not applicable

Measured by

Computed as an inverse-variance weighted mean, with a heterogeneity statistic reporting how far the studies disagree

The grouping of many independent risks so that, although any one loss is uncertain, the total across the group is far steadier and can be covered by shared premiums: this steadiness is what makes insurance possible. Arrow's 1963 Uncertainty and the welfare economics of medical care analysed how pooling and shared payment let people trade an uncertain large loss for a fixed small cost, and traced where such markets break down. The referent is a group of people or contracts sharing exposure to loss, measured in money and probability, and it is a different thing from averaging study results or reducing the size of a feature map.[3]

Unit

A group of independent exposures whose losses are shared across members

Recovery means

Not applicable

Measured by

Assessed by the variance of the group's average loss, premiums, and loss ratios

A step in an image-recognition network that takes a small local patch of the internal representation and replaces it with a single summary value, such as the largest value in that patch, which shrinks the representation and makes it less sensitive to exactly where a feature sits. Fukushima's 1980 Neocognitron introduced these summarising layers so a pattern could be recognised even when shifted in position, and LeCun and colleagues' 1998 Gradient-based learning applied to document recognition made the step standard in trainable convolutional networks. The referent is a fixed arithmetic operation inside a model, sized in pixels and channels, not a shared insurance risk or an average of study results.[4][5]

Unit

One summary value standing in for a local patch of a feature map

Recovery means

Not applicable

Measured by

Defined by its window size, stride, and rule, such as taking the maximum or the mean of the patch