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Let's say you have multiple sources of observation weights for a dataset. For example, you have a $[0,1]$ weight coming from the label's certainty ($w_c$) and another one coming from its recency ($w_t$). What would be the best way to combine those into a single number to be used when training a classifier?

Some options I have considered:

  • Product: $w_cw_t$
  • Arithmetic mean: $\frac{w_c+w_t}{2}$
  • Geometric mean: $\sqrt{w_cw_t}$
  • Harmonic mean: $\frac{2w_cw_t}{w_c+w_t}$

All of the above make (intuitive) sense on some level. Any ideas as to what is best practice or at least some pointers to literature on the topic?

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