Surprise Bits

The Average Hides the Row

A mean loss is exact, but it can hide which row supplied the large contribution. This lesson keeps the row losses visible before summarizing.

highlighted = computed this step

Show the row losses

Use 3 displayed rows with exact losses 1, 1, and 7 bits. These are pinned row losses for this summary lesson.

row bits=(1,1,7)\text{row bits}=(1,1,7)
The average hides the rowExact row-loss bits show which row drives this mean.the average hides the rowrowrow loss bitsbits barrunning sumwhat it showsrow 11#1small rowrow 21#2small rowrow 37#######9row that moves the meansum=9 bitsmean=3 bits over 3 rowsrow 3 contributes 7 of the 9 bitsassigned exact row losses; loss-summary arithmetic; NOT accuracy; NOT calibration;NOT training; NOT learning; NOT generalization; NOT probability truth; NOT modelquality

Add the exact sum

The first two rows add 1 bit each. The third row adds 7 bits, so the exact sum is 9 bits.

1+1+7=91 + 1 + 7 = 9
The average hides the rowExact row-loss bits show which row drives this mean.the average hides the rowrowrow loss bitsbits barrunning sumwhat it showsrow 11#1small rowrow 21#2small rowrow 37#######9row that moves the meansum=9 bitsmean=3 bits over 3 rowsrow 3 contributes 7 of the 9 bitsassigned exact row losses; loss-summary arithmetic; NOT accuracy; NOT calibration;NOT training; NOT learning; NOT generalization; NOT probability truth; NOT modelquality

Average the rows

The mean is 9 bits divided by 3 rows, which is exactly 3 bits.

93=3{9\over3}=3
The average hides the rowExact row-loss bits show which row drives this mean.the average hides the rowrowrow loss bitsbits barrunning sumwhat it showsrow 11#1small rowrow 21#2small rowrow 37#######9row that moves the meansum=9 bitsmean=3 bits over 3 rowsrow 3 contributes 7 of the 9 bitsassigned exact row losses; loss-summary arithmetic; NOT accuracy; NOT calibration;NOT training; NOT learning; NOT generalization; NOT probability truth; NOT modelquality

The row is still visible

The mean 3 is exact, but the table shows row 3 contributed 7 of the 9 bits. This is loss-summary arithmetic only: NOT accuracy, NOT calibration, NOT training, NOT learning, NOT generalization, NOT probability truth, NOT model quality.

row 3 contributes 7/9\text{row }3\text{ contributes }7/9
The average hides the rowExact row-loss bits show which row drives this mean.the average hides the rowrowrow loss bitsbits barrunning sumwhat it showsrow 11#1small rowrow 21#2small rowrow 37#######9row that moves the meansum=9 bitsmean=3 bits over 3 rowsrow 3 contributes 7 of the 9 bitsassigned exact row losses; loss-summary arithmetic; NOT accuracy; NOT calibration;NOT training; NOT learning; NOT generalization; NOT probability truth; NOT modelquality