Find Cross Entropy Loss by using R/Python/Matlab... programming.

Solutions without programming codes will not receive full credit. Round three decimal places. Answer = [Fill in the blank],

Question

Find Cross Entropy Loss by using R/Python/Matlab... programming.

Solutions without programming codes will not receive full credit. Round three decimal places. Answer = [Fill in the blank],

BlackTom AI · Accepted Answer

We start by identifying the setup: a binary cross-entropy loss computed for four samples, with each sample contributing -[ y ln(p) + (1 - y) ln(1 - p) ]. The table provides for each sample: the true label y and the predicted probability p = f_w,b(x).

For each row, compute the per-sample loss: 
- Row 1: y = 1, p = 0.8. Loss = -[1 * ln(0.8) + (0) * ln(0.2)] = -ln(0.8) ≈ 0.2231435513. 
- Row 2: y = 0, p = 0.1. Loss = -[0 * ln(0.1) + 1 * ln(0.9)] = -ln(0.9) ≈ 0.1053605157. 
- Row 3: y = 1, p = 0.7. Loss = -[1 * ln(0.7) + (0) * ln(0.3)] = -ln(0.7) ≈ 0.3566749439. 
- Row 4: y = 0, p = 0.3. Loss = -[0 * ln(0.3) + 1 * ln(0.7)] = -ln(0.7) ≈ 0.3566749439.

Sum of all four losses: 0.2231435513 + 0.1053605157 + 0.3566749439 + 0.3566749439 = 1.0418539548.

Option 1 corresponds to the full-precision sum, approximately 1.0418539548, which rounds to 1.041854 when expressed with six decimal places. 
Option 2 rounds this total to three decimal places, giving 1.042.

Now, evaluating the two provided choices: 
- Choice 1: 1.041854. This matches the precise sum rounded to six decimals, so it is the full-precision representation of the total loss. 
- Choice 2: 1.042. This is the same total rounded to three decimal places, which aligns with the instruction to round to three decimals.

In terms of potential misconceptions, note that:
- If someone expects integer or a different rounding, they may mis-handle the log terms or the rounding step. 
- The cross-entropy loss for each sample is always nonnegative and the total is the sum of the nonnegative per-sample losses; here all terms are finite because p is strictly between 0 and 1.

Thus, both options are different representations of the same total loss, one at higher precision (1.041854) and one at three-decimal precision (1.042).

STATISTICAL DEEP LEARNING DONE_2025 Mid-term Close-book Exam

Find Cross Entropy Loss by using R/Python/Matlab... programming. Solutions without programming codes will not receive full credit. Round three decimal places. Answer = [Fill in the blank],

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