fix(julia): add init=0 to sum() calls in build_metrics to handle empty generators

[dajiaohuang]

Fixes #434 - When demo_threshold_tuning produces all-zero predictions, the generator comprehensions in build_metrics become empty, causing ArgumentError: reducing over an empty collection is not allowed.

Adding init=0 to each sum() call prevents the crash when the model predicts zero positive cases.

[coderabbitai]

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Reviewing files that changed from the base of the PR and between 14b0efb and 1e677ad.

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• BACKERS.md

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• BACKERS.md

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📝 Walkthrough

Walkthrough

Added Backer sponsorship documentation and explicit zero initialization for logistic-regression confusion-matrix sums.

Changes

Backer documentation

Layer / File(s)	Summary
Backer sponsorship documentation BACKERS.md	Documents the Backer tier, sponsorship link, and current absence of listed backers.

Logistic-regression metrics fix

Layer / File(s)	Summary
Confusion-matrix sum initialization phases/02-ml-fundamentals/03-logistic-regression/code/main.jl	Initializes tp, tn, fp, and fn sums with init=0.

Estimated code review effort: 2 (Simple) | ~10 minutes

Merge Risk: ⚪ Minimal · up to d346c

The change adds empty-input fallbacks for logistic-regression metric sums so strict threshold tuning can complete when predictions are all zero. No current merge-blocking risk is identified.

🚥 Pre-merge checks | ✅ 4 | ❌ 1

❌ Failed checks (1 warning)

Check name	Status	Explanation	Resolution
Out of Scope Changes check	⚠️ Warning	The Julia fix is in scope, but the added BACKERS.md sponsorship documentation is unrelated to issue #434 and the stated bug-fix objective.	Remove BACKERS.md from this pull request, or provide a linked issue and explicit objective that requires the sponsorship documentation change.

✅ Passed checks (4 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title clearly identifies the Julia fix and the specific change: adding init=0 to sum() calls in build_metrics for empty generators.
Description check	✅ Passed	The description directly explains issue #434, the empty-generator failure, and how init=0 prevents the crash.
Linked Issues check	✅ Passed	The build_metrics changes satisfy issue #434 by adding init=0 to all four sum() calls, preventing failures when strict thresholds produce empty generator comprehensions.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check. Docstring coverage is scoped to functions touched by this diff. Analyzed 0 functions across 0…

✨ Finishing Touches 💡 1

🛠️ Fix failing CI checks 💡

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• Commit on current branch

🧪 Generate unit tests (beta)

• Create PR with unit tests

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Actionable comments posted: 1

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Inline comments:
In `@BACKERS.md`:
- Line 3: Update the sponsor link in BACKERS.md to reference the repository-root
file as SPONSORS.md instead of ../SPONSORS.md.

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ℹ️ Review info

⚙️ Run configuration

Configuration used: Path: .coderabbit.yaml

Review profile: CHILL

Plan: Team

Run ID: cc3b2b02-e0e7-4b01-b220-bc15c4ffca7a

📥 Commits

Reviewing files that changed from the base of the PR and between a56b4b8 and 14b0efb.

📒 Files selected for processing (2)

• BACKERS.md
• phases/02-ml-fundamentals/03-logistic-regression/code/main.jl

Included review availability: Your plan provides up to 10 included reviews per hour; 9 remain after this review.

[dajiaohuang]

Fixed the repository-root link in BACKERS.md: ../SPONSORS.md -> SPONSORS.md (the target exists at the repository root). Pushed as commit 8b24f56 to fix/445-backers-md, which updates both PRs #448 and #449. git diff --check passes.

[dajiaohuang]

Fixed the BACKERS.md link in commit 1e677ad: the repository root's SPONSORS.md is now linked as SPONSORS.md instead of ../SPONSORS.md. Validation: git diff --check passed.

[dajiaohuang]

Separated the unrelated sponsorship change from this PR in commit d346cf4. This branch now changes only the Julia metric sums for #434. Validation: git diff --check passed; Julia is unavailable in this Windows workspace.