Fehlklassifizierte Tupel betrachten, prüfen

• Welcher Klasse eigentlich zugehörig
• Welche Features geholfen hätte, diese Klasse zu erkennen

Schwierige Beispiele identifizieren.

Problem:

99% Accuracy, aber nur 0,5 % der Fälle true. Immer false, würde bessere Accuracy bringen.

Andere Evaluationsmetrik:

Precision/Recall

y = 1, wenn true

Predicted | 1 | True positive | False positive class | 0 | False negative | True negative

Precision: Anteil der tatsächlichen true positives von allen als true vorhergesagten.

$\frac{TP}{TP + FP}$

Recall: Von allen Patienten, welchen Anteil wurde korrekt als true erkannt?

$\frac{TP}{TP + FN}$

Für y = 0 ⇒ Recall würde 0 sein.

Angenommen, $h_\theta(x) >= 0.7$ anstelle von 0.5 und h_\theta(x) < 0.7 Dann hohe Präzision, niedrigerer Recall

Und umgekehrt wenn z.B. $h_\theta(x) >= 0.3$

Zum Vergleich von Precision/Recall.

Durchschnitt: $(P+R)/2$ nicht gut, da es möglich ist immer 1 oder 0 zu tippen.

$F_1$ Score : $2 * \frac{P*R}{P+R}$

• High Bias (underfit): High train and validation error (similar level, e.g. error of train: 15% | val: 16%)
• High Variance (overfit): Low train, high validation error (e.g. error of train: 1% | val: 11%)
• High Bias and High Variance: High train error, significant higher validation error (e.g. error of train: 15% | val: 30%)

Plot: Error / Degree of Polynom (with Training and cross validation error)

• Hohes $\lambda$: Underfit
• Niedriges $\lambda$: Overfit

Strategie: Increase regularization parameter stepwise (x2), and check what leads to lowest CV error. Then check for test set.

Plot: Error/m (training set size)

• Trainingsetfehler nimmt mit höherer Zahl an Trainingsbeispielen zu.
• Testsetfehler nimmt mit höherer Zahl an Trainingsbeispielen ab.

High bias:

• Trainingsetfehler nimmt mit höherer Zahl an Trainingsbeispielen zu, sehr nah an Testsetfehler.
• Testsetfehler nimmt mit höherer Zahl an Trainingsbeispielen ab, bleibt schneller auf einem Niveau.
• Generell höheres Fehlerniveau

Wenn von High bias betroffen, dann helfen mehr Trainingsdaten i.d.R nicht.

High variance:

• Trainingsetfehler nimmt mit höherer Zahl an Trainingsbeispielen zu, bleibt aber eher gering.
• Testsetfehler nimmt mit höherer Zahl an Trainingsbeispielen ab.
• Lücke zwischen Training und Crossvalidation error.

Wenn von High bias betroffen, dann helfen mehr Trainingsdaten i.d.R.

1. High Bias:
   • Additional features
   • Additional polynomial features
   • Decrease Lambda (regularization parameter)
2. High Variance:
   • More data
   • Smaller number of features
   • Increase Lambda (regularization parameter)

Recommended order:

1. High bias (look at train set performance):
   • Bigger network (more hidden layers / units)
   • Train longer
   • Advanced optimization algorithms
   • Better NN architecture
2. High variance (look at dev set performance)
   • More data (won't help for high bias problems)
   • Regularization
   • Better NN architecture

Bigger network almost always improves bias and more data improves variance (not necessarily a tradeoff between the two).

Best case performance if no false positives?

E.g. 100 mislabeled dev set examples, how many are dog images (when training a cat classifier). When 50% could be worth to work on problem (if error is currently at 10% ⇒ 5%).

Evaluate multiple ideas in parallel - Fix false positives - Fix false negatives - Improve performance on blurry images

Create spread sheet: Image / Problem

Result: Calc percentage of problem category (potential improvement “ceiling”)

General rule: Build your first system quickly, then iterate (dev/test setup, build system, bias/variance & error analyis)

DL algos: If % or errors is low and errors are random, they are robust

Add another col “incorrectly labeled” in error analysis spread sheet.

Principles when fixing labels:

• Apply same process to dev and test set (same distribution)
• Also see what examples algo got right (not only wrong)
• Train and dev/test data may come from different distribution (no problem if slightly different)

• 200.000 high qual pics
• 10.000 low qual blurry pics

• Option 1: Combine images, random shuffle in train/dev/test set
  • Advantage: Same distribution
  • Disadvantage: Lot of images come from high qual pics (most time is spend on optimizing for high qual pics)
• Option 2:
  • Train set: 205.000 with high and low qual; Dev & Test: 2500 low quality
  • Advantage: Optimizing right data
  • Disadvantage: Train distr. is different than dev and test set

Not always good idea to use different dist in train and dev

• Human error ~ 0
• Train 1%
• Dev 10%

Training-dev set: same distribution as training set, but not used for training

• Train 1%
• Train-dev: 9%
• Dev: 10%

Still high gap between train and train-dev ⇒ variance problem

If Train and Train-dev would be closer ⇒ data-mismatch problem.

Summary:

• Human level 4%
  • Avoidable bias
• Train 7%
  • Variance
• Train-dev: 10%
  • Data mismatch
• Dev: 12%
  • Degree of overfitting to dev set (if to high ⇒ bigger dev set)
• Test: 12%

• Error analysis to understand difference between training and dev/test set
• Make training more similar / collect more data similar to dev/test set (e.g. simulate audio environment)
  • Artificial data synthesis
    • Problems: Possible that sampling from too few data (for human it might appear ok)