Error Analysis

Fehlklassifizierte Tupel betrachten, prüfen

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

Schwierige Beispiele identifizieren.

Skewed classes

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. $h_\theta(x) >= 0.3$

$F_1$ Score

Zum Vergleich von Precision/Recall.

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

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

Bias / Variance

  • 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)

Regularisierung

  • 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).

Working on most promising problems

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)

Misslabeled data

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)

Missmatched train and dev/test set

  • 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

Problems with different train and dev/test set dist

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%

Data mismatch problems

  • 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)