The Bias-Variance Trade-Off PowerPoint Presentation

The Bias-Variance Trade-Off PowerPoint Presentation

2017-08-21 64K 64 0 0

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Oliver Schulte. Machine Learning 726. Estimating Generalization Error. Presentation Title At Venue. The basic problem: Once I’ve built a classifier, how accurate will it be on future test data?. Problem of Induction: It’s hard to make predictions, especially about the future (Yogi Berra).. ID: 580894

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Presentations text content in The Bias-Variance Trade-Off

Slide1

The Bias-Variance Trade-Off

Oliver Schulte

Machine Learning 726

Slide2

Estimating Generalization Error

Presentation Title At Venue

The basic problem: Once I’ve built a classifier, how accurate will it be on future test data?

Problem of Induction: It’s hard to make predictions, especially about the future (Yogi Berra).

Cross-validation: clever computation

on the training data

to predict test performance.

Other variants: jackknife, bootstrapping.

Today:

Theoretical insights

into generalization performance.

Slide3

The Bias-Variance Trade-off

The Short Story:generalization error = bias2 + variance + noise.Bias and variance typically trade off in relation to model complexity.

Presentation Title At Venue

Bias2

Variance

Error

Model complexity

-

+

+

+

Slide4

Dart Example

Presentation Title At Venue

Slide5

Analysis Set-up

Random Training Data

Learned Model

y(

x;D)

True Model

h

Average Squared Difference

{

y(x;D)-h(x)}2for fixed input features x.

Slide6

Presentation Title At Venue

Slide7

Formal Definitions

E[{y(x;D)-h(x)}2] = average squared error (over random training sets).E[y(x;D)] = average predictionE[y(x;D)] - h(x) = bias = average prediction vs. true value =E[{y(x;D) - E[y(x;D)]}2] = variance= average squared diff between average prediction and true value.Theoremaverage squared error = bias2 + varianceFor set of input features x1,..,xn, take average squared error for each xi.

Presentation Title At Venue

Slide8

Bias-Variance Decomposition for Target Values

Observed Target Value t(x) = h(x) + noise.Can do the same analysis for t(x) rather than h(x).Result: average squared prediction error = bias2 + variance+ average noise

Presentation Title At Venue

Slide9

Training Error and Cross-Validation

Suppose we use the training error to estimate the difference between the true model prediction and the learned model prediction.The training error is downward biased: on average it underestimates the generalization error.Cross-validation is nearly unbiased; it slightly overestimates the generalization error.

Presentation Title At Venue

Slide10

Classification

Can do bias-variance analysis for classifiers as well.General principle: variance dominates bias.Very roughly, this is because we only need to make a discrete decision rather than get an exact value.

Presentation Title At Venue

Slide11

Presentation Title At Venue


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