You have also evaluated your model on the test set, and find the following:

- Human-level performance: 0.1%
- Training set error: 2.0%
- Dev set error: 2.1%
- Test set error: 7.0%

Human Level Performance: Continuing from the previous question, what does this mean?

You define 0.1% as “human-level performance.” After working further on your algorithm, you end up with the following: 

- Human-level performance: 0.1%
- Training set error: 2.0%
- Dev set error: 2.1%

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Human-Level Performance is the error a person may get. It's usually based on what your objective is. 
On the opposite to that is the Bayes (optimal) error which is the theoretical error. And this error may not be 0. Since there might be some impossible cases to classify, e.g., a picture that is too blurry to be recognized.
Before surpassing human-level performance, the accuracy will be improved greatly. However, when it passes the line, it will get harder since you cannot learn from human, and you don't know what the true Bayes error is.

Human Level Performance

Regularization is a modification made to a learning algorithm with the goal of reducing generalization error, but not training error.

Linear Regression is useful for modeling outputs whose relation to their inputs is linear. However, linear regression performs poorly when trying to model non-linear relationships. We can use regularization to help learning algorithms select certain models over others, particularly to avoid overfitting. 

Regularization

Machine Learning Yearning, a free ebook from Andrew Ng, teaches you how to structure Machine Learning projects.
https://www.deeplearning.ai/machine-learning-yearning/

Note: The content of the book is aligned with the Coursera Deeplearning.ai specialization.  https://www.deeplearning.ai/deep-learning-specialization/ 

Machine Learning Yearning (Deeplearning.ai)

To find a reasonable proxy for Bayes error, you should clearly identify what the purpose of your human level performance should be.
For example, since doctors have an error of 0.5%, in a given problem we would define 0.5% as the human level error as a proxy for Bayes error. 
The more specific in what you are defining, the better your outcome, e.g., the error rate by doctors who are above 50 years old and specialize in brain surgery.

Human Level Proxy for Bayes Error

You ask a few people to label the dataset to find out what is human-level performance. You find the following levels of accuracy:

- Expert #1: 0.3% error
- Expert #2: 0.5% error
- Normal Person #1 (not an expert): 1.0% error
- Normal Person #2 (not an expert): 1.2% error

If your goal is to have “human-level performance” be a proxy (or estimate) for Bayes error, how would you define “human-level performance”?

Human Level Performance: Based on the evidence below, which two of the following four options seem the most promising to try? 

Which of the following statements about algorithmic performance do you agree with?

While adding an extra term penalizes the weight matrix from becoming too large, why does this prevent overfitting? This is because if lambda becomes very large the weight of the matrices is incentivized to be close to 0. In other words, you are zeroing the impact of hidden units so that a simpler network is the result. The hidden units are still there, but now they have a much smaller effect. With a small W and and small Z, the activation function will likely be fairly linear. 


Why does regularization prevent overfitting? 

- L1 Regularization
- L2 Regularization
- Dropout Regularization
- Data Augmentation
- Early Stopping
- Tangent Distance
- Tangent Prop
- Manifold Tangent Classifier

Popular Regularization Techniques in Deep Learning

Local constancy and smoothness priors are prior beliefs or assumptions used in machine learning stating that the function being learned should be locally constant or smooth. These priors rely on the assumption that a function should satisfy $$f(x) \approx f(x+\epsilon)$$ for a small $$\epsilon$$. For example, $$k$$-nearest neighbor algorithms directly copy output values from nearby data points, while most kernel methods interpolate between nearby data points. Smoothness priors work best for functions with sufficient examples and low dimensionality. However, more complicated functions can be estimated and generalized effectively by dividing their domain into regions and using underlying assumptions to associate each region. For instance, a function with $$O(2^k)$$ regions can be defined by $$O(k)$$ examples if additional assumptions are used to connect these regions.

Local Constancy and Smoothness Priors

While a parameter norm penalty is one way to regularize parameters to be close to one another, the more popular way is to use constraints: to force sets of parameters to be equal. This method of regularization is often referred to as parameter sharing, because we interpret the various models or model components as sharing a unique set of parameters. A signiﬁcant advantage of parameter sharing over regularizing the parameters to be close (via a norm penalty) is that only a subset of the parameters (the unique set) needs to be stored in memory. In certain models—such as the convolutional neural network—this can lead to signiﬁcant reduction in the memory footprint of the model.



	Parameter sharing: to force sets of parameters to be equal

	Main application: Convolutional Neural Network (CNN)

	Advantages: signiﬁcant reduction in the memory footprint of the model




Parameter Sharing

Parameter tying refers to the fact that the two models, A and B, have a certain correlation. For example, both models are doing a classification task. Based on this prior knowledge, we can assume that the parameters of model A and model B should be similar, and then we can use this information through regularization.

Parameter Tying

What do L1 regularization and L2 regularization have in common?

L1 regularization and L2 regularization

MTL acts as a regularizer by introducing an inductive bias. As such, it reduces the risk of overfitting and improves its ability to fit random noise.

MTL as a Regularizer

Classical regularization techniques mitigate overfitting by adding a parameter norm penalty to the loss function during training. This extra penalty term restricts the capacity of the model, thereby keeping the learned model simple and reducing its overall complexity. Different parameter norm penalties lead to different regularization behaviors and preferred solutions.

Parameter Penalties in Classical Regularization

Increasing model size can increase variance and overfitting risk, but this overfitting problem usually arises when regularization is not used. With a well-designed regularization method, such as tuned L2 regularization or dropout in deep learning, one can usually increase model size without significantly worsening performance; the main reason to avoid a bigger model is computational cost.

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