Self-Taught Learning to Deep Networks
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| - | + | In the previous section, you used an autoencoder to learn features that were then fed as input | |
| + | to a softmax or logistic regression classifier. In that method, the features were learned using | ||
| + | only unlabeled data. In this section, we describe how you can '''fine-tune''' and further improve | ||
| + | the learned features using labeled data. When you have a large amount of labeled | ||
| + | training data, this can significantly improve your classifier's performance. | ||
| - | In | + | In self-taught learning, we first trained a sparse autoencoder on the unlabeled data. Then, |
| + | given a new example <math>\textstyle x</math>, we used the hidden layer to extract | ||
| + | features <math>\textstyle a</math>. This is illustrated in the following diagram: | ||
| - | + | [[File:STL_SparseAE_Features.png|300px]] | |
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| - | + | We are interested in solving a classification task, where our goal is to | |
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predict labels <math>\textstyle y</math>. We have a labeled training set <math>\textstyle \{ (x_l^{(1)}, y^{(1)}), | predict labels <math>\textstyle y</math>. We have a labeled training set <math>\textstyle \{ (x_l^{(1)}, y^{(1)}), | ||
| - | (x_l^{(2)}, y^{(2)}), \ldots (x_l^{(m_l)}, y^{(m_l)}) \}</math> of <math>\textstyle m_l</math> examples. | + | (x_l^{(2)}, y^{(2)}), \ldots (x_l^{(m_l)}, y^{(m_l)}) \}</math> of <math>\textstyle m_l</math> labeled examples. |
| - | + | We showed previously that we can replace the original features <math>\textstyle x^{(i)}</math> with features <math>\textstyle a^{(l)}</math> | |
| - | computed by the sparse autoencoder. This gives us a training set | + | computed by the sparse autoencoder (the "replacement" representation). This gives us a training set <math>\textstyle \{(a^{(1)}, |
| - | y^{( | + | y^{(1)}), \ldots (a^{(m_l)}, y^{(m_l)}) \}</math>. Finally, we train a logistic |
| - | classifier to map from the features <math>\textstyle a^{(i)}</math> to the classification label <math>\textstyle y</math>. | + | classifier to map from the features <math>\textstyle a^{(i)}</math> to the classification label <math>\textstyle y^{(i)}</math>. |
| + | To illustrate this step, similar to [[Neural Networks|our earlier notes]], we can draw our logistic regression unit (shown in orange) as follows: | ||
| - | + | ::::[[File:STL_Logistic_Classifier.png|380px]] | |
| - | + | ||
| - | + | Now, consider the overall classifier (i.e., the input-output mapping) that we have learned | |
| - | + | using this method. | |
| - | + | In particular, let us examine the function that our classifier uses to map from from a new test example | |
| - | + | <math>\textstyle x</math> to a new prediction <math>p(y=1|x)</math>. | |
| - | + | We can draw a representation of this function by putting together the | |
| - | particular, the final classifier looks like this: | + | two pictures from above. In particular, the final classifier looks like this: |
[[File:STL_CombinedAE.png|500px]] | [[File:STL_CombinedAE.png|500px]] | ||
| - | + | The parameters of this model were trained in two stages: The first layer of weights <math>\textstyle W^{(1)}</math> | |
mapping from the input <math>\textstyle x</math> to the hidden unit activations <math>\textstyle a</math> were trained | mapping from the input <math>\textstyle x</math> to the hidden unit activations <math>\textstyle a</math> were trained | ||
as part of the sparse autoencoder training process. The second layer | as part of the sparse autoencoder training process. The second layer | ||
| - | of weights <math>\textstyle W^{(2)}</math> mapping from the activations to the output <math>\textstyle y</math> was | + | of weights <math>\textstyle W^{(2)}</math> mapping from the activations <math>\textstyle a</math> to the output <math>\textstyle y</math> was |
| - | trained using logistic regression. | + | trained using logistic regression (or softmax regression). |
| + | |||
| + | But the form of our overall/final classifier is clearly just a whole big neural network. So, | ||
| + | having trained up an initial set of parameters for our model (training the first layer using an | ||
| + | autoencoder, and the second layer | ||
| + | via logistic/softmax regression), we can further modify all the parameters in our model to try to | ||
| + | further reduce the training error. In particular, we can '''fine-tune''' the parameters, meaning perform | ||
| + | gradient descent (or use L-BFGS) from the current setting of the | ||
| + | parameters to try to reduce the training error on our labeled training set <math>\textstyle \{ (x_l^{(1)}, y^{(1)}), | ||
| + | (x_l^{(2)}, y^{(2)}), \ldots (x_l^{(m_l)}, y^{(m_l)}) \}</math>. | ||
| + | |||
| + | When fine-tuning is used, sometimes the original unsupervised feature learning steps | ||
| + | (i.e., training the autoencoder and the logistic classifier) are called '''pre-training.''' | ||
| + | The effect of fine-tuning is that the labeled data can be used to modify the weights <math>W^{(1)}</math> as | ||
| + | well, so that adjustments can be made to the features <math>a</math> extracted by the layer | ||
| + | of hidden units. | ||
| + | |||
| + | So far, we have described this process assuming that you used the "replacement" representation, where | ||
| + | the training examples seen by the logistic classifier are of the form <math>(a^{(i)}, y^{(i)})</math>, | ||
| + | rather than the "concatenation" representation, where the examples are of the form <math>((x^{(i)}, a^{(i)}), y^{(i)})</math>. | ||
| + | It is also possible to perform fine-tuning too using the "concatenation" representation. (This corresponds | ||
| + | to a neural network where the input units <math>x_i</math> also feed directly to the logistic | ||
| + | classifier in the output layer. You can draw this using a slightly different type of neural network | ||
| + | diagram than the ones we have seen so far; in particular, you would have edges that go directly | ||
| + | from the first layer input nodes to the third layer output node, "skipping over" the hidden layer.) | ||
| + | However, so long as we are using finetuning, usually the "concatenation" representation | ||
| + | has little advantage over the "replacement" representation. Thus, if we are using fine-tuning usually we will do so | ||
| + | with a network built using the replacement representation. (If you are not using fine-tuning however, | ||
| + | then sometimes the concatenation representation can give much better performance.) | ||
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| + | When should we use fine-tuning? It is typically used only if you have a large labeled training | ||
| + | set; in this setting, fine-tuning can significantly improve the performance of your classifier. | ||
| + | However, if you | ||
| + | have a large ''unlabeled'' dataset (for unsupervised feature learning/pre-training) and | ||
| + | only a relatively small labeled training set, then fine-tuning is significantly less likely to | ||
| + | help. | ||
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| + | {{CNN}} | ||
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