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Figure 7.7: Stabilization and new learning time when « is decreased

Figure 7 7: Stabilization and new learning time when « is decreased

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learning. First of all, we will start with the biological definition: Learning is the process of acquiring knowledge, skills, attitudes, or values, through Nowadays, the meaning of ” learning” has many definitions. The purpose of this first
learning. First of all, we will start with the biological definition: Learning is the process of acquiring knowledge, skills, attitudes, or values, through Nowadays, the meaning of ” learning” has many definitions. The purpose of this first
knowledge is the lowest order of cognition and evaluation the highest: e Knowledge is the memory of previously-learnt materials such as facts, terms,
knowledge is the lowest order of cognition and evaluation the highest: e Knowledge is the memory of previously-learnt materials such as facts, terms,
a sequence of 0 and 1, without semantic understanding. Figure 2.3: How machines see characters
a sequence of 0 and 1, without semantic understanding. Figure 2.3: How machines see characters
analysis, voice recognition, and many others. Figure 2.4: Machine learning applications: virus detection and speech recognition
analysis, voice recognition, and many others. Figure 2.4: Machine learning applications: virus detection and speech recognition
Figure 2.5: Supervised learning algorithms: a decision tree, a neural network and a
Figure 2.5: Supervised learning algorithms: a decision tree, a neural network and a
Figure 2.6: Unsupervised algorithm example: clustering 2.4. The machine learning process 4.3 Semi-Supervised learning
Figure 2.6: Unsupervised algorithm example: clustering 2.4. The machine learning process 4.3 Semi-Supervised learning
using a different, and ideally independent, set of features for each example. Figure 2.7: Semi-supervised learning example
using a different, and ideally independent, set of features for each example. Figure 2.7: Semi-supervised learning example
ment learning. Figure 2.8: Reinforced learning example The principal algorithms are temporal difference learning and actor critic reinforce-
ment learning. Figure 2.8: Reinforced learning example The principal algorithms are temporal difference learning and actor critic reinforce-
and output makes up how they should be catalogued. Each example can be written as a pair (input, output) where input is the data s« Mathematically, examples can be regarded as a pair (x, y) where x is a vector of real numbers and output can be a boolean value (like as yes/no, 1/-1, true/false),
and output makes up how they should be catalogued. Each example can be written as a pair (input, output) where input is the data s« Mathematically, examples can be regarded as a pair (x, y) where x is a vector of real numbers and output can be a boolean value (like as yes/no, 1/-1, true/false),
Figure 3.2: From a conceptual to a mathematical view yenerates the function which interpolates, to the best of its capability these series or a real number. In the first case, we speak of a problem of classification, in the
Figure 3.2: From a conceptual to a mathematical view yenerates the function which interpolates, to the best of its capability these series or a real number. In the first case, we speak of a problem of classification, in the
suppose we know the value of these figurative companies: Zoogle, Ciat, Carmalat
suppose we know the value of these figurative companies: Zoogle, Ciat, Carmalat
Figure 3.4: The yellow line shows the result of the training all the information we need to make the SVM work. The results obtained are as whereas Carmalat and Karmacotto have not had much success. We therefore have
Figure 3.4: The yellow line shows the result of the training all the information we need to make the SVM work. The results obtained are as whereas Carmalat and Karmacotto have not had much success. We therefore have
we just have a look at its position in the chart to get a good idea: Because of the fact that it is positioned above the yellow line, the SVM considers
we just have a look at its position in the chart to get a good idea: Because of the fact that it is positioned above the yellow line, the SVM considers
a little higher or lower?”. In theory, all these are possible solutions: The observer may ask himself ” why is the line exactly there where it is,why isn’t it 3 A more detailed analysis
a little higher or lower?”. In theory, all these are possible solutions: The observer may ask himself ” why is the line exactly there where it is,why isn’t it 3 A more detailed analysis
solution and examples is called margin. In our case, it can be represented as: Suppose that the possible outputs are 1 and -1, they are shown on those two
solution and examples is called margin. In our case, it can be represented as: Suppose that the possible outputs are 1 and -1, they are shown on those two
Figure 3.8: Coyota is not a good stock, but is placed near some good stocks. Now happen. For example, let us suppose that added to our list of 4 stocks is the Coyota In the former example, the data were linearly separable or, in other words, it exists If Coyota isn’t a good stock we would not be able to find a line to divide it.
Figure 3.8: Coyota is not a good stock, but is placed near some good stocks. Now happen. For example, let us suppose that added to our list of 4 stocks is the Coyota In the former example, the data were linearly separable or, in other words, it exists If Coyota isn’t a good stock we would not be able to find a line to divide it.
case of the Coyota stock, we can visualize the probable solution like this: Figure 3.9: A solution at the Coyota problem other problems require more elaborate and complex solutions. For example, in the But how can one obtain different functions from a line? How can we introduce
case of the Coyota stock, we can visualize the probable solution like this: Figure 3.9: A solution at the Coyota problem other problems require more elaborate and complex solutions. For example, in the But how can one obtain different functions from a line? How can we introduce
it becomes much more complex, a not linear function. Figure 3.11: From features space back to linear space
it becomes much more complex, a not linear function. Figure 3.11: From features space back to linear space
Figure 3.10: From linear to features space 3.5. More generic Support Vector Machines
Figure 3.10: From linear to features space 3.5. More generic Support Vector Machines
Figure 3.12: A difficult problem solved using a gaussian kernel 3.5. More generic Support Vector Machines
Figure 3.12: A difficult problem solved using a gaussian kernel 3.5. More generic Support Vector Machines
also make wrong classifications, like provided by this example: Figure 3.13: An example of a bad parameters setting
also make wrong classifications, like provided by this example: Figure 3.13: An example of a bad parameters setting
3.6. SVR - Support Vector Machines for Regression It is obviously not possible to know when its the best moment to buy or sell
3.6. SVR - Support Vector Machines for Regression It is obviously not possible to know when its the best moment to buy or sell
many websites that have as a function to analyze the financial market. Here’s a1 in the training (dates, quotations of the stock on those date) can be extracted from
many websites that have as a function to analyze the financial market. Here’s a1 in the training (dates, quotations of the stock on those date) can be extracted from
part of the error is tolerated. individualizing the hyperplane which maximizes the margin, keeping in mind that The figure shows how the error of SVR is calculated. Up until the threshold e,
part of the error is tolerated. individualizing the hyperplane which maximizes the margin, keeping in mind that The figure shows how the error of SVR is calculated. Up until the threshold e,
Coming back to the mathematical point of view, the quadratic optimization
Coming back to the mathematical point of view, the quadratic optimization
up of pairs (day, market quotes) which correspond to this plot: To make the SVR work, let’s make the tolerance margin at 0.01 over the fina
up of pairs (day, market quotes) which correspond to this plot: To make the SVR work, let’s make the tolerance margin at 0.01 over the fina
over information that give us the best solution. The result of this would be: The yellow line corresponds to prevision of the SVR in the following days. In
over information that give us the best solution. The result of this would be: The yellow line corresponds to prevision of the SVR in the following days. In
Figure 3.20: When buy and sell the stocks
Figure 3.20: When buy and sell the stocks
and based upon certain predictions, when to sell and buy the stock. Figure 3.21: A virtual stock broker build using SVM and SVR knowledge to decide whether a particular stock will be a good or bad investment.
and based upon certain predictions, when to sell and buy the stock. Figure 3.21: A virtual stock broker build using SVM and SVR knowledge to decide whether a particular stock will be a good or bad investment.
The constant C determines the trade-off between the flatness of the function and the
The constant C determines the trade-off between the flatness of the function and the
all the constraints, introducing some Lagrange multipliers:
all the constraints, introducing some Lagrange multipliers:
Finally also the C parameter can be deleted, using the derivative constraints And deleting some unnecessary parts:
Finally also the C parameter can be deleted, using the derivative constraints And deleting some unnecessary parts:
As before, we can compute another Lagrange function that includes all the con- straints, introducing other Lagrange multipliers: After many math passages, minimizing a, a* values, there is another dual optimiza-
As before, we can compute another Lagrange function that includes all the con- straints, introducing other Lagrange multipliers: After many math passages, minimizing a, a* values, there is another dual optimiza-
Like exposed above, this is an optimization problem with a convex domain. The
Like exposed above, this is an optimization problem with a convex domain. The
And margin function is defined as:
And margin function is defined as:
All we need to find is the relation of h(x) and ¢ at the changing of a:
All we need to find is the relation of h(x) and ¢ at the changing of a:
because they are always |e|.
because they are always |e|.
Replacing the variations of 6 and b with the results obtained in the equation (4.13): In this way, AO; and Ab values can be updated by computing 3, and A(x;) value: can be updated by computing 7.
Replacing the variations of 6 and b with the results obtained in the equation (4.13): In this way, AO; and Ab values can be updated by computing 3, and A(x;) value: can be updated by computing 7.
h(x) as follows: In this image, each circle corresponds to a sample. The red circles are error sam- ples, the yellow-ones are support samples and the green-ones are remaining samples.
h(x) as follows: In this image, each circle corresponds to a sample. The red circles are error sam- ples, the yellow-ones are support samples and the green-ones are remaining samples.
The first possibility is that the new sample error is less than €. This is the easiest
The first possibility is that the new sample error is less than €. This is the easiest
Otherwise, when the error is bigger than € the situation is more complicated:
Otherwise, when the error is bigger than € the situation is more complicated:
In this situation 0. or h(x.) value of the new sample changes until it reaches the
In this situation 0. or h(x.) value of the new sample changes until it reaches the
The problem is that these variations influence other samples: At the end of the updating procedure, if variation is too big, some samples could Notice that the arrow represents the sample movements of 6; or h(x;) components.
The problem is that these variations influence other samples: At the end of the updating procedure, if variation is too big, some samples could Notice that the arrow represents the sample movements of 6; or h(x;) components.
4.9. From Support to Error Set The direction of a sample is determined by the sign of 3; for support samples and
4.9. From Support to Error Set The direction of a sample is determined by the sign of 3; for support samples and
When a sample goes from support to error set, his 0; from 0 < |0;| < C becomes
When a sample goes from support to error set, his 0; from 0 < |0;| < C becomes
10 From Support to Remaining Set When a sample goes from support to remaining set, his 0; from 0 < |6;| < C becomes For support samples, the updating formula is:
10 From Support to Remaining Set When a sample goes from support to remaining set, his 0; from 0 < |6;| < C becomes For support samples, the updating formula is:
When a sample goes from error to support set, his |h(x;)| from > € becomes = e. For error samples, the updating formula is:
When a sample goes from error to support set, his |h(x;)| from > € becomes = e. For error samples, the updating formula is:
From Remaining to Support Set When a sample goes from remaining to support set, his |h(x;)| from < € becomes For error samples, the updating formula is:
From Remaining to Support Set When a sample goes from remaining to support set, his |h(x;)| from < € becomes For error samples, the updating formula is:
Before a new sample is added, all the samples that requires a less variation are
Before a new sample is added, all the samples that requires a less variation are
In the next paragraphs are listed all the possible variations. Note that if KKT conditions aren’t violated, this part of the algorithm isn’t used. them with new possible moves permitted only when a sample exit from its set.
In the next paragraphs are listed all the possible variations. Note that if KKT conditions aren’t violated, this part of the algorithm isn’t used. them with new possible moves permitted only when a sample exit from its set.
An error sample becomes invalid when its |h(x;)| becomes < e. In this case the sample, is neither an error sample, neither a remaining sample,
An error sample becomes invalid when its |h(x;)| becomes < e. In this case the sample, is neither an error sample, neither a remaining sample,
4.14.3 Invalid Remaining Samples In this case the sample, is neither a remaining sample, neither an error sample,
4.14.3 Invalid Remaining Samples In this case the sample, is neither a remaining sample, neither an error sample,
Variation value is: The second variation measures the distance of new sample from error set. new sample reaches |e] and consequently the SupportSet. Variation value is:
Variation value is: The second variation measures the distance of new sample from error set. new sample reaches |e] and consequently the SupportSet. Variation value is:
The third variation measures the distance of each Support sample to Error or Re-
The third variation measures the distance of each Support sample to Error or Re-
Variation values are: The fourth variation measures the distance of each error sample to SupportSet. position inside the SupportSet.
Variation values are: The fourth variation measures the distance of each error sample to SupportSet. position inside the SupportSet.
The last variation measures the distance of each remaining sample to SupportSet.
The last variation measures the distance of each remaining sample to SupportSet.
one should recompute also @ and 4; as follows: The remove procedure delete the line and the column of the erased sample anc Otherwise, if the new sample is moved from Error or RemainingSet to SupportSet, update the others:
one should recompute also @ and 4; as follows: The remove procedure delete the line and the column of the erased sample anc Otherwise, if the new sample is moved from Error or RemainingSet to SupportSet, update the others:
Figure 7.1: Samples trained compared with iteration count
Figure 7.1: Samples trained compared with iteration count
So, we can compare the exact time to add a new sample using the two methods: Figure 7.3: OnlineSVR and LibSVM compared in an online training 10t the total speed of the training.
So, we can compare the exact time to add a new sample using the two methods: Figure 7.3: OnlineSVR and LibSVM compared in an online training 10t the total speed of the training.
Table 7.1: Training parameters of the stabilization test The table shows the parameters of the SVR used during the stabilization test. all the parameters and compared the results.
Table 7.1: Training parameters of the stabilization test The table shows the parameters of the SVR used during the stabilization test. all the parameters and compared the results.
be changed to avoid overfitting and underfitting. Figure 7.4: Stabilization and new learning time when C is increased
be changed to avoid overfitting and underfitting. Figure 7.4: Stabilization and new learning time when C is increased
Figure 7.5: Stabilization and new learning time when C is decreased
Figure 7.5: Stabilization and new learning time when C is decreased
we were to restart the training. Figure 7.6: Stabilization and new learning time when € is increased
we were to restart the training. Figure 7.6: Stabilization and new learning time when € is increased
Figure 7.8: Stabilization and new learning time when kernel param is increased
Figure 7.8: Stabilization and new learning time when kernel param is increased
Figure 7.9: Stabilization and new learning time when kernel param is decreased
Figure 7.9: Stabilization and new learning time when kernel param is decreased
up by a head and an arm: Figure 7.10: The James robot
up by a head and an arm: Figure 7.10: The James robot
Here are a summary scheme: Figure 7.11: The training scheme
Here are a summary scheme: Figure 7.11: The training scheme
Figure 7.12: The first graph shows the error of a sample before learning, the second one the mean error and the third one the standard deviation To measure the training worth we have observed the mean and standard deviation
Figure 7.12: The first graph shows the error of a sample before learning, the second one the mean error and the third one the standard deviation To measure the training worth we have observed the mean and standard deviation
Here are the result obtained from the first motor: Figure 7.13: Motor Arm 1 results
Here are the result obtained from the first motor: Figure 7.13: Motor Arm 1 results
The second motor: Figure 7.14: Motor Arm 2 results
The second motor: Figure 7.14: Motor Arm 2 results
And the third motor:
And the third motor:
Figure 7.16: The results are not as good as we would
Figure 7.16: The results are not as good as we would
Figure 7.17: Noisy problem: these two arm positions for the robot are the same. were somewhat suspicious. For example two positions of the robot seemed identical:
Figure 7.17: Noisy problem: these two arm positions for the robot are the same. were somewhat suspicious. For example two positions of the robot seemed identical:
It is available for Linux and Windows.
It is available for Linux and Windows.
the training and test sets. It is very useful for manual estimation of the parameters. It also plots the errors of
the training and test sets. It is very useful for manual estimation of the parameters. It also plots the errors of
available on http://onlinesvr.altervista.org.
available on http://onlinesvr.altervista.org.
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