Given data samples and derised corresponding
labels , find a mapping function
between and so that is true most of the time.
Linear Regression
Which coefficients best explain the relationship between and so that
?
Linear Regression
Brute-force learning
– a modern way for
"testing plenty of solutions"
Linear Regression
is the label predicted by the model for a given data sample
With the true label , we can define the prediction loss:
Linear Regression
The task becomes finding
so that
How do we infer efficiently?
Overfitting
Many parameters may be used for complex regressions.
The green model error 0, yet the model does not generalize.
training & testing data
The parameters are learned from the training data with the training loss
The algorithm must also minimize the testing loss
(= generalization error)
regularization penalty
Adding a penalty to the loss function for preventing noise contamination
Support-vector machine
hyperplane
In two dimensions, a hyperplane is a straight line.
What if te data cannot be split by a line?
kernel trick
Increase the data dimension with non-linear feature combinations, and find the hyperplane "there" in the high-dimensional space.
Here, we have the Radial Basis Function (RBF) kernel
Machine learning for signal analysis
A -point waveform can be seen as a
single data sample with features
These two waveforms are shifted a tiny little bit in the time domain.
This makes a huge change in the feature comparison...
Manual feature extraction for time-to-failure earthquake prediction
Manual feature extraction for time-to-failure earthquake prediction
Deep neural networks
Which features should matter?
Where is an input data sample, are the weights and the bias, and the function is the non-linear activation. The output is a new feature .
ConvNetQuake
– a CNN for earthquake detection and location
ConvNetQuake
– a CNN for earthquake detection and location
PhaseNet
– a seismic phase detector
PhaseNet
– a seismic phase detector
PhaseNet
– a seismic phase detector
PhaseNet
– a seismic phase detector
Unsupervised learning
Clustering
– most common definitions
Find cluster centroids that minimize
the within-cluster variance. In order words:
Principal component analysis
Let consider , find a decomposition of so that
Principal component analysis
for compression
Independant component analysis
Independant component analysis
for blind-source separation
Deep unsupervised learning
Task: learn to reconstrut the data () from itself () with constrains
Learn to encode a 512-point seismogram into a 32-point with best reconstuction quality
Rejecting the seismograms that are hard to decode with low errow.