```
#!/usr/bin/python
# The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
#
# This is an example illustrating the use of the structural SVM solver from
# the dlib C++ Library. Therefore, this example teaches you the central ideas
# needed to setup a structural SVM model for your machine learning problems. To
# illustrate the process, we use dlib's structural SVM solver to learn the
# parameters of a simple multi-class classifier. We first discuss the
# multi-class classifier model and then walk through using the structural SVM
# tools to find the parameters of this classification model. As an aside,
# dlib's C++ interface to the structural SVM solver is threaded. So on a
# multi-core computer it is significantly faster than using the python
# interface. So consider using the C++ interface instead if you find that
# running it in python is slow.
#
#
# COMPILING/INSTALLING THE DLIB PYTHON INTERFACE
# You can install dlib using the command:
# pip install dlib
#
# Alternatively, if you want to compile dlib yourself then go into the dlib
# root folder and run:
# python setup.py install
#
# Compiling dlib should work on any operating system so long as you have
# CMake installed. On Ubuntu, this can be done easily by running the
# command:
# sudo apt-get install cmake
#
import dlib
def main():
# In this example, we have three types of samples: class 0, 1, or 2. That
# is, each of our sample vectors falls into one of three classes. To keep
# this example very simple, each sample vector is zero everywhere except at
# one place. The non-zero dimension of each vector determines the class of
# the vector. So for example, the first element of samples has a class of 1
# because samples[0][1] is the only non-zero element of samples[0].
samples = [[0, 2, 0], [1, 0, 0], [0, 4, 0], [0, 0, 3]]
# Since we want to use a machine learning method to learn a 3-class
# classifier we need to record the labels of our samples. Here samples[i]
# has a class label of labels[i].
labels = [1, 0, 1, 2]
# Now that we have some training data we can tell the structural SVM to
# learn the parameters of our 3-class classifier model. The details of this
# will be explained later. For now, just note that it finds the weights
# (i.e. a vector of real valued parameters) such that predict_label(weights,
# sample) always returns the correct label for a sample vector.
problem = ThreeClassClassifierProblem(samples, labels)
weights = dlib.solve_structural_svm_problem(problem)
# Print the weights and then evaluate predict_label() on each of our
# training samples. Note that the correct label is predicted for each
# sample.
print(weights)
for k, s in enumerate(samples):
print("Predicted label for sample[{0}]: {1}".format(
k, predict_label(weights, s)))
def predict_label(weights, sample):
"""Given the 9-dimensional weight vector which defines a 3 class classifier,
predict the class of the given 3-dimensional sample vector. Therefore, the
output of this function is either 0, 1, or 2 (i.e. one of the three possible
labels)."""
# Our 3-class classifier model can be thought of as containing 3 separate
# linear classifiers. So to predict the class of a sample vector we
# evaluate each of these three classifiers and then whatever classifier has
# the largest output "wins" and predicts the label of the sample. This is
# the popular one-vs-all multi-class classifier model.
# Keeping this in mind, the code below simply pulls the three separate
# weight vectors out of weights and then evaluates each against sample. The
# individual classifier scores are stored in scores and the highest scoring
# index is returned as the label.
w0 = weights[0:3]
w1 = weights[3:6]
w2 = weights[6:9]
scores = [dot(w0, sample), dot(w1, sample), dot(w2, sample)]
max_scoring_label = scores.index(max(scores))
return max_scoring_label
def dot(a, b):
"""Compute the dot product between the two vectors a and b."""
return sum(i * j for i, j in zip(a, b))
################################################################################
class ThreeClassClassifierProblem:
# Now we arrive at the meat of this example program. To use the
# dlib.solve_structural_svm_problem() routine you need to define an object
# which tells the structural SVM solver what to do for your problem. In
# this example, this is done by defining the ThreeClassClassifierProblem
# object. Before we get into the details, we first discuss some background
# information on structural SVMs.
#
# A structural SVM is a supervised machine learning method for learning to
# predict complex outputs. This is contrasted with a binary classifier
# which makes only simple yes/no predictions. A structural SVM, on the
# other hand, can learn to predict complex outputs such as entire parse
# trees or DNA sequence alignments. To do this, it learns a function F(x,y)
# which measures how well a particular data sample x matches a label y,
# where a label is potentially a complex thing like a parse tree. However,
# to keep this example program simple we use only a 3 category label output.
#
# At test time, the best label for a new x is given by the y which
# maximizes F(x,y). To put this into the context of the current example,
# F(x,y) computes the score for a given sample and class label. The
# predicted class label is therefore whatever value of y which makes F(x,y)
# the biggest. This is exactly what predict_label() does. That is, it
# computes F(x,0), F(x,1), and F(x,2) and then reports which label has the
# biggest value.
#
# At a high level, a structural SVM can be thought of as searching the
# parameter space of F(x,y) for the set of parameters that make the
# following inequality true as often as possible:
# F(x_i,y_i) > max{over all incorrect labels of x_i} F(x_i, y_incorrect)
# That is, it seeks to find the parameter vector such that F(x,y) always
# gives the highest score to the correct output. To define the structural
# SVM optimization problem precisely, we first introduce some notation:
# - let PSI(x,y) == the joint feature vector for input x and a label y
# - let F(x,y|w) == dot(w,PSI(x,y)).
# (we use the | notation to emphasize that F() has the parameter vector
# of weights called w)
# - let LOSS(idx,y) == the loss incurred for predicting that the
# idx-th training sample has a label of y. Note that LOSS()
# should always be >= 0 and should become exactly 0 when y is the
# correct label for the idx-th sample. Moreover, it should notionally
# indicate how bad it is to predict y for the idx'th sample.
# - let x_i == the i-th training sample.
# - let y_i == the correct label for the i-th training sample.
# - The number of data samples is N.
#
# Then the optimization problem solved by a structural SVM using
# dlib.solve_structural_svm_problem() is the following:
# Minimize: h(w) == 0.5*dot(w,w) + C*R(w)
#
# Where R(w) == sum from i=1 to N: 1/N * sample_risk(i,w) and
# sample_risk(i,w) == max over all
# Y: LOSS(i,Y) + F(x_i,Y|w) - F(x_i,y_i|w) and C > 0
#
# You can think of the sample_risk(i,w) as measuring the degree of error
# you would make when predicting the label of the i-th sample using
# parameters w. That is, it is zero only when the correct label would be
# predicted and grows larger the more "wrong" the predicted output becomes.
# Therefore, the objective function is minimizing a balance between making
# the weights small (typically this reduces overfitting) and fitting the
# training data. The degree to which you try to fit the data is controlled
# by the C parameter.
#
# For a more detailed introduction to structured support vector machines
# you should consult the following paper:
# Predicting Structured Objects with Support Vector Machines by
# Thorsten Joachims, Thomas Hofmann, Yisong Yue, and Chun-nam Yu
#
# Finally, we come back to the code. To use
# dlib.solve_structural_svm_problem() you need to provide the things
# discussed above. This is the value of C, the number of training samples,
# the dimensionality of PSI(), as well as methods for calculating the loss
# values and PSI() vectors. You will also need to write code that can
# compute:
# max over all Y: LOSS(i,Y) + F(x_i,Y|w). To summarize, the
# ThreeClassClassifierProblem class is required to have the following
# fields:
# - C
# - num_samples
# - num_dimensions
# - get_truth_joint_feature_vector()
# - separation_oracle()
C = 1
# There are also a number of optional arguments:
# epsilon is the stopping tolerance. The optimizer will run until R(w) is
# within epsilon of its optimal value. If you don't set this then it
# defaults to 0.001.
# epsilon = 1e-13
# Uncomment this and the optimizer will print its progress to standard
# out. You will be able to see things like the current risk gap. The
# optimizer continues until the
# risk gap is below epsilon.
# be_verbose = True
# If you want to require that the learned weights are all non-negative
# then set this field to True.
# learns_nonnegative_weights = True
# The optimizer uses an internal cache to avoid unnecessary calls to your
# separation_oracle() routine. This parameter controls the size of that
# cache. Bigger values use more RAM and might make the optimizer run
# faster. You can also disable it by setting it to 0 which is good to do
# when your separation_oracle is very fast. If If you don't call this
# function it defaults to a value of 5.
# max_cache_size = 20
def __init__(self, samples, labels):
# dlib.solve_structural_svm_problem() expects the class to have
# num_samples and num_dimensions fields. These fields should contain
# the number of training samples and the dimensionality of the PSI
# feature vector respectively.
self.num_samples = len(samples)
self.num_dimensions = len(samples[0])*3
self.samples = samples
self.labels = labels
def make_psi(self, x, label):
"""Compute PSI(x,label)."""
# All we are doing here is taking x, which is a 3 dimensional sample
# vector in this example program, and putting it into one of 3 places in
# a 9 dimensional PSI vector, which we then return. So this function
# returns PSI(x,label). To see why we setup PSI like this, recall how
# predict_label() works. It takes in a 9 dimensional weight vector and
# breaks the vector into 3 pieces. Each piece then defines a different
# classifier and we use them in a one-vs-all manner to predict the
# label. So now that we are in the structural SVM code we have to
# define the PSI vector to correspond to this usage. That is, we need
# to setup PSI so that argmax_y dot(weights,PSI(x,y)) ==
# predict_label(weights,x). This is how we tell the structural SVM
# solver what kind of problem we are trying to solve.
#
# It's worth emphasizing that the single biggest step in using a
# structural SVM is deciding how you want to represent PSI(x,label). It
# is always a vector, but deciding what to put into it to solve your
# problem is often not a trivial task. Part of the difficulty is that
# you need an efficient method for finding the label that makes
# dot(w,PSI(x,label)) the biggest. Sometimes this is easy, but often
# finding the max scoring label turns into a difficult combinatorial
# optimization problem. So you need to pick a PSI that doesn't make the
# label maximization step intractable but also still well models your
# problem.
#
# Create a dense vector object (note that you can also use unsorted
# sparse vectors (i.e. dlib.sparse_vector objects) to represent your
# PSI vector. This is useful if you have very high dimensional PSI
# vectors that are mostly zeros. In the context of this example, you
# would simply return a dlib.sparse_vector at the end of make_psi() and
# the rest of the example would still work properly. ).
psi = dlib.vector()
# Set it to have 9 dimensions. Note that the elements of the vector
# are 0 initialized.
psi.resize(self.num_dimensions)
dims = len(x)
if label == 0:
for i in range(0, dims):
psi[i] = x[i]
elif label == 1:
for i in range(dims, 2 * dims):
psi[i] = x[i - dims]
else: # the label must be 2
for i in range(2 * dims, 3 * dims):
psi[i] = x[i - 2 * dims]
return psi
# Now we get to the two member functions that are directly called by
# dlib.solve_structural_svm_problem().
#
# In get_truth_joint_feature_vector(), all you have to do is return the
# PSI() vector for the idx-th training sample when it has its true label.
# So here it returns
# PSI(self.samples[idx], self.labels[idx]).
def get_truth_joint_feature_vector(self, idx):
return self.make_psi(self.samples[idx], self.labels[idx])
# separation_oracle() is more interesting.
# dlib.solve_structural_svm_problem() will call separation_oracle() many
# times during the optimization. Each time it will give it the current
# value of the parameter weights and the separation_oracle() is supposed to
# find the label that most violates the structural SVM objective function
# for the idx-th sample. Then the separation oracle reports the
# corresponding PSI vector and loss value. To state this more precisely,
# the separation_oracle() member function has the following contract:
# requires
# - 0 <= idx < self.num_samples
# - len(current_solution) == self.num_dimensions
# ensures
# - runs the separation oracle on the idx-th sample.
# We define this as follows:
# - let X == the idx-th training sample.
# - let PSI(X,y) == the joint feature vector for input X
# and an arbitrary label y.
# - let F(X,y) == dot(current_solution,PSI(X,y)).
# - let LOSS(idx,y) == the loss incurred for predicting that the
# idx-th sample has a label of y. Note that LOSS()
# should always be >= 0 and should become exactly 0 when y is the
# correct label for the idx-th sample.
#
# Then the separation oracle finds a Y such that:
# Y = argmax over all y: LOSS(idx,y) + F(X,y)
# (i.e. It finds the label which maximizes the above expression.)
#
# Finally, separation_oracle() returns LOSS(idx,Y),PSI(X,Y)
def separation_oracle(self, idx, current_solution):
samp = self.samples[idx]
dims = len(samp)
scores = [0, 0, 0]
# compute scores for each of the three classifiers
scores[0] = dot(current_solution[0:dims], samp)
scores[1] = dot(current_solution[dims:2*dims], samp)
scores[2] = dot(current_solution[2*dims:3*dims], samp)
# Add in the loss-augmentation. Recall that we maximize
# LOSS(idx,y) + F(X,y) in the separate oracle, not just F(X,y) as we
# normally would in predict_label(). Therefore, we must add in this
# extra amount to account for the loss-augmentation. For our simple
# multi-class classifier, we incur a loss of 1 if we don't predict the
# correct label and a loss of 0 if we get the right label.
if self.labels[idx] != 0:
scores[0] += 1
if self.labels[idx] != 1:
scores[1] += 1
if self.labels[idx] != 2:
scores[2] += 1
# Now figure out which classifier has the largest loss-augmented score.
max_scoring_label = scores.index(max(scores))
# And finally record the loss that was associated with that predicted
# label. Again, the loss is 1 if the label is incorrect and 0 otherwise.
if max_scoring_label == self.labels[idx]:
loss = 0
else:
loss = 1
# Finally, return the loss and PSI vector corresponding to the label
# we just found.
psi = self.make_psi(samp, max_scoring_label)
return loss, psi
if __name__ == "__main__":
main()
```