Machine learning pytorch | Computer Science homework help

CMSC 510 HW2 –

The goal of the homework is to gain familiarity with PyTorch (to install it, see:
https://pytorch.org/get-started/locally/ ), a machine learning library for python that allows for
defining the machine learning model and performing gradient descent for it in an automated
way.

Complete 4 exercises described below, and submit via Canvas a zip file with four Jupyter
Notebook files, one per each exercise. Each notebook should contain the code, as well as short
reports on the results of experiments.

Exercise 1.

Train a linear classifier for the Iris dataset (a 3-class classification problem, file iris.csv in
Canvas), using Mean Squared Error as loss (see pytorch_linear_Iris_MSE.py file on Canvas).
Perform an analysis of the behavior of training risk and accuracy for different learning rates.

Detailed steps:
a) Use pandas to load the iris dataset. Create dummy variables for the classes

b) Define pytorch tensors for the dataset using:
torch.tensor

c) Define pytorch tensors (with gradient) for weights and biases (W & b). W should be
n_features x n_classes, b should be 1 x n_classes. Initialize b to zeros (torch.zeros), and W to
random values sampled from a normal distribution with null mean – try different values for the
standard deviation and observe changes in the training behavior.

d) Define pytorch optimizer over variables W & b
torch.optim.SGD or torch.optim.Adam

e) Create the main loop that goes over the dataset in multiple epochs. In each epoch
e1) clear gradients (using optimizer.zero_grad)
e2) calculate linear predictions: pred=X W + b using
torch.matmul
e3) pass the linear predictions through the unipolar sigmoid: sigmoid(pred)=1/(1+exp(-
pred)). Use these functions:
torch.log, torch.exp
e4) calculate the squared difference between the predictions (after sigmoid) and the
true classes, for all three output neurons. Use:
torch.pow
e5) calculate risk = average the squared difference over the training samples. Use:
torch.mean e6) calculate gradients of risk with respect to W & b (call risk.backwards)
e7) make optimizer step (using optimizer.step)
e8) calculate accuracy

Experiment with different learning rates for the two optimizers and report the behavior of the
training loss and accuracy.

Exercise 2.

Train a linear classifier for the Iris dataset, using CrossEntropy as loss. Perform an analysis of the
behavior of training risk and accuracy for different learning rates.

Detailed steps – follow Exercise 1, but replace MSE with CrossEntropy:

e3) pass the linear predictions through softmax (i.e., normalize the unipolar sigmoids for classes
i=1,…,3 to sum up to 1 for each sample)

e4) calculate the cross entropy after softmax (sum_{i=1}^3 y_i ln(softmax_i)).
torch.multiply, torch.log, torch.sum

e5) calculate risk = average the cross entropy over the training samples

Experiment and report results as in Exercise 1.

Exercise 3.

Starting from Exercise 2, add a split of the Iris dataset into a training set and a test set. Also, in
the training loop, go over small batches of samples (e.g. 20 samples) instead of always over the
whole training set. Experiment with batch size and learning rate.

Exercise 4:

Linear classifier for MNIST Digits dataset. Explore the behavior of the code from Exercise 3 on a
larger, more complicated dataset and report the results.
The number of training samples is 50,000 – analyze training behavior if a random subset of 100,
500, 1000, 2000 samples is used instead. Also, experiment with the learning rate and the batch
size.

For loading the dataset, use: import torchvision.datasets as datasets
full_train_dataset = datasets.MNIST(root=”./data”, train=True, download=True, transform=None)
full_test_dataset = datasets.MNIST(root=”./data”, train=False, download=True, transform=None)
x_train = full_train_dataset.data.numpy().reshape(-1,n_features).astype(dtype=np.float)/255.0;
x_test = full_test_dataset.data.numpy().reshape(-1,n_features).astype(dtype=np.float)/255.0;
y_train_cat = full_train_dataset.targets.numpy()
y_test_cat = full_test_dataset.targets.numpy()
Note that the download of the dataset may take long time. As with Iris, convert categorical
variables for classes into dummy variables (there are 10 classes).

Continue to order Get a quote

July 1, 2023

Distinguishing Inductive and Deductive Reasoning

Required Resources
Read/review the following resources for this activity:

· Textbook: Chapter 8, 9, 17 (Introduction)

· Lesson

· Minimum of 1 scholarly source (in addition to the textbook)

Click on the following tabs to review the concepts that will be addressed in this activity:

A valid structure is the way in which an argument is put together that assures it will pass the test of logical strength.

Deductive: In deductive arguments, the speaker asserts that her premises are true and, therefore, her conclusion must be accepted. Remember that in a deductive argument, logical strength does not depend on the literal truth of the premises. When we test for logical strength, we assume the premises are true. Once we determine that the argument is logically valid, we can then look at the actual – not presumed – truth of the premises.

Inductive: In inductive arguments, the speaker presents evidence that she claims support the probable truth of her conclusion – that her conclusion is the most likely true – and so you should accept it.

The Basic Structure of Deductive and Inductive Arguments
Argument examples:

Deductive Argument Example: “Tightening laws restricting the use and possession of firearms does not protect average law-abiding citizens; it only puts them at greater risk. Enforcing licensing restrictions, trigger locks, and waiting periods makes it more difficult for law-abiding citizens to defend themselves, and, as a result, encourages criminal activity. Only criminals benefit when ordinary citizens are deprived of their right to own a firearm and protect themselves, their homes, and their families" (Lott, 2000, p. 169)

Lott, J., (2000). More guns, less crime: Understanding crime and gun-control laws. University of Chicago Press.

The argument boils down to this:

· Laws that are obeyed by ordinary citizens and not obeyed by criminals are laws that put ordinary citizens at risk.

· Tight gun laws are laws that are obeyed only by ordinary citizens.

· Tight gun laws put ordinary citizens at risk.

However, the argument itself is composed of three intertwined syllogisms:

Only ordinary citizens are persons who respect tight gun laws.
Criminal persons are not ordinary citizens.
Therefore, criminals do not respect tight gun laws.

Tight gun laws restrict only ordinary citizens.
No criminal is an ordinary citizen.
No criminal is restricted by tight gun laws.

Laws that disfavor the good are laws that favor the bad.
Tight gun laws favor the bad.
Therefore, tight gun laws disfavor the good.

Notice that you cannot remove any of the “legs” and maintain the claim. Notice, also, that the reasons are closely connected and depend on or follow from each other. Notice, also, that the first premise (called the major premise) must be accepted as true, or the entire argument fails.

Inductive Argument: The United States is too dependent upon foreign oil. According to the U.S. Department of Energy, we rely on imported foreign oil for about 45% of our needs. Of the imported oil, most comes from Canada, but 22% comes from countries in the Middle East. Undeniably, this dependence shapes our foreign policy. We have vast oil reserves that could make us energy independent. Development of these resources would produce much-needed jobs, many of them in areas of the country suffering most from the recession. We should be developing an energy policy that makes us energy independent.

· Reason: We import 45% of our oil.

· Reason: Middle East oil imports shape our foreign policy.

· Reason: Our vast oil reserves could make us energy independent.

· Reason: Development of oil reserves could produce much needed jobs.

· Conclusion: For any or all of the above, independent reasons, we should become energy independent.

Notice that any one of these reasons, standing alone, could support the conclusions; they are not logically related to one another as they would be in a syllogism.

Initial Post Instructions
For the initial post, address the following:

· Find and post examples of deductive and inductive arguments. Do NOT use an argument example which clearly indicates it is an example of an inductive/deductive argument.

· For each example, evaluate its logical strength, using the concepts and ideas presented in the textbook readings, the lesson, and any other source you find that helps you to evaluate the validity (deductive) or strength (inductive) of the argument. You can use examples from the text, or you can find examples elsewhere.

oEditorials and opinion columns are a good source, as are letters to the editor. Blogs will also often be based on arguments.

oUse mapping and evaluative techniques to make sure it is an argument.

· Is it inductive or deductive? Explain why.

· Does it pass the tests of validity and strength? Explain.