•   Introduction to Machine Learning – CSE-41327, ucsd
• CPSC 340 Machine Learning and Data Mining ubc Models of algorithms for dimensionality reduction, nonlinear regression, classification, clustering and unsupervised learning; applications to computer graphics, computer games, bio-informatics, information retrieval, e-commerce, databases, computer vision and artificial intelligence.
• COMP 551 Applied Machine Learning (4 credits) – https://www.mcgill.ca/
• COMS 4771 columbia The course covers basic statistical principles of supervised machine learning, as well as some common algorithmic paradigms.

## Overfitting

Assume that the data is drawn from some fixed, unknown probability distribution

Every hypothesis has a “true” error $J^*(h)$, which is the expected error when data is drawn from the distribution.

Because we do not have all the data, we measure the error on the training set $J_D(h)$
Suppose we compare hypotheses $h_1$ and $h_2$ on the training set, and $J_D\left(h_1\right)<J_D\left(h_2\right)$
If $h_2$ is “truly” better, i.e. $J^\left(h_2\right)\left(h_1\right)$, our algorithm is overfitting. We need theoretical and empirical methods to guard against it!

## Typical overfitting plot

The training error decreases with the degree of the polynomial $M$, i.e. the complexity of the hypothesis
The testing error, measured on independent data, decreases at first, then starts increasing
Cross-validation helps us:

• Find a good hypothesis class ( $M$ in our case), using a validation set of data
• Report unbiased results, using a test set, untouched during either parameter training or validation

## Cross-validation

A general procedure for estimating the true error of a predictor The data is split into two subsets:

• A training and validation set used only to find the right predictor
• A test set used to report the prediction error of the algorithm These sets must be disjoint!
The process is repeated several times, and the results are averaged to provide error estimates.

## Leave-one-out cross-validation

1. For each order of polynomial, $d$ :
(a) Repeat the following procedure $m$ times:
i. Leave out $i$ th instance from the training set, to estimate the true prediction error; we will put it in a validation set
ii. Use all the other instances to find best parameter vector, $\mathbf{w}{d, i}$ iii. Measure the error in predicting the label on the instance left out, for the $\mathbf{w}{d, i}$ parameter vector; call this $J_{d, i}$
iv. This is a (mostly) unbiased estimate of the true prediction error
(b) Compute the average of the estimated errors: $J_d=\frac{1}{m} \sum_{i=1}^m J_{d, i}$
2. Choose the $d$ with lowest average estimated error: $d^*=\arg \min _d J(d)$

## Regularization

Remember the intuition: complicated hypotheses lead to overfitting
Idea: change the error function to penalize hypothesis complexity:
$$J(\mathbf{w})=J_D(\mathbf{w})+\lambda J_{p e n}(\mathbf{w})$$
This is called regularization in machine learning and shrinkage in statistics $\lambda$ is called regularization coefficient and controls how much we value fitting the data well, vs. a simple hypothesis

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### CSE 365LR Introduction to Computer Security

View ScheduleCSE 365LR Introduction to Computer SecurityLecture

This is an undergraduate-level course intended for junior and senior-level students and will teach them introductory concepts of computer security. The main foci of this course will be network, web security, and application security. Part of the work will be dedicated to ethical aspects of security, and online privacy. The course will be heavily hands-on, as opposed to theoretical teaching.Credits: 4