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Intro to Machine Learning Analysis

This 3 sentence summary provides the key points about the document: The document introduces machine learning techniques that will be covered in a class, including how to critically analyze findings to determine if they are statistically significant. It reviews basic probability and statistical concepts like probability distributions, the law of large numbers, the central limit theorem, and how inferences can be made about populations based on random samples using estimates, confidence intervals, and p-values. The goal is for students to understand these principles in order to critically read papers using these machine learning and statistical methods.

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Sridhar Sundaramurthy
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118 views3 pages

Intro to Machine Learning Analysis

This 3 sentence summary provides the key points about the document: The document introduces machine learning techniques that will be covered in a class, including how to critically analyze findings to determine if they are statistically significant. It reviews basic probability and statistical concepts like probability distributions, the law of large numbers, the central limit theorem, and how inferences can be made about populations based on random samples using estimates, confidence intervals, and p-values. The goal is for students to understand these principles in order to critically read papers using these machine learning and statistical methods.

Uploaded by

Sridhar Sundaramurthy
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Lecture 0: Background

Rafael A. Irizarry and Hector Corrada Bravo


January 2010

The purpose of this class is for you to learn machine learning techniques commonly used in data analysis. By the end of the term, you should be able to read
papers that used these methods critically and analyze data using them.
When using any of these tools we will be we will be asking ourselves if our
findings are statistically significant. For example, if we make use of a particular classification algorithm and find that we can predict the outcome of 7 out
of our 10 cases, how can we determine if this could have happened by chance
alone? To be able to answer these questions, we need to understand some basic probabilistic and statistical principles. Today we will review some of these
principles.

Probability
If I toss a coin, what is the chance it lands heads?
In this class we will sometimes be using notation like this:
Let X be a random variable that takes values 0 (tails) or 1 (heads) such that
P r(X = 1) = 1/2
For die, we would write:
P r(X = k) = 1/6, k = 1, . . . , 6.
We will refer to these as probability distributions.
More complicated distributions can be defined, for example, by considering
the random variable

Y =

N
X
i=1

Xi

where the Xi s, i = 1, . . . , N are independent tosses of the same die (or coin).
What are possible values of Y ? What is the distribution of Y ? What does
independent mean?

Populations, LLN and CLT


In science, randomness usually comes from either random sampling or randomization.
Side note: What about observational studies?
How does the above relate to populations?
The coin toss can be related to a very large population where each subject is
either, say, a democrat (heads) or a republican (tails). If half are democrats
and half are republican, then if we pick a person at random, its just like a coin
toss.
If dems are 1, and reps are 0, what is the population average x
?
If I take a random sample with replacement (a poll) of N = 10 subjects, what
is the distribution of the sample average?
What happens to the difference between the sample average and the population
average as the sample size gets bigger?
a random variable? What about the distribuWhy is the sample average X
tion? Is the population average a random variable? What does the law of large
numbers (LLN) say? What does the central limit theorem (CLT) say?

Inference
How does this all relate to scientific problems? Many times in science we can
model the process producing data with a stochastic (probabilistic) model where
parameters (such as population averages) are unkowns. We then make inferences based on the data.
For example, in the dems and reps problem we may not know the percentages
of 1s and 0s. To find out, we take a random sample, and construct estimates
(the sample average), confidence intervals and p-values.
How do we construct a confidence interval for the percentage of democrats?
What would be an interesting null hypothesis in this case? How would we
construct a p-value for this null hypothesis?
For continuous data, this is all pretty much the same. For example, we may want
to know if the average weight of Baltimore women is over some recommended
ideal weight.

Note: In this case, we could use a t-test if the sample is small.


This inferential approach is used in any situation where a population average
is of interest and we can only obtain a random sample. It is also used when
randomization is used.

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