Week 6
With homework 5, you need to complete the midterm survey. This will help me evaluate how well I am teaching.
There are 13 total questions. Only one question is required, so if you do not feel strongly or do not have suggestions, don’t feel like you need to answer. I want to hear your opinion! I want to make meaningful changes in the classroom that will help you!
Don’t forget that this is 2% of your grade. This survey is also due November 9th at 11pm.
Resources
| Chapter | Topic | Slides | Annotated Slides | Recording |
|---|---|---|---|---|
| 17 | Negative Binomial RV | |||
| 18 | Poisson RV |
Exam Materials
The exam will cover all materials from Week 1 - Week 4
This translates to Chapter 1-11 and 22
This also translates to HW 1-4
Types of problems that you do not need to worry about:
Problems with chairs in a circle - we never covered these in detail in class
- If you’re curious, the book does have a few trick for these problems
Problems asking about the expected values for RVs that resemble a geometric distribution (or any of the RVs where the number of trials extends to infinity)
- I do not expect you to know how to sum over infinite values - I did not cover these series and tricks enough in class!
Practice materials
You can go back to do the Extra Problems from each homework
Exam Review document (made by Meike in 2021)
Exam Review Answers (made by Meike in 2021)
Questions that are not covered on our exam:
Fall 2020: 5
Fall 2019: 4, 5b
Fall 2018: 5b
Fall 2017: 4, 5, 6
Fall 2016: 5b, 6
During the exam, I will give you scratch paper!
Class Exit Tickets
Additional Information
Announcements 10/30
Any questions about the exam on Wednesday?
On the Monday and Tuesday before the exam, I will hold virtual office hours
Monday, 10/30, 4-5pm
Tuesday, 10/31, 1:30-2:30pm
If you cannot make those hours and want to ask me questions, we can set up a short meeting for Monday or Tuesday
Statistician of the Week: Lester Mackey
Dr. Mackey is a machine learning researcher at Microsoft Research New England and an adjunct professor at Stanford University. His PhD (Computer Science 2012) and MA (Statistics 2011) are both from University of California, Berkeley, while his undergraduate degree (Computer Science 2007) is from Princeton University.
He is involved in Stanford’s initiative of Statistics for Social Good and has the following quote on his website:
Quixotic though it may sound, I hope to use computer science and statistics to change the world for the better.
Topics covered
From Dr. Mackey’s personal website his areas of research are:
- statistical machine learning
- scalable algorithms
- high-dimensional statistics
- approximate inference
- probability
Relevant work
- Koulik Khamaru, Yash Deshpande, Lester Mackey, and Martin J. Wainwright, Near-optimal inference in adaptive linear regression
When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality can lead to erroneous results. We propose a family of online debiasing estimators to correct these distributional anomalies in least squares estimation. Our proposed methods take advantage of the covariance structure present in the dataset and provide sharper estimates in directions for which more information has accrued. We establish an asymptotic normality property for our proposed online debiasing estimators under mild conditions on the data collection process and provide asymptotically exact confidence intervals…
- Pierre Bayle, Alexandre Bayle, Lucas Janson, and Lester Mackey, Cross-validation Confidence Intervals for Test Error Advances in Neural Information Processing Systems (NeurIPS), December 2020.
This work develops central limit theorems for cross-validation and consistent estimators of its asymptotic variance under weak stability conditions on the learning algorithm. Together, these results provide practical, asymptotically-exact confidence intervals for k-fold test error and valid, powerful hypothesis tests of whether one learning algorithm has smaller k-fold test error than another. These results are also the first of their kind for the popular choice of leave-one-out cross-validation. In our real-data experiments with diverse learning algorithms, the resulting intervals and tests outperform the most popular alternative methods from the literature…
Outside links
Please note the statisticians of the week are taken directly from the CURV project by Jo Hardin.
Other
The precursor to kaggle was a $1 million prize given by Netflix to the most accurate prediction of ratings that people give to the movies they watch. As undergraduates, Dr. Mackey and two friends led the competition for a few hours in its first year. Later, groups merged and Dr. Mackey’s group merged with a few others, forming The Ensemble. Their final analysis came in second with the exact same error rates as the winning entry. The winning entry, however, had been submitted 20 minutes prior. Sigh.
Muddiest Points
1. Subtracting two independent Poisson RVs
When we subtract two independent Poisson RVs, we get the Skellam distribution. We do not get a Poisson distribution with a rate ($\lambda$) that is just the difference between the two Poisson RVs.