shells include
I found my shell on my MacBook is not Bash. What is it?
21 Matching Annotations
- Jan 2026
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ucla-biostat-203b.github.io ucla-biostat-203b.github.io
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- Jun 2025
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nih-r25-modelersandstorytellers.github.io nih-r25-modelersandstorytellers.github.io
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double machine learning
What is DML?
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- Nov 2024
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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indepenent
also assumes X and Y have mean 0
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- Oct 2024
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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porjector
typo
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m=dim(S)+dim(S⊥).
Part 4 is the hint for HW4 Q3.2.
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immediate corollary
Because dim(C(A)) + dim(N(A')) = m by rank-nullity theorem, $R^m = C(A) + N(A')$.
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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non-null
Non-null matrix means a matrix that is not a zero matrix.
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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a set of vectors
Change to "... a non-empty set of vectors" for clarity?
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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Projection of x∈Rn on the line through 0n and a:
One can derive this as a corollary of BV 3.12 (HW1)
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For A∈Rm×n and b∈Rn,
Warning: The $a_i$s are different in these two views.
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For a∈Rn and B∈Rn×p,
Warning: The $b_i$s are different in these two views.
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ucla-biostat-216.github.io ucla-biostat-216.github.io
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Triangle inequality
Does L0 norm satisfy triangle inequality? Yes, because $$ 1_{x_i+y_i \ne 0} \le 1_{x_i \ne 0} + 1_{y_i \ne 0} $$ for all \(i\).
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Proof
Can we write a proof without matrix notation?
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- Jun 2024
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nih-r25-modelersandstorytellers.github.io nih-r25-modelersandstorytellers.github.io
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following steps
I can demo these steps if needed.
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many
Again don't worry about syntaxes. Focus on concepts of data wrangling, which are universal among many languages (SQL, Python, Julia).
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Tidyverse
Tidyverse is not the only choice. data.table package is a popular framework for data wrangling as well.
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the life cycle of a data science project
Don't be overwhelmed by syntax. GenAI tools such as GitHub Copilot and ChatGPT alleviate lots of programming details. More important to grasp the tasks and workflow.
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nih-r25-modelersandstorytellers.github.io nih-r25-modelersandstorytellers.github.io
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Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1-C68.
Thousands of citations already. Called "the monster" in big tech. Save billions of $$$ at Amazon by applying DML to online experimentation such as A/B testing.
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nih-r25-modelersandstorytellers.github.io nih-r25-modelersandstorytellers.github.io
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CART
Tree-based methods such as random forest and boosting have been one of the most successful out-of-box machine learning methods for structured/tabular data.
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nih-r25-modelersandstorytellers.github.io nih-r25-modelersandstorytellers.github.io
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tidycensus
Last year's R25 program had many examples of using tidycensus to explore the Census and ACS data.
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as_tibble() |>
Optional.
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