ML Math Index
Last edited: August 8, 2025https://web.stanford.edu/class/cs205l/
Lectures
- SU-CS205L JAN072025
- SU-CS205L JAN092025
- SU-CS205L JAN142025
- SU-CS205L JAN162025
- SU-CS205L JAN212025
- SU-CS205L JAN232025
Logistics
MLE for Conditional Gaussian
Last edited: August 8, 2025Let’s say we want to find MLE parameters \(\theta\) for a conditional Gaussian with constant variance. That is:
\begin{equation} p\qty(y_{i} | x_{i}) = \mathcal{N} \qty(y_{i}|f_{\theta } \qty(x_{i}), \sigma^{2}) \end{equation}
and we have a corresponding dataset: \(\qty(x_1, y_1), …, \qty(x_{m}, y_{m})\).
where:
\begin{align} \hat{\theta} &= \arg\max_{\theta} \sum_{i=1}^{m} \log p\qty(y_{i}|x_{i}) \\ &= \arg\max_{\theta} \sum_{i=1}^{m} \log \mathcal{N} \qty(y_{i}| f_{\theta} \qty(x_{i}), \sigma^{2}) \\ &= \arg\max_{\theta } \sum_{i=1}^{m} \log \frac{1}{\sqrt{{2 \pi \sigma^{2}}}} \exp \qty(- \frac{\qty(y_{i}- f_{\theta }\qty(x_{i}))^{2}}{2\sigma^{2}}) \end{align}
MLib
Last edited: August 8, 2025MLib is a machine learning library built on top of Spark.
from pyspalk.mllib.clustering import KMeans
KMeans(rdd)
where you pass the MLib a PySpark RDD
MLK and Malcom X Reading
Last edited: August 8, 2025Reading notes
Malcom X’s father was an active prechear in the scene
Malcom X and MLK are both made mostly charactures out of context
Malcom X had a belligent upbringing with a belligent father, whereas MLK lived in relative comfort as a son of a successful minister
Malcom was sent into white foster families as his mother became institutionalized
Becasue of his experience in foster system, Malcom tried to pass/be white
King’s nonviolent priciples not understood and became conflicted with ideas of local leaders
Malcom found a father figure in the Nation of Islam, changing his name in prison
MLK had more positive African American role models in life
Malcom X disallusioned with the policy of nonengagement by the nation of islam
Malcom X had support over racial seperatism
Nation of Islam wanted to create a completely seperate Black state, promoting Black Nationalism secret
Malcom X wanted break because of skeptism again Eli Mohammed
Malcom charged MLK with infiltration
Martin believes that the process of voilence is a form of naïve expression
King believes that the “strong demagogic oratory” of Malcom was detrimental and extremist
Martin believes that the personal nature of assults from Malcom maybe result in physical assult
Malcom was suspended during 1963, and became independent—wanted to combine religion and politics like King
Malcom began forging ties with millitan Black movement
Martin regretted that integration has not proceeded, but believed it would have been difficult anyways
Rejected nonviolent and intergrational movement
People saw King and X’s ideas inrecosiliable
But, King and X themselves made a possible shared ending by the end
Believes that suicides were cut short
Racial pride was a centering point: while Malcom saw it as something to be harbored, Martin saw it as inate
Modal
Last edited: August 8, 2025Modal is a cloud deployment system that’s entirely programmatic. No yaml:
import modal
stub = modal.stub(gpu="a100")
@stub.function()
def fit(x):
import whatever
whatever.thing()
So think run.house, but they have the infra.
fine-tuning with Modal
https://github.com/modal-labs/llama-recipes
You can store the serverless functions, and Modal can serve stored serverless functions. Modal have web hooks as well to do inference at a front end.
Modal can serve most the management as well.
pricing
13B: 500 tokens/s on 40GB AA10 (3.73 / hour) 70B: 300 tok /s 80 GB( 2* 5.59/hour)
