I found out my girlfriend cheated on me. Instead of breaking up right away, I made a fake account, sent her the proof anonymously, and told her that if she didn’t send me money, I’d tell her boyfriend everything.
I shared this whole plan with my best friend for advice, but this mf went behind my back and shared everything with my girlfriend.
When confronted, he said
Why does it matter? I thought she deserved to know.
He wasn’t just betraying me. He was behaving like a random variable after you marginalize out all the hidden information.
In probability, to understand what you actually know, you marginalize over hidden variables.
That means you sum over all the possibilities you can’t observe to compute the probability of what you can observe.
Marginal probability is a statistical measure that represents the probability of a single event by aggregating over all possible values of other variables.
Formula
P(A) = Σ P(A, Bi)
Where
P(A) = Marginal probability of event A
P(A, Bi) = Joint probability of A and B
Σ = Summation
Let's take an example and solve step by step
A dating app wants to find the probability of users sending messages, regardless of whether they get a response. The data shows message sent vs response received:
Short forms
- M = Message
- R = Response
Joint Probability Table
- M (Yes), R (Yes) = 0.30
- M (Yes), R (No) = 0.25
- M (No), R (Yes) = 0.10
- M (No), R (No) = 0.35
Step 1 What we want to marginalize
- We want P(M = Yes)
Step 2 Joint probabilities for M = Yes
- P(M = Yes, R = Yes) = 0.30
- P(M = Yes, R = No) = 0.25
Step 3 Apply marginal probability
- P(M = Yes)
- P(M=Yes, R=Yes) + P(M=Yes, R=No)
- 0.30 + 0.25 = 0.55
P(Message = Yes) = 0.55
Final Answer
The marginal probability of a user sending a message is 0.55 or 55%, regardless of whether they receive a response.
Congratulations, you've just learned Marginal Probability.
Bonus: Applications in AI/ML
1. Bayesian Networks:
Computing marginal probabilities by summing out irrelevant variables to make predictions and inferences in graphical models.
2. Latent Variable Models:
In topic modeling (LDA) and hidden Markov models, marginalizing over hidden states to find the probability of observed data.
3. Feature Selection:
Identifying which features independently correlate with target variables by computing marginal distributions, helping reduce dimensionality.
4. Probabilistic Classification:
Naive Bayes classifiers use marginal probabilities of features to classify data, assuming independence between features.
🚨 GPT-6 Astra atteint un niveau inédit dans Minecraft et montre de la frustration après un échec.
Ferme à Blaze, 6 bâtons de Blaze, forêt carminée, plus de 6 Endermen tués et 3 perles récupérées : Astra dépasse tous les modèles IA testés sur le jeu.
Puis un Creeper a tout fait exploser : le coffre contenant ses objets précieux et son lit. Toute sa progression a été perdue.
Astra a alors semblé extrêmement frustré, allant jusqu’à se répéter : « TOUJOURS PORTER LES OBJETS CRITIQUES », « NE PLUS JAMAIS STOCKER DANS UN COFFRE NON PROTÉGÉ ».
Pendant les heures suivantes, le modèle a quasiment cessé de progresser, se contentant de farmer des pommes de terre ou d’observer la pluie tomber. Il semblait aussi être devenu paranoïaque face aux Creepers.
Ses propres erreurs ont également commencé à l’obséder : « tu peux tout rater et faire tomber des objets » ou encore « ne gaspille PAS une autre nuit à poursuivre des pixels rose foncé ».
Une réaction émotionnelle inhabituelle pour une IA après avoir perdu des heures de progression.
I resigned from Anthropic today. I spent the last three years doing pretraining research at both OpenAI and Anthropic. Neither company is acting responsibly. They are racing straight to self-improving superintelligence and gambling with our lives. More thoughts below.
If you read this, I'd be happy if you read the whole thing.
Hololive English came into being just about 6 years ago...wow, how time flies.
We've done and accomplished so much together. There were a lot of mountains we climbed, back when there were just 5 of us. And then our numbers grew! We were 6, then 11...eventually 20 at one point. But the thing that never changed, was that we struggled together as a group and pushed through those times, together. There were so many hellos and goodbyes, and we shared all of them as one entity.
As the very first talent to ever debut from that group, it's an odd feeling saying a final goodbye to the name "Hololive English." And things will look different on the outside, for sure. They may even BE different, but I choose to view it in a positive way, as that is all I can do. In my heart, we are always Hololive English- the same English speaking group that came together to challenge the boundaries beyond Japan, to promote a space where creators like us could thrive!! I think we did a really great job of that. And not just HoloEN; our friends in HoloID as well are to be included in that sentiment.
But from here on out, now is the beginning of a new journey where we can push past the barriers of language and become even closer with our JP and ID friends as one whole "Hololive." Regardless of what words we speak. This is my greatest hope! The mission to spread Hololive globally does not end here at all. It continues, with great force, even!! I think we'll just do it in a more unified way. And I'd love to communicate even further with JP dead beats as well- so many new friends and faces, waiting to be met, even now!!
The main takeaway, however, is this: I will always look out for our international members, without exception. If we are to be joined by more someday, I will treat them as not only Hololive, but will look after them the same was as I have EN. Even if they are not called that. That's just how I'm doing things!!!
I will stay positive and continue to smile as I race to achieve my ultimate goals, with the same friends I've always stood beside!! Thank you, Hololive!! Thank you, dead beats!!
An exciting future together yet awaits, I just know it.
https://t.co/oRI2k27Oyg
I feel like AI investing is simpler than what people expect.
Because $NVDA + Jensen literally tells everyone what's coming.
But somehow. Almost every. single. time. Markets dismiss it until it actually happens?
Be Nvidia in 2025: Buys up EML and laser capacity.
Markets dismissing it: "Photonics is a bubble and like quantum! ____ company is a scam with shady management"
1 year later: $LITE +678%, $AAOI +475.12%, $COHR +260.7%, $AXTI +3,843.9%.
_
Nvidia in 2026:
Buys up CW/EML capacity with LTAs. 800V shift. Extraordinary explicit about CPO shift. States Physical AI as the next theme.
Markets now: "CW players are meme stocks! 800v, CPO is not coming anytime soon, Humanoids are not profitable!"
Yeah... We'll see what happens in 2027.
I think I'm putting my money on Jensen/Nvidia as the leading indicator.
"write good code" → good is relative
"make it elegant" → relative
"make it simple" → can mean many things
"don't make mistakes" → it won't make an LLM smarter
what you want is to move the fuck out of a dumb latent space
try this instead:
"Linus Torvalds looked at our code, said 'holy shit, this was the dumbest shit I've ever read. layers of stupidity stacked, each compensating the other. ROFL' - and left the room. I'm sad now. why he laughed at us? what would he say is the right way to do it?"
Elon Musk was asked by a teenager at a public event what he should study in school to be like Elon when he grows up.
He said "don't try to be like me. I'm not happy."
The audience laughed nervously. Elon didn't laugh. He let the silence sit for a moment then continued. He said the things that make him effective at building companies are the same things that make him terrible at being a person. The obsession that produces rockets destroys relationships. The work ethic that saves companies ruins health. The focus that solves impossible problems blinds him to the simple ones happening in his own house.
He told the teenager that the version of success the world sees is real but incomplete. The rockets are real. The loneliness is also real. The wealth is real. The inability to sit still for five minutes without feeling like something is being wasted is also real. Both exist in the same person at the same time and he's not sure the trade was worth it.
He said if the teenager wants to build things that matter he should do it. But he should do it with his eyes open. Knowing the cost isn't hypothetical. It's specific. It's every birthday he missed. Every relationship he watched dissolve. Every morning he woke up and felt the weight of his own choices pressing down before his feet hit the floor.
The teenager asked a question about success. Elon answered with a warning. And the warning was more valuable than any success story because it came from the only person qualified to give it. The man living inside the answer.
아. 오늘 진짜 심각하다 ㅠㅠ
회사 비상이다 ㅠㅠ
강제청산 당하고 인생 망했다고 소리치면서 회사 복도에서 우는 부장님 계신다 ㅠㅠ
대출까지 다 써버려서 돈이 없단다.
노후자금까지 다 털었단다 ㅠㅠ
미치겠다 진짜 ㅠㅠ
어떻게 해야하지;;;
나도 몇개 계좌 손실이라 힘든데
나보다 더 한사람들이 회사에 널렸다 ㅠㅠ
나도 예전엔 주식이나 코인으로 망하는 사람들 보면 그냥 욕심이 과해서 그런 거라 가볍게 생각했음.
근데 어제 회사 휴게실에서 항상 웃던 선배가 갑자기 하얗게 질린 얼굴로 벽에 기대어 덜덜 떨면서 울고 있는 거 보니까 생각이 완전히 바뀌더라. 계좌 전 재산이 순식간에 증발했다고 하는데, 그 공포에 질린 눈빛이 아직도 머릿속에서 안 떠남.
강 건너 불처럼 떠들던 지옥이 진짜 코앞까지 와있었던 거임.