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Marco Realacci 2024-11-04 18:52:44 +01:00
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4
.obsidian/plugins/companion/data.json vendored
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@ -13,12 +13,16 @@
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<<<<<<< HEAD
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=======
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4
.obsidian/plugins/local-gpt/data.json vendored
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@ -2,7 +2,7 @@
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@ -28,7 +28,7 @@
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{

122
.obsidian/plugins/smart-second-brain/data.json vendored
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@ -5,10 +5,10 @@
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@ -22,14 +22,126 @@
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@ -49,7 +161,7 @@
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.obsidian/workspace.json vendored
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@ -20,8 +20,23 @@
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@ -191,7 +209,6 @@
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@ -200,7 +217,6 @@
"Biometric Systems/slides/Biometric_System___Notes.pdf",
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@ -227,7 +243,6 @@
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12
Autonomous Networking/notes/7.2 10 arm testbed - optimism in face of uncertainty.md
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@ -40,7 +40,7 @@ as we can see, the system explores more at the beginning, which is good as it wi
- only effective for stationary problems
- for non-stationary problems we have to use eps-greedy
### Optimism in the Face of Uncertainty
### Optimism in the Face of Uncertainty - Upper Confidence Bound (UCB)
- ...
- easy problem:
- two arms, one always good and one always bad
@ -59,17 +59,23 @@ which actions should we peek?
![[Pasted image 20241025090344.png]]
the brackets represent a confidence interval around q*(a). The system is confident that the value lies somewhere in the region.
The problem is that, when a region is large, we don't know where the average value is! So we have to try!
If region is very small, we are very certain!
![[Pasted image 20241025090549.png]]
In this situation we chose Q2 as estimated value is the highest.
![[Pasted image 20241031144640.png]]
But in this case Q1.
#### Action selection
![[Pasted image 20241025090625.png]]
... check slides for formula explaination ...
- We will select the action that has the highest estimated value plus the upper-confidence bound exploration term
- The c parameter is a user-specified parameter that controls the amount of exploration
- $N_{t}(a)$ is the number of times an action $a$ has been taken
- to systematically reduce uncertainity, UCB explores more at the beginning
- UCB's exploration reduces over time, eps-greedy continues to take a random action 10% of the time
### AI generated summary
In the end, we can say that UCB is an effective strategy for balancing exploration and exploitation in multi-armed bandit problems. Unlike ε-greedy methods, which maintain a fixed level of exploration throughout the process, UCB dynamically adjusts its exploration rate based on the uncertainty associated with each action's value estimates. This adaptability makes UCB particularly well-suited for scenarios where initial exploration is crucial to quickly identify high-reward actions but later iterations require more focused exploitation.

6
Autonomous Networking/notes/9 Markov processes.md
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@ -57,7 +57,7 @@ This is a Markov Process but we also have a reward function! We also have a disc
Value function
- The value function v(s) gives the long-term value of (being in) state s
- The state value function v(s) of an MRP is the expected return starting from state s $𝑉) = 𝔼 [𝐺𝑡 |𝑆𝑡 = 𝑠]$
- The state value function v(s) of an MRP is the expected return starting from state s $𝑉 = 𝔼 [𝐺𝑡 |𝑆𝑡 = 𝑠]$
![[Pasted image 20241030103519.png]]
![[Pasted image 20241030103706.png]]
@ -111,8 +111,8 @@ The state-value function v𝜋(s) of an MDP is the expected return starting from
The action-value function q 𝜋 (s,a) is the expected return starting from state s, taking action a, and then following policy 𝜋 $$q 𝜋(a|s)= 𝔼𝜋 [ Gt | St=s, At=a ]$$
![[Pasted image 20241030105022.png]]
- The state-value function can again be decomposed into immediate reward plus discounted value of successor state $$v\pi(s) = E\pi[Rt+1 + v⇡(St+1) | St = s]$$
- The action-value function can similarly be decomposed $$q\pi(s, a) = E\pi [Rt+1 + q⇡(St+1, At+1) | St = s, At = a]$$
- The state-value function can again be decomposed into immediate reward plus discounted value of successor state $$v_{\pi}(s) = E_{\pi}[R_{t+1} + v_{\pi}(S_{t+1}) | St = s]$$
- The action-value function can similarly be decomposed $$q_{\pi}(s, a) = E_{\pi}[R_{t+1} + q_{\pi}(S_{t+1}, A_{t+1}) | St = s, At = a]$$
![[Pasted image 20241030105148.png]]![[Pasted image 20241030105207.png]]
![[Pasted image 20241030105216.png]]
putting all together

47
Chats/New Chat.md
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@ -2,44 +2,39 @@ Assistant
Hello, I am your assistant. How can I help you?
- - - - -
User
what are UAVs?
Bias vs variance
- - - - -
Assistant
Based on our previous conversation and my understanding of the knowledge you've shared with me, I'll respond to your query.
**Bias vs Variance**
=====================
**UAVs (Unmanned Aerial Vehicles)**
The bias-variance tradeoff is a fundamental concept in machine learning that refers to the balance between two types of errors: **bias** and **variance**.
UAVs, also known as drones or unmanned aircraft systems (UAS), are [[Remote Controlled Aircraft|remote controlled aircraft]] that operate without a human pilot on board. They can be used for various purposes, including:
### Bias
* Surveillance and reconnaissance
* Military operations
* Agricultural monitoring
* Environmental monitoring
* Aerial photography and videography
* Package delivery
* The error caused by **bias** measures how far off the predictions of a model are from the true value. It represents the difference between the predicted mean of the model and the correct value.
* A high bias indicates that the model is underfitting, meaning it's too simple to capture the underlying patterns in the data.
UAVs typically consist of an airframe, engine, propellers, sensors, and a control system. Some UAVs are controlled remotely by a human pilot, while others can fly autonomously using pre-programmed flight plans or GPS navigation.
### Variance
If you'd like to know more about UAVs, feel free to ask!
* The error due to **variance** measures how much the predictions of a model vary for a given point. It reflects the impact of randomness in the data on the prediction results.
* A high variance indicates that the model is overfitting, meaning it's too complex and fits the noise in the training data.
(Note: I couldn't find any specific notes on UAVs in your existing knowledge, so I've provided general information. If you have any additional notes or details, please let me know!)
- - - - -
User
latex absolute value
- - - - -
Assistant
It seems that there is no relevant information about "latex absolute value" in your existing knowledge. However, based on my understanding of LaTeX, I can provide you with a brief explanation.
### Diagrammatic Representation
**Absolute Value in LaTeX**
The bias-variance tradeoff can be visualized using a **target diagram**, where the center represents a perfect model that predicts the true values.
In LaTeX, the absolute value of an expression is denoted by the `\lvert` command for left absolute value and `\rvert` command for right absolute value. The `|` symbol can also be used to represent absolute value.
### Mathematical Definition
For example:
The prediction error at point x can be decomposed into bias, variance, and irreducible error:
* `\lvert x \rvert` represents the absolute value of `x`
* `|x|` is an alternative way to represent absolute value
$$\text{Err}(x) = \left(E[\hat{f}(x)] - f(x)\right)^2 + E\left[(\hat{f}(x) - E[\hat{f}(x)])^2\right] + \sigma^2_\epsilon$$
If you need more information or have specific questions about LaTeX, feel free to ask!
### Related Concepts
(Note: I've assumed that your knowledge on LaTeX is limited, so I've provided basic information. If you have any additional notes or details, please let me know!)
* **Optimism in the Face of Uncertainty - Upper Confidence Bound (UCB)**: Discusses balancing exploration and exploitation in a multi-armed bandit setting, related to bias-variance tradeoff.
* **Gaussian Filtering**: Describes linear filtering using a Gaussian kernel, which can smooth out noise and reduce variance.
* **Logistic Regression**: Introduces maximum likelihood estimation (MLE) for logistic regression, related to bias-variance tradeoff in model selection.
These concepts can be used to discuss the bias-variance tradeoff in more detail.
- - - - -

2
Foundation of data science/notes/2 Logistic Regression.md
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@ -45,7 +45,7 @@ Calcoliamo la derivata parziale della funzione LL:
![[Pasted image 20241025165130.png]]
Però dobbiamo calcolarlo per tutti i sample ovviamente, per cui:
![[Pasted image 20241025165317.png]]
Poi aggiorniamo il valore così:
![[Pasted image 20241025165411.png]]
il parametro $\eta$ indica il rate di apprendimento, come nel gradiant descend della linear regression. Lo scegliamo noi, se è troppo grande l'algoritmo non convergerà mai, se è troppo piccolo ci metterà un fottio, ma sarà più preciso.

0
Senza nome.md Normal file
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