2nov2024
This commit is contained in:
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15 changed files with 35749 additions and 63 deletions
3
.obsidian/community-plugins.json
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.obsidian/community-plugins.json
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"obsidian-latex-suite",
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.obsidian/plugins/companion/data.json
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.obsidian/plugins/companion/data.json
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35514
.obsidian/plugins/companion/main.js
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.obsidian/plugins/companion/main.js
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.obsidian/plugins/companion/manifest.json
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.obsidian/plugins/companion/manifest.json
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.obsidian/plugins/companion/styles.css
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.obsidian/plugins/companion/styles.css
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4
.obsidian/plugins/local-gpt/data.json
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.obsidian/plugins/local-gpt/data.json
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@ -2,7 +2,7 @@
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@ -28,7 +28,7 @@
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120
.obsidian/plugins/smart-second-brain/data.json
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.obsidian/plugins/smart-second-brain/data.json
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@ -5,11 +5,109 @@
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"ChatOllama"
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"langchain",
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"chat_models",
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"model": "nomic-embed-text",
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"baseUrl": "http://localhost:11434",
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"k": 100
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"openAIGenModel": {
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"Chats",
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"*.excalidraw.md"
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.obsidian/workspace.json
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.obsidian/workspace.json
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@ -4,21 +4,21 @@
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"file": "Autonomous Networking/notes/9 Markov processes.md",
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@ -187,11 +188,27 @@
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"Autonomous Networking/notes/7.1 K-Armed bandit problem.md",
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@ -207,36 +224,22 @@
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"Autonomous Networking/notes/9 Markov processes.md",
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"Autonomous Networking/notes/6.1 RL.md",
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BIN
Autonomous Networking/images/Pasted image 20241031144640.png
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Autonomous Networking/images/Pasted image 20241031144640.png
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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
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- only effective for stationary problems
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- for non-stationary problems we have to use eps-greedy
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### Optimism in the Face of Uncertainty
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### Optimism in the Face of Uncertainty - Upper Confidence Bound (UCB)
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- ...
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- easy problem:
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- two arms, one always good and one always bad
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![[Pasted image 20241025090344.png]]
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the brackets represent a confidence interval around q*(a). The system is confident that the value lies somewhere in the region.
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The problem is that, when a region is large, we don't know where the average value is! So we have to try!
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If region is very small, we are very certain!
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![[Pasted image 20241025090549.png]]
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In this situation we chose Q2 as estimated value is the highest.
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![[Pasted image 20241031144640.png]]
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But in this case Q1.
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#### Action selection
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![[Pasted image 20241025090625.png]]
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... check slides for formula explaination ...
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- We will select the action that has the highest estimated value plus the upper-confidence bound exploration term
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- The c parameter is a user-specified parameter that controls the amount of exploration
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- $N_{t}(a)$ is the number of times an action $a$ has been taken
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- to systematically reduce uncertainity, UCB explores more at the beginning
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- UCB's exploration reduces over time, eps-greedy continues to take a random action 10% of the time
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### AI generated summary
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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.
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Value function
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- The value function v(s) gives the long-term value of (being in) state s
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- The state value function v(s) of an MRP is the expected return starting from state s $𝑉) = 𝔼 [𝐺𝑡 |𝑆𝑡 = 𝑠]$
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- The state value function v(s) of an MRP is the expected return starting from state s $𝑉 = 𝔼 [𝐺𝑡 |𝑆𝑡 = 𝑠]$
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![[Pasted image 20241030103519.png]]
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![[Pasted image 20241030103706.png]]
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@ -111,8 +111,8 @@ The state-value function v𝜋(s) of an MDP is the expected return starting from
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The action-value function q 𝜋 (s,a) is the expected return starting from state s, taking action a, and then following policy 𝜋 $$q 𝜋(a|s)= 𝔼𝜋 [ Gt | St=s, At=a ]$$
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![[Pasted image 20241030105022.png]]
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- The state-value function can again be decomposed into immediate reward plus discounted value of successor state $$v\pi(s) = E\pi[Rt+1 + v⇡(St+1) | St = s]$$
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- The action-value function can similarly be decomposed $$q\pi(s, a) = E\pi [Rt+1 + q⇡(St+1, At+1) | St = s, At = a]$$
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- The state-value function can again be decomposed into immediate reward plus discounted value of successor state $$v_{\pi}(s) = E_{\pi}[R_{t+1} + v_{\pi}(S_{t+1}) | St = s]$$
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- The action-value function can similarly be decomposed $$q_{\pi}(s, a) = E_{\pi}[R_{t+1} + q_{\pi}(S_{t+1}, A_{t+1}) | St = s, At = a]$$
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![[Pasted image 20241030105148.png]]![[Pasted image 20241030105207.png]]
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![[Pasted image 20241030105216.png]]
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putting all together
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@ -2,44 +2,39 @@ Assistant
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Hello, I am your assistant. How can I help you?
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- - - - -
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User
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what are UAVs?
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Bias vs variance
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- - - - -
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Assistant
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Based on our previous conversation and my understanding of the knowledge you've shared with me, I'll respond to your query.
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**Bias vs Variance**
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=====================
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**UAVs (Unmanned Aerial Vehicles)**
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The bias-variance tradeoff is a fundamental concept in machine learning that refers to the balance between two types of errors: **bias** and **variance**.
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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:
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### Bias
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|
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* Surveillance and reconnaissance
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* Military operations
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* Agricultural monitoring
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* Environmental monitoring
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* Aerial photography and videography
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* Package delivery
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* 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.
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* A high bias indicates that the model is underfitting, meaning it's too simple to capture the underlying patterns in the data.
|
||||
|
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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.
|
||||
|
||||
**Absolute Value in LaTeX**
|
||||
|
||||
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.
|
||||
|
||||
For example:
|
||||
|
||||
* `\lvert x \rvert` represents the absolute value of `x`
|
||||
* `|x|` is an alternative way to represent absolute value
|
||||
|
||||
If you need more information or have specific questions about LaTeX, feel free to ask!
|
||||
|
||||
(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!)
|
||||
### Diagrammatic Representation
|
||||
|
||||
The bias-variance tradeoff can be visualized using a **target diagram**, where the center represents a perfect model that predicts the true values.
|
||||
|
||||
### Mathematical Definition
|
||||
|
||||
The prediction error at point x can be decomposed into bias, variance, and irreducible error:
|
||||
|
||||
$$\text{Err}(x) = \left(E[\hat{f}(x)] - f(x)\right)^2 + E\left[(\hat{f}(x) - E[\hat{f}(x)])^2\right] + \sigma^2_\epsilon$$
|
||||
|
||||
### Related Concepts
|
||||
|
||||
* **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.
|
||||
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