mathematical model
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mathematical model is a configuration of variables and parameters, often in terms of equations, expressions, theorems, propositions or formulae(so all mathematical language)
1. example
\[ p_0 + x_1 p_1 + x_2^2 p_2 \text{ or } p_0 + x_1 p_1 + x_2^2 p_2 = 0 \] would be a polinomial model1 with variables \(x_1, x_2\) and parameters \(p_0,p_1,p_2\)
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confident
mental state of being sure of your action/knowledge, whatever reason or objective.
The mathematical model of intelligent agent’s confidence is a good example: if you have an agent predicting weather, it will be confident about its prediction that tomorrow will rain if from the prediction, 90% of the chances it will rain tomorrow; if you have an agent driving car, it will be confident about turning right if it have a .9 confidence on the action “turn right”. The reason or objective is irrelevent; What is relevent is consistency, safety and stability.
Therefore, the shakier your action/knowledge is, the less confident you will be.
Often, the components of confident are:
- somewhere up the line - a set of assumptions (faith)
- a reasoning system - algorithm of weather prediction; action policy(observation -> confidence of a series of actions), which allows you to get a confidence score on your action or knowledge (by reasoning on their truthfulness, stochastically or deterininstically)
- a set of options - for knowledge, possible right answers (tommrow: rainy, sunny, windy, code, hot…); for action, considered actions (to run, to exercise, to open computer, to drink water, to read book, to play game, to open music, to open youtube…)
And a series of tricks working each component could help you establish the confident state:
- perfecting reasoning system
- if you have a better algorithm, of course you’d be confident about your results - they deliver
- narrow options
- do not consider much options, and concentrate the whole option space each time you cut something out: for example, when you decided to go to the gym(which here is a random thought), you cut “start video game” out of the action space, then you only have 1 action to do, “go to gym”, and there’s nothing you can be not confident about it, as the option space only have 1 item, your confidence is 100%.
- bring assumption closer to options, to reduce work needed for reasoning system
- If your assumption includes “[you should] go to gym every 2 days, alternating exerces set A and B”, or better, “[you should] never drink alcohol”, there’s not much reasoning needed: you are just 100% sure you are going to gym now doing exercise set A with a look on the calendar, or when someone handed you a drink, just 100% sure you are not drinking it.