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Modelling it

Training a dog is like training a model. You want to make sure your dog can generalize its skills across many different situations (aka low bias, low variance), and you want to use the best training methods (cross-validation and model selection) while continuously testing and improving (bootstrapping and resampling). You also might combine multiple trainers or methods to get the best possible performance (ensemble methods).

Find out more about probability and statistics applications below!

import random
# Dog class to represent the dog and its training progress
class Dog:
    def __init__(self):
        self.x = 400  # This is the center position of the dog (we'll ignore actual graphical representation)
        self.y = 500  # This is the dog's height position
        self.skill = 0  # Represents the skill level (0 - 100)

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1. Overfitting & Underfitting – “The Bias-Variance Tradeoff“

Imagine you have a dog, and you train it so well to sit when you say “sit” in your living room that the dog only responds when you’re in that exact spot. It’s like the dog has memorized the environment, but it might not respond as well in new environments (like the park). It’s “overfitted” to your living room.

If the dog doesn’t really learn how to sit at all, it’s because the training was too simplistic. Maybe you just waved your hand once and expected the dog to get it—too little effort, too little attention. That’s like underfitting.

So, the bias-variance tradeoff is about finding the right balance. You want your dog trained enough to generalize (not just memorize), but not so little that it can’t perform the task at all.

2. Cross-validation & Model Selection – “Techniques for Selecting the Best Model“

When training your dog, you don’t want to just judge its performance on one single trick in one setting. You might want to test it in different environments (different parks, with different distractions) to make sure it generalizes well. This is like cross-validation in machine learning.

It’s like taking your dog to several parks (or rooms, or training spots) to test its ability to sit in various conditions. You divide the whole pool of training data (dog behaviors in different environments) into smaller “batches” and test on each one to get a more accurate sense of how the dog is performing.

This is choosing the right “trainer” or method that works best. Maybe some trainers focus on positive reinforcement while others use a stricter method. You would compare these methods (models) and select the one that leads to the best overall trained dog (model performance).

3. Bootstrapping & Resampling: Methods for Model Validation and Error Estimation

Imagine you want to know how good your dog is at performing a trick, but you’re not sure because some days it seems great and other days, not so much. You can test your dog repeatedly on different days, with different treats, and across various environments.

You might take a subset of your dog’s training (say, a random collection of training sessions) and test it multiple times. Bootstrapping is like resampling from the original training sessions (with replacement) to get an average estimate of how well your dog performs overall.

You could also just take random samples from different training experiences. This lets you estimate how much variability there is in the dog’s behavior and get a more robust sense of its skill level.

4. Ensemble Methods – “Random Forests, Boosting, Bagging“

Imagine you have several trainers helping you train your dog, and each one uses a slightly different technique to teach your dog to sit. Some use treats, others use praise, and some even try clickers.

Instead of relying on just one trainer’s method, you combine the strengths of all the trainers to get the best result. This is like ensemble methods in machine learning, where you combine the outputs of multiple models to improve performance.

Random Forests: This is like having a large team of trainers, each using a different method or approach. Random forests use a bunch of decision trees (different trainers) to make a decision (whether your dog sits or not). The team votes on the best answer, and you go with the majority decision. Even if one trainer is bad, the group as a whole tends to do well.

Boosting: Boosting is like giving each trainer a second chance to fix their mistakes. If one trainer messes up, you let that trainer try again with a new approach, focusing more on what went wrong. Over time, the collective team gets better and better at training your dog by correcting errors.

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