"As with all issues involving overfitting, how early to stop depends on the gap between what you can measure and what really matters. If you have all the facts, they’re free of all error and uncertainty, and you can directly assess whatever is important to you, then don’t stop early. Think long and hard: the complexity and effort are appropriate." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"Bayes’s Rule tells us that when it comes to making predictions based on limited evidence, few things are as important as having good priors - that is, a sense of the distribution from which we expect that evidence to have come. Good predictions thus begin with having good instincts about when we’re dealing with a normal distribution and when with a power-law distribution. As it turns out, Bayes’s Rule offers us a simple but dramatically different predictive rule of thumb for each." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"Game theory covers an incredibly broad spectrum of scenarios of cooperation and competition, but the field began with those resembling heads-up poker: two-person contests where one player’s gain is another player’s loss. Mathematicians analyzing these games seek to identify a so-called equilibrium: that is, a set of strategies that both players can follow such that neither player would want to change their own play, given the play of their opponent. It’s called an equilibrium because it’s stable—no amount of further reflection by either player will bring them to different choices. I’m content with my strategy, given yours, and you’re content with your strategy, given mine." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"In other words, overfitting poses a danger any time we’re dealing with noise or mismeasurement—and we almost always are. There can be errors in how the data were collected, or in how they were reported. Sometimes the phenomena being investigated, such as human happiness, are hard to even define, let alone measure. Thanks to their flexibility, the most complex models available to us can fit any patterns that appear in the data, but this means that they will also do so even when those patterns are mere phantoms and mirages in the noise." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"Many prediction algorithms, for instance, start out by searching for the single most important factor rather than jumping to a multi-factor model. Only after finding that first factor do they look for the next most important factor to add to the model, then the next, and so on. Their models can therefore be kept from becoming overly complex simply by stopping the process short, before overfitting has had a chance to creep in. A related approach to calculating predictions considers one data point at a time, with the model tweaked to account for each new point before more points are added; there, too, the complexity of the model increases gradually, so stopping the process short can help keep it from overfitting." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"Randomness seems like the opposite of reason - a form of giving up on a problem, a last resort. Far from it. The surprising and increasingly important role of randomness in computer science shows us that making use of chance can be a deliberate and effective part of approaching the hardest sets of problems. In fact, there are times when nothing else will do." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"The effectiveness of regularization in all kinds of machine-learning tasks suggests that we can make better decisions by deliberately thinking and doing less. If the factors we come up with first are likely to be the most important ones, then beyond a certain point thinking more about a problem is not only going to be a waste of time and effort - it will lead us to worse solutions. Early Stopping provides the foundation for a reasoned argument against reasoning, the thinking person’s case against thought. But turning this into practical advice requires answering one more question: when should we stop thinking?" (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
"The greater the uncertainty, the bigger the gap between what you can measure and what matters, the more you should watch out for overfitting - that is, the more you should prefer simplicity." (Brian Christian & Thomas L Griffiths, "Algorithms to Live By: The Computer Science of Human Decisions", 2016)
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