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What is the logic behind logarithm?
In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.
Why we use logarithms in statistics?
Logarithms (or logs for short) are much used in statistics. We often analyse the logs of measurements rather than the measurements themselves, and some widely used methods of analysis, such as logistic and Cox regression, produce coefficients on a logarithmic scale.
Why do we use logarithms in machine learning?
Using logarithm is the same: You need to find the parameters that minimize the loss function, which is one of the main problems that you try to solve in Machine Learning. When a function is convex, we know that it has only one minimum, so every local minimum is actually the global one.
What’s the difference between algorithm and logarithm?
An algorithm is usually a bunch of steps that you take in order to do something– often to find a particular answer. An algorithm is a finite procedure for producing a structure, object or solution to a mathematical problem A logarithm is an exponent.
Is learning about logarithms necessary or helpful?
Logarithms are defined as the solutions to exponential equations and so are practically useful in any situation where one needs to solve such equations (such as finding how long it will take for a population to double or for a bank balance to reach a given value with compound interest).
What is the intuition for maximum likelihood in logistic regression?
The intuition for maximum-likelihood for logistic regression is that a search procedure seeks values for the coefficients (Beta values) that minimize the error in the probabilities predicted by the model to those in the data (e.g. probability of 1 if the data is the primary class).
How did the logistic regression method get its name?
Logistic Function Logistic regression is named for the function used at the core of the method, the logistic function. The logistic function, also called the sigmoid function was developed by statisticians to describe properties of population growth in ecology, rising quickly and maxing out at the carrying capacity of the environment.
How to calculate y in logistic regression for machine learning?
y = e^(b0 + b1*x) / (1 + e^(b0 + b1*x)) Where y is the predicted output, b0 is the bias or intercept term and b1 is the coefficient for the single input value (x). Each column in your input data has an associated b coefficient (a constant real value) that must be learned from your training data.
How are the coefficients of logistic regression estimated?
The coefficients (Beta values b) of the logistic regression algorithm must be estimated from your training data. This is done using maximum-likelihood estimation.