SVM

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Logistic Regression

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 Logistic regression is a statistical method for binary classification. The classes can be considered as Y={0,1}. For a dataset X, we are trying to find P(Y=1|X)  Logistic Regression Workflow Linear Combination(logit) The logit is calculated first as shown in the blog on Softmax. This is a linear combination of the input features given by logit = t = w0 + w1 x1 + w2 x2 + ... + wn xn This can be a value between (-INF, +INF). This value also reflects the log odds of P(Y=1|X). Odds The odds of an event occurring is the ratio between the probability of the event occurring to the probability of the event not occurring. Odds = {P(Y=1|X} / {1 - P(Y=1|X} Log Odds This is the natural logarithm of the odds. In logistic regression we see that the log odds of P(Y=1|X) is the logit(t). The proof can be found in the pdf below. Sigmoid Transformation The logit(t) is passed through a sigmoid function to get a value between 0 and 1 and is interpreted as the probability of getting class Y=1. i....
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Regression 9 - Maximum Likelihood Estimation(MLE) Approach for Regression - Derivation

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  MLE Approach: When performing linear regression using MLE under the assumption that the residuals (errors) are independently and identically distributed (i.i.d.) with a normal distribution, we estimate the regression coefficients that maximize the likelihood of observing the given data. In this blog we see how to perform regression on a dataset that applies MLE for model fitting. The mathematical assumptions and derivations are given in detail.   The MLE approach gives you point estimates for the coefficients (mean of the likelihood distribution), and you can also compute the variance-covariance matrix of these estimates, which gives you the variances (and covariances) of the estimates. These variances are a measure of the uncertainty or the spread of the likelihood distribution of the parameter estimates. For simple linear regression, the MLE estimates of the coefficients will actually be the same as the Ordinary Least Squares (OLS) estimates, which are also the same as wha...
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