**Instrumental Variable (IV)**

In statistics, econometrics, epidemiology and related disciplines, the method of instrumental variables (IV) is used to estimate causal relationships when controlled experiments are not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment. Instrumental variable methods allow consistent estimation when the explanatory variables (covariates) are correlated with the error terms of a regression relationship. Such correlation may occur when the dependent variable causes at least one of the covariates (‘reverse’ causation), when there are relevant explanatory variables which are omitted from the model, or when the covariates are subject to measurement error. In this situation, ordinary linear regression generally produces biased and inconsistent estimates. However, if an instrument is available, consistent estimates may still be obtained. An instrument is a variable that does not itself belong in the explanatory equation and is correlated with the endogenous explanatory variables, conditional on the other covariates. In linear models, there are two main requirements for using an IV:

• The instrument must be correlated with the endogenous explanatory variables, conditional on the other covariates.

• The instrument cannot be correlated with the error term in the explanatory equation (conditional on the other covariates), that is, the instrument cannot suffer from the same problem as the original predicting variable. … **Fuzzy Constraint Linear Discriminant Analysis (FC-LDA)**

In this paper we introduce a fuzzy constraint linear discriminant analysis (FC-LDA). The FC-LDA tries to minimize misclassification error based on modified perceptron criterion that benefits handling the uncertainty near the decision boundary by means of a fuzzy linear programming approach with fuzzy resources. The method proposed has low computational complexity because of its linear characteristics and the ability to deal with noisy data with different degrees of tolerance. Obtained results verify the success of the algorithm when dealing with different problems. Comparing FC-LDA and LDA shows superiority in classification task. … **Generative Learning Algorithms**

Algorithms that try to learn p(y|x) directly (such as logistic regression), or algorithms that try to learn mappings directly from the space of inputs X to the labels {0, 1}, (such as the perceptron algorithm) are called discrim- inative learning algorithms. Here, we’ll talk about algorithms that instead try to model p(x|y) (and p(y)). These algorithms are called generative learning algorithms. For instance, if y indicates whether an example is a dog (0) or an elephant (1), then p(x|y = 0) models the distribution of dogs’ features, and p(x|y = 1) models the distribution of elephants’ features.

Naive Bayes Generative Learning Algorithms …

# If you did not already know

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