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Linear regression model generate continuous output variable.

Logistic regression is widely used in machine learning for classification problems. It is well-known that regularization is required to avoid over-fitting, especially when there is a only small number of training examples, or when there are a large number of parameters to be learned. In particular L1 regularized logistic regression is often used for feature selection, and has been shown to have good generalization performance in the presence of many irrelevant features. (Ng 2004; Goodman 2004) Unregularized logistic regression is an unconstrained convex optimization problem with a continuously differentiate objective function. As a consequence, it can be solved fairly efficiently with standard convex optimization methods, such as Newton's method or conjugate gradient. However, adding the L1 regularization makes the optimization

problem com-putationally more expensive to solve. If the L1 regulariza-tion is enforced by an L1 norm constraint on the parameLogistic regression is a classifier and L1 regularization tends to produce models that ignore dimensions of the input that are not predictive. This is particularly useful when the input contains many dimensions, k-nearest neighbors classification is also a classification technique, but relies on notions of distance. In a high-dimensional space, most every data point is "far" from others (the curse of dimensionality) and so these techniques break down. Naive Bayes is not inherently regularizing. Random forests represent an ensemble method; but an ensemble method is not necessarily more suitable to high-dimensional data. Practically, I think the biggest reasons for regularization are 1) to avoid overfitting by not generating high coefficients for predictors that are sparse. 2) to stabilize the estimates especially when there's collinearity in the data.

1) is inherent in the regularization framework. Since there are two forces pulling each other in the objective function, if there's no meaningful loss reduction, the increased penalty from the regularization term wouldn't improve the overall objective function. This is a great property since a lot of noise would be automatically filtered out from the model. To give you an example for 2), if you have two predictors that have same values, if you just run a regression algorithm on it since the data matrix is singular your beta coefficients will be Inf if you try to do a straight matrix inversion. But if you add a very small regularization lambda to it, you will get stable beta coefficients with the coefficient values evenly divided between the equivalent two variables. For the difference between L1 and L2, the following graph demonstrates why people bother to have L1 since L2 has such an elegant analytical solution and is so computationally straightforward. Regularized regression can also be represented as a constrained regression problem (since they are Lagrangian equivalent). The implication of this is that the L1 regularization gives you sparse estimates. Namely, in a high dimensional space, you got mostly zeros and a small number of non-zero coefficients. This is huge since it incorporates variable selection to the modeling problem. In addition, if you have to score a large sample with your model, you can have a lot of computational savings since you don't have to compute features(predictors) whose coefficient is 0. I personally think L1 regularization is one of the most beautiful things in machine learning and convex optimization. It is indeed widely used in bioinformatics and large scale machine learning for companies like Facebook, Yahoo, Google and Microsoft.

(Change the explanation even it is correct)A normalizing constant is positive, and multiplying or dividing a series of values by a positive number does not affect which of them is the largest. Maximum likelihood estimation is concerned only with finding a maximum value, so normalizing constants can be ignored.

Classification is the process of using several inputs to produce one or more outputs. For example the input might be the income, education and current debt of a customer The output might be a risk class, such as "good", "acceptable", "average", or "unacceptable". Contrast this to regression where the output is a number not a class.

One approach to the design of recommender systems that has seen wide use is collaborative filtering. Collaborative filtering methods are based on collecting and analyzing a large amount of information on users' behaviors, activities or preferences and predicting what users will like based on their similarity to other users. A key advantage of the collaborative filtering approach is that it does not rely on machine analyzable content and therefore it is capable of accurately recommending complex items such as movies without requiring an "understanding" of the item itself. Many algorithms have been used in measuring user similarity or item similarity in recommender systems. For example the k-nearest neighbor (k-NN) approach and the Pearson Correlation

Depending on the size of the data you are uploading, Amazon S3 offers the following options:

Logistic regression

Pros: Computationally inexpensive, easy to implement knowledge representation easy to interpret Cons: Prone to underfitting, may have low accuracy Works with: Numeric values^ nominal values

In this problem you have been given high-dimensional independent variables like texts, corrections, test results etc. and you have to predict either valid or not valid (One of two). So all of the below technique can be applied to this problem.

Support vector machines Naive Bayes Logistic regression Random decision forests

The opposite of supervised learning is a set of tasks known as unsupervised learning. In unsupervised learning, there's no label or target value given for the data. A task where we group similar items together is known as clustering. In unsupervised learning, we may also want to find statistical values that describe the data. This is known as density estimation. Another task of unsupervised learning may be reducing the data from many features to a small number so that we can properly visualize it in two or three dimensions

In this case, Precision = 50%, Recall = 83%, Specificity = 95%: and Accuracy = 95%. In this case, Precision is low, which means the classifier is predicting positives poorly. However, the three other measures seem to suggest that this is a good classifier. This just goes to show that the problem domain has a major impact on the measures that should be used to evaluate a classifier within it, and that looking at the 4 simple cases presented is not sufficient.

SVMs can be used to solve various real world problems:

• SVMs are helpful in text and hypertext categorization as their application can significantly reduce the need for labeled training instances in both the standard inductive and transductive settings.

• Classification of images can also be performed using SVMs. Experimental results show that SVMs achieve significantly higher search accuracy than traditional query refinement schemes after just three to four rounds of relevance feedback.

• SVMs are also useful in medical science to classify proteins with up to 90% of the compounds classified correctly.

• Hand-written characters can be recognized using SVM