One of the main drawbacks of R is the inefficiency of looping operations. Since R inherently is a functional programming language, many looping operations can be converted into map operations by choosing the appropriate functional forms. Although such a mapping operation speeds up the program, but sometimes we need still better speedups (if we compare similar programs written in C or C++). In such cases, we will see that by […]
Given a supervised classification problem with the set of N training examples along with the class labels , i.e. , we need to build a model to predict the class label for an unseen example. Some of the algorithms we have already encountered and some we will encounter in later posts such as the Logistic Regression, Naive Bayes, Adaboost, Gradient Boosting, KNN, Support Vector Machines, Neural Networks etc. In this […]
In an earlier post, we introduced one of the most widely used optimization technique, the gradient descent and its scalable variant, the Stochastic Gradient Descent. Although the SGD is an efficient and scalable technique to optimize a function, but the drawbacks with both gradient descent and SGD is that they are susceptible to find local optimum. The gradient descent technique is not suited to find local or global optimum with […]
Clustering algorithms comes with lots of challenges. For centroid based clustering algorithms like K-Means, the primary challenges are : Initialising the cluster centroids. Choosing the optimum number of clusters. Evaluating clustering quality in the absence of labels. Reduce dimensionality of data. In this post we will focus on different ways of choosing the optimum number of clusters. The basic idea is to minimize the sum of the within cluster sum […]
Boosting is a general technique by which multiple "weak" classifiers are combined to produce a "super strong" single classifier. The idea behind boosting technique is very simple. Boosting consists of incrementally building a final classifier from an ensemble of classifiers in a way such that the next classifier chosen should be able to perform better on training instances that the current classifier is not able to do.
Given two random variables X and Y, mutual information measures how much knowing one of these variables reduces uncertainty about the other. For example, if X and Y are independent, then knowing X does not give any information about Y and vice-verse, so their mutual information is zero. At the other extreme, if X is completely correlated with Y then all information conveyed by X is also conveyed by Y, […]
In the last post, we introduced a technique called the Maximum Likelihood Estimation (MLE) to estimate unknown parameters of a probability distribution given a set of observations. Although it is a very useful technique, but it assumes that all information about the observation is available to us. Consider the example of a two coin toss : "Given two coins A and B, with probability of heads being 'p' and 'q' […]
Observations from a probability distribution, depends on the parameters of that model. For example, given an unbiased coin with equal probability of landing heads as well as tails, what is probability of observing the sequence "HHTH". Our knowledge from probability theory says that since the toss of a coin follows the binomial distribution, the probability of the observation should be 0.54 = 0.0625, but what if the coin was biased and the […]