Deep learning has a wide range of applications, from speech recognition, computer vision, to self-driving cars and mastering the game of Go. While the concept is intuitive, the implementation is often tedious and heuristic. We will take a stab at sim... [Read more...]

Linear regression probably is the most familiar technique of data analysis, but its application is often hamstrung by model assumptions. For instance, if the data has a hierarchical structure, quite often the assumptions of linear regression are feas... [Read more...]

Despite prowess of the support vector machine, it is not specifically designed to extract features relevant to the prediction. For example, in network intrusion detection, we need to learn relevant network statistics for the network defense. In consu... [Read more...]

In our previous statistics tutorials, we have treated population parameters as fixed values, and provided point estimates and confidence intervals for them. An alternative approach is the Bayesian statistics. It treats population parameters as random... [Read more...]

A variation of the standard definition of Kendall correlation coefficient is necessary in order to deal with data samples with tied ranks. It known as the Kendall’s tau-b coefficient and is more effective in determining whether two non-parametric data samples with ties are correlated. read more [Read more...]

In our last tutorial on SVM training with GPU, we mentioned a necessary step to pre-scale the data with rpusvm-scale, and to reverse scaling the prediction outcome. This cumbersome procedure is now simplified with the latest RPUSVM. read more [Read more...]

Most elementary statistical inference algorithms assume that the data can be modeled by a set of linear parameters with a normally distributed noise component. A new class of algorithms called support vector machine (SVM) remove such constraint. rea... [Read more...]

The correlation coefficient is a measurement of correlation between two random variables. While its computation is straightforward, it is not readily applicable to non-parametric statistics. read more [Read more...]

With the distance matrix found in previous tutorial, we can use various techniques of cluster analysis for relationship discovery. For example, in the data set mtcars, we can run the distance matrix with hclust, and plot a dendrogram that displays a ... [Read more...]

Statistics is computationally intensive. Routine statistical tasks such as data extraction, graphical summary, and technical interpretation all require heavy use of modern computing machinery. Obviously, these tasks can benefit greatly from a paralle... [Read more...]

In hypothesis testing, a type II error is due to a failure of rejecting an invalid null hypothesis. The probability of avoiding a type II error is called the power of the hypothesis test, and is denoted by the quantity 1 - β . read more [Read more...]

A statistical method is called non-parametric if it makes no assumption on the population distribution or sample size. This is in contrast with most parametric methods in elementary statistics that assume the data is quantitative, the population... [Read more...]

A multiple linear regression (MLR) model that describes a dependent variable y by independent variables x1, x2, ..., xp (p __ 1) is expressed by the equation as follows, where the numbers α and βk (k = 1, 2, ..., p) are the parameter... [Read more...]

In an experiment study, various treatments are applied to test subjects and the response data is gathered for analysis. A critical tool for carrying out the analysis is the Analysis of Variance (ANOVA). It enables a researcher to differentiate treatm... [Read more...]

Ever wonder how to finish your statistics homework real fast? Or you just want a quick way to verify your tedious calculations in your statistics class assignment. We provide an answer here by solving statistics exercises with R. read more [Read more...]