Computer-Intensive Statistics: A Promising Interplay between Statistics and Computer Science

Editorial Statistics and computer science have grown as separate disciplines with little interaction for the past several decades. This however, has changed radically in recent years with the availability of massive and complex datasets in medicine, social media, and physical sciences. The statistical techniques developed for regular datasets simply cannot be scaled to meet the challenges of big data, notably the computational and statistical curses of dimensionality. The dire need to meet the challenges of big data has led to the development of statistical learning, machine learning and deep learning techniques. Rapid improvements in the speed and lower costs of statistical computation in recent years have freed statistical theory from its two serious limitations: the widespread assumption that the data follow the bell-shaped curve and exclusive focus on measures, such as mean, standard deviation, and correlation whose properties could be analyzed mathematically [1]. Computer-intensive statistical techniques have freed practical applications from the constraints of mathematical tractability and today can deal with most problems without the restrictive assumption of Gaussian distribution. These methods can be classified into frequentist and Bayesian methods. The former methods utilize the sample information only while the latter methods utilize both the sample and prior information. Statistics and computer science have grown as separate disciplines with little interaction for the past several decades. This however, has changed radically in recent years with the availability of massive and complex datasets in medicine, social media, and physical sciences. The statistical techniques developed for regular datasets simply cannot be scaled to meet the challenges of big data, notably the computational and statistical curses of dimensionality. The dire need to meet the challenges of big data has led to the development of statistical learning, machine learning and deep learning techniques. Rapid improvements in the speed and lower costs of statistical computation in recent years have freed statistical theory from its two serious limitations: the widespread assumption that the data follow the bell-shaped curve and exclusive focus on measures, such as mean, standard deviation, and correlation whose properties could be analyzed mathematically [1]. Computer-intensive statistical techniques have freed practical applications from the constraints of mathematical tractability and today can deal with most problems without the restrictive assumption of Gaussian distribution. These methods can be classified into frequentist and Bayesian methods. The former methods utilize the sample information only while the latter methods utilize both the sample and prior information. Bayesian statistical methods have also benefited greatly from computer-intensive methods, notably the Markov Chain Monte Carlo (MCMC) approach [11], which is a class of methods for sampling from a probability distribution. Chief among these methods are the Gibbs sampling procedure designed for sampling from the conditional distribution and the MetropolisHastings algorithm designed for sampling from the posterior distribution as well as for multidimensional integration problems [12,13]. These methods construct a Markov chain that has the desired distribution as its equilibrium distribution and obtain a sample of the desired distribution by observing the chain after several steps. Development of MCMC methods has been a key step in making it possible to compute large hierarchical models that require integrations over hundreds or even thousands of unknown parameters. Over the past six decades, the center of statistics has steadily moved away from its traditional foothold in mathematics and logic towards a more computational focus [14]. Some may argue that with the popularity of the new field of data science, emphasis has shifted from statistical inference to algorithmic thinking. Impressive, ambitious predictive algorithms, such as random forests, boosting, support vector machines, and neural networks all illustrate algorithmic thinking of data scientists as opposed to traditional statistical thinking. Surprisingly, probability models, the main building blocks of statistical inference are largely missing from the development of these algorithms. Development of these predictive algorithms without parametric probability models has been made possible by computer-intensive non-parametric techniques, such as bootstrap, cross-validation, and permutation. Regrettably, related fields of Econometrics, Sociometry, and Psychometrics have been too slow to embrace these developments and remain reluctant to use these successful algorithmic methods absent statistical inference justification for them. While interaction between computer science and statistics is growing rapidly with the development of algorithmic models, such as bagging, boosting, random forests, and support vector machines, we need to understand why these techniques work by developing theoretical justification and inference for these methods. The field of statistics has been energized by computer science with the rise of data science as a discipline. It is fair to expect that the field of computer science is likely to be enriched by statistics as well through the development of techniques for analysis of massive data sets and probability models to understand why black box algorithmic models, such as neural networks work for pattern recognition and other predictive tasks. All scientific and business disciplines are likely to benefit from the interplay between computer science and statistics as demonstrated by the development of fast, powerful and versatile applications, such as CART® and Bayesia Lab for advanced analytics employed by applied researchers across many different fields.Advances in Computer Sciences (ISSN:2517-5718