Application of MARS for the Construction of Nonparametric Models

2000 Mathematics Subject Classification: 62G08, 62P30.

Seeking Relationships in Big Data: A Bayesian Perspective

The real purpose of collecting big data is to identify causality in the hope that this will facilitate credible predictivity . But the search for causality can trap one into infinite regress, and thus one takes refuge in seeking associations between variables in data sets. Regrettably, the mere knowledge of associations does not enable predictivity. Associations need to be embedded within the framework of probability calculus to make coherent predictions. This is so because associations are a feature of probability models, and hence they do not exist outside the framework of a model. Measures of association, like correlation, regression, and mutual information merely refute a preconceived model. Estimated measures of associations do not lead to a probability model; a model is the product of pure thought. This paper discusses these and other fundamentals that are germane to seeking associations in particular, and machine learning in general. ACM Computing Classification System (1998): H.1.2, H.2.4., G.3.

On the Lp-Norm Regression Models for Estimating Value-at-Risk

Analysis of risk measures associated with price series data movements and its predictions are of strategic importance in the financial markets as well as to policy makers in particular for short- and longterm planning for setting up economic growth targets. For example, oilprice risk-management focuses primarily on when and how an organization can best prevent the costly exposure to price risk. Value-at-Risk (VaR) is the commonly practised instrument to measure risk and is evaluated by analysing the negative/positive tail of the probability distributions of the returns (profit or loss). In modelling applications, least-squares estimation (LSE)-based linear regression models are often employed for modeling and analyzing correlated data. These linear models are optimal and perform relatively well under conditions such as errors following normal or approximately normal distributions, being free of large size outliers and satisfying the Gauss-Markov assumptions. However, often in practical situations, the LSE-based linear regression models fail to provide optimal results, for instance, in non-Gaussian situations especially when the errors follow distributions with fat tails and error terms possess a finite variance. This is the situation in case of risk analysis which involves analyzing tail distributions. Thus, applications of the LSE-based regression models may be questioned for appropriateness and may have limited applicability. We have carried out the risk analysis of Iranian crude oil price data based on the Lp-norm regression models and have noted that the LSE-based models do not always perform the best. We discuss results from the L1, L2 and L∞-norm based linear regression models. ACM Computing Classification System (1998): B.1.2, F.1.3, F.2.3, G.3, J.2.