A central problem in statistics is model selection, the choice between competing models of a stochastic process whose observables are corrupted by noise. In the information-based paradigm of inference, model selection is performed by estimating the predictive performance of the com- peting models. The candidate model with the best estimated predictive performance is selected. Information-based inference is dependent on the accuracy of the estimate of the predictive complexity, a measure of the flexibility of the model in fitting the data. A large-sample-size approximation for the performance is the Akaike Information Criterion (AIC). The AIC approximation fails in a wide range of important applications, either significantly under or over-estimating the complexity. We introduce an improved approximation for the complexity which we use to define a new information criterion: the frequentist information criterion (FIC). FIC extends the applicability of information-based infer- ence to the finite-sample-size regime of regular models and to singular models. We demonstrate the power of the approach in a number of example problems.

But there is a check; the regression analysis cannot be applied in scenarios where the response variable is not continuous. In our case the response variable is not a continuous variable but a value among a fixed set of classes. We call such scenarios as Classification problem rather than prediction problem. In such scenarios where the response variables are more of qualitative nature rather than continuous nature, we have to apply more suitable models namely logistic regression for classification.

In the last few blog posts of this series, we discussed simple linear regression model. We discussed multivariate regression model and methods for selecting the right model. Fernando has now created a better model. In this article will address that question. This article will elaborate about Log-Log regression models.

About this course: Case Studies: Finding Similar Documents A reader is interested in a specific news article and you want to find similar articles to recommend. What is the right notion of similarity? Moreover, what if there are millions of other documents? Each time you want to a retrieve a new document, do you need to search through all other documents? How do you group similar documents together?

Want to use something more interpertable, something that trains faster and performs pretty much just as well as the old Logistic Regression or even Neural Networks? You should consider Decision Trees for classification and regression. Decision Trees and their extension Random Forests are robust and easy-to-interpret machine learning algorithms for Classification and Regression tasks. Decision Trees and Decision Tree Learning together comprise a simple and fast way of learning a function that maps data x to outputs y, where x can be a mix of categorical and numeric variables and y can be categorical for classification, or numeric for regression. Methods such as SVMs, Logistic Regression and Deep Neural Nets pretty much do the same thing.

I am relatively new to predictive modeling techniques and would like to get a few concepts cleared/discussed. I am currently in the process of building a logistic regression model using Weight of Evidence (WOE) technique. I understand that the log odds and WOEs tend to have a linear relationship - a pre-requisite for the model. In case of categorical variables, WOEs can be used to make them continuous. But what if, the Log odds have a U-shaped relationship with the independent variable.

You don't need to know K-NN to understand this article -- but click here if you want to learn more about it. You don't need a background in statistical science either. Let's describe this new algorithm and its various components, in simple English We are dealing here with a supervised learning problem, and more specifically, clustering (also called supervised classification.). In particular, we want to assign a class label to a new observation that does not belong to the training set. Instead of checking out individual points (the nearest neighbors) and using a majority (voting) rule to assign the new observation to a cluster based on nearest neighbor counts, we are checking out cliques of points, and focus on the nearest cliques rather than on the nearest points. The cliques considered here are defined by circles (in two dimensions) or spheres (in three dimensions.)

You don't need to know K-NN to understand this article -- but click here if you want to learn more about it. You don't need a background in statistical science either. Let's describe this new algorithm and its various components, in simple English We are dealing here with a supervised learning problem, and more specifically, clustering (also called supervised classification.). In particular, we want to assign a class label to a new observation that does not belong to the training set. Instead of checking out individual points (the nearest neighbors) and using a majority (voting) rule to assign the new observation to a cluster based on nearest neighbor counts, we are checking out cliques of points, and focus on the nearest cliques rather than on the nearest points.

Clustering, or cluster analysis, is used for analyzing data which does not include pre-labeled classes. Data instances are grouped together using the concept of maximizing intraclass similarity and minimizing the similarity between differing classes. This translates to the clustering algorithm identifying and grouping instances which are very similar, as opposed to ungrouped instances which are much less-similar to one another. As clustering does not require the pre-labeling of classes, it is a form of unsupervised learning. At the core of cluster analysis is the concept of measuring distances between a variety of different data point dimensions.

Gaussian process (GP) regression is a powerful interpolation technique due to its flexibility in capturing non-linearity. In this paper, we provide a general framework for understanding the frequentist coverage of point-wise and simultaneous Bayesian credible sets in GP regression. As an intermediate result, we develop a Bernstein von-Mises type result under supremum norm in random design GP regression. Identifying both the mean and covariance function of the posterior distribution of the Gaussian process as regularized $M$-estimators, we show that the sampling distribution of the posterior mean function and the centered posterior distribution can be respectively approximated by two population level GPs. By developing a comparison inequality between two GPs, we provide exact characterization of frequentist coverage probabilities of Bayesian point-wise credible intervals and simultaneous credible bands of the regression function. Our results show that inference based on GP regression tends to be conservative; when the prior is under-smoothed, the resulting credible intervals and bands have minimax-optimal sizes, with their frequentist coverage converging to a non-degenerate value between their nominal level and one. As a byproduct of our theory, we show that the GP regression also yields minimax-optimal posterior contraction rate relative to the supremum norm, which provides a positive evidence to the long standing problem on optimal supremum norm contraction rate in GP regression.