We study Doob’s martingale convergence theorem for computable continuous time martingales on Brownian motion, in the context of algorithmic randomness. A characterization of the class of sample points for which the theorem holds is given. Such points are given the name of Doob random points. It is shown that a point is Doob random if its tail is computably random in a certain sense. Moreover, D...

Random forest method is one of the most widely applied classification algorithms at present. From the actual big data scene and requirements, the application of random forest method in the big data environment to conduct in-depth study. Due to the big data needs to process a huge number of features at the same time, and the data pattern changes constantly over time, the accuracy of a random for...

For random CNF formulae with m clauses, n variables and an unrestricted number of literals per clause the transition from high to low satisfiability can be determined exactly for large n. The critical density m/n turns out to be strongly n-dependent, ccr ln(2)/(1-p) , where pn is the mean number of positive literals per clause.This is in contrast to restricted random SAT problems (random K-SAT...

In this paper we propose using the principle of boosting to reduce the bias of a random forest prediction in the regression setting. From the original random forest fit we extract the residuals and then fit another random forest to these residuals. We call the sum of these two random forests a one-step boosted forest. We have shown with simulated and real data that the one-step boosted forest h...

Random Forest is an Ensemble Supervised Machine Learning technique. Research work in the area of Random Forest aims at either improving accuracy or improving performance. In this paper we are presenting our research towards improvement in learning time of Random Forest by proposing a new approach called Disjoint Partitioning. In this approach, we are using disjoint partitions of training datase...

We present a geometric method to determine confidence sets for the ratio E(Y )/E(X) of the means of random variables X and Y . This method reduces the problem of constructing confidence sets for the ratio of two random variables to the problem of constructing confidence sets for the means of one-dimensional random variables. It is valid in a large variety of circumstances. In the case of normal...

We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characterize the selection function that preserves normal numbers. Another one is the Steinhaus (1922) theorem on normal numbers, which characterize the normality from their subsequences. In van Lambalgen (1987), an algorithmic...

We consider the satisfiability phase transition in skewed random k-SAT distributions. It is known that the random k-SAT model, in which the instance is a set of m k-clauses selected uniformly from the set of all k-clauses over n variables, has a satisfiability phase transition at a certain clause density. The essential feature of the random k-SAT is that positive and negative literals occur wit...

Random Forest is an ensemble supervised machine learning technique. Machine learning techniques have applications in the area of Data mining. Random Forest has tremendous potential of becoming a popular technique for future classifiers because its performance has been found to be comparable with ensemble techniques bagging and boosting. Hence, an in-depth study of existing work related to Rando...

Random forests have emerged as one of the most commonly used nonparametric statistical methods in many scientific areas, particularly in analysis of high throughput genomic data. A general practice in using random forests is to generate a sufficiently large number of trees, although it is subjective as to how large is sufficient. Furthermore, random forests are viewed as "black-box" because of ...