Classification and Regression Trees (CARTs) are off-the-shelf techniques in modern Statistics and Machine Learning. CARTs are traditionally built by means of a greedy procedure, sequentially deciding the splitting predictor variable(s) and the associated threshold. This greedy approach trains trees very fast, but, by its nature, their classification accuracy may not be competitive against other state-of-the-art procedures. Moreover, controlling critical issues, such as the misclassification rates in each of the classes, is difficult. To address these shortcomings, optimal decision trees have been recently proposed in the literature, which use discrete decision variables to model the path each observation will follow in the tree. Instead, we propose a new approach based on continuous optimization. Our classifier can be seen as a randomized tree, since at each node of the decision tree a random decision is made. The computational experience reported demonstrates the good performance of our procedure.

Decision trees are important both as interpretable models amenable to high-stakes decision-making, and as building blocks of ensemble methods such as random forests and gradient boosting. Their statistical properties, however, are not well understood. The most cited prior works have focused on deriving pointwise consistency guarantees for CART in a classical nonparametric regression setting. We take a different approach, and advocate studying the generalization performance of decision trees with respect to different generative regression models. This allows us to elicit their inductive bias, that is, the assumptions the algorithms make (or do not make) to generalize to new data, thereby guiding practitioners on when and how to apply these methods. In this paper, we focus on sparse additive generative models, which have both low statistical complexity and some nonparametric flexibility. We prove a sharp squared error generalization lower bound for a large class of decision tree algorithms fitted to sparse additive models with $C^1$ component functions. This bound is surprisingly much worse than the minimax rate for estimating such sparse additive models. The inefficiency is due not to greediness, but to the loss in power for detecting global structure when we average responses solely over each leaf, an observation that suggests opportunities to improve tree-based algorithms, for example, by hierarchical shrinkage. To prove these bounds, we develop new technical machinery, establishing a novel connection between decision tree estimation and rate-distortion theory, a sub-field of information theory.

Random forests and recursive trees are widely used in applied statistics and computer science. The popularity of recursive trees relies on several factors: their easy interpretability, the fact that they can be used for both regression and classification tasks, the small number of hyper-parameters to be tuned and finally, their non-parametric nature that allows their use to infer arbitrarily complex relations between the input and the output space. A random forest combines several randomized trees, improving the prediction accuracy at a cost of a slight lost in interpretation. This technique is easily parallelizable which has made it one of the most popular tools for handling high dimensional data sets. It has been successfully involved in various practical problems, including chemioinformatics, ecology, 3D object recognition, bioinformatics and econometrics. Biau and Scornet (2016) present a detailed list of applications as well as a review on random forests. In the present work we have focused on the ability of random forests to deal with missing values.

In this blog we are going to talk about decision tree algorithm. Yeah, you read it right. It is a tree, or it looks like a tree (upside down tree) which helps to take decision. How come a tree helps us to take decision? So how do we take any decision?

Machine learning has successfully leveraged modern data and provided computational solutions to innumerable real-world problems, including physical and biomedical discoveries. Currently, estimators could handle both scenarios with all samples available and situations requiring continuous updates. However, there is still room for improvement on streaming algorithms based on batch decision trees and random forests, which are the leading methods in batch data tasks. In this paper, we explore the simplest partial fitting algorithm to extend batch trees and test our models: stream decision tree (SDT) and stream decision forest (SDF) on three classification tasks of varying complexities. For reference, both existing streaming trees (Hoeffding trees and Mondrian forests) and batch estimators are included in the experiments. In all three tasks, SDF consistently produces high accuracy, whereas existing estimators encounter space restraints and accuracy fluctuations. Thus, our streaming trees and forests show great potential for further improvements, which are good candidates for solving problems like distribution drift and transfer learning.

Modern pattern recognition tasks use complex algorithms that take advantage of large datasets to make more accurate predictions than traditional algorithms such as decision trees or k-nearest-neighbor better suited to describe simple structures. While increased accuracy is often crucial, less complexity also has value. This paper proposes a training data selection algorithm that identifies multiple subsets with simple structures. A learning algorithm trained on such a subset can classify an instance belonging to the subset with better accuracy than the traditional learning algorithms. In other words, while existing pattern recognition algorithms attempt to learn a global mapping function to represent the entire dataset, we argue that an ensemble of simple local patterns may better describe the data. Hence the sub-setting algorithm identifies multiple subsets with simple local patterns by identifying similar instances in the neighborhood of an instance. This motivation has similarities to that of gradient boosted trees but focuses on the explainability of the model that is missing for boosted trees. The proposed algorithm thus balances accuracy and explainable machine learning by identifying a limited number of subsets with simple structures. We applied the proposed algorithm to the international stroke dataset to predict the probability of survival. Our bottom-up sub-setting algorithm performed on an average 15% better than the top-down decision tree learned on the entire dataset. The different decision trees learned on the identified subsets use some of the previously unused features by the whole dataset decision tree, and each subset represents a distinct population of data.

Random Forest is a supervised model that implements both decision trees and the bagging method. The idea is that the training dataset is resampled according to a procedure called "bootstrap". Each sample contains a random subset of the original columns and is used to fit a decision tree. The number of models and the number of columns are hyperparameters to be optimized. Finally, the predictions of the trees are mixed together calculating the mean value (for regression) or using soft voting (for classification).

Decision trees are one of the most used machine learning models because of their ease of implementation and simple interpretations. To better learn from the data they are applied to, the nodes of the decision trees need to be split based on the attributes of the data. In this article, we will understand the need of splitting a decision tree along with the methods used to split the tree nodes. Gini impurity, information gain and chi-square are the three most used methods for splitting the decision trees. Here we will discuss these three methods and will try to find out their importance in specific cases.

Decision Tree is a disseminated algorithm to solve problems. It tries to simulate the human thinking process by binarizing each step of the decision. So, at each step, the algorithm chooses between True or False to move forward. That algorithm is simple, yet very powerful, thus widely applied in machine learning models. However, one of the problems with Decision Trees is its difficulty in generalizing a problem.

Decision Tree is a Supervised literacy manner that can be used for both group and Reversion cases, but mostly it's preferred for solving Set problems. It's a tree-structured classifier, where interior bumps represent the features of a dataset, branches character the decision rules and each slice bump represents the outcome. In a Decision tree, there are two nodes, which are the Decision Nodule and Leaf Node. Decision nodules are used to make any decision and have multiple branches, whereas Leaf nodules are the output of those judgments and don't contain any fresh branches. The diagnoses or the test are performed on the keystone of features of the given dataset.