The sustained success random forests has led naturally to the desire to better understand the statistical and mathematical properties of the procedure. Lin and Jeon (2006) introduced the potential nearest neighbor framework and Biau and Devroye (2010) later established related consistency properties. In the last several years, a number of important statistical properties of random forests have also been established whenever base learners are constructed with subsamples rather than bootstrap samples. Scornet et al. (2015) provided the first consistency result for Breiman's original random forest algorithm whenever the true underlying regression function is assumed to be additive. Despite the impressive volume of research from the past two decades and the exciting recent progress in establishing their statistical properties, a satisfying explanation for the sustained empirical success of random forests has yet to be provided.

The Gradient Boosting Decision Tree (GBDT) is a popular machine learning model for various tasks in recent years. In this paper, we study how to improve model accuracy of GBDT while preserving the strong guarantee of differential privacy. \textit{Sensitivity} and \textit{privacy budget} are two key design aspects for the effectiveness of differential private models. Existing solutions for GBDT with differential privacy suffer from the significant accuracy loss due to too loose sensitivity bounds and ineffective privacy budget allocations (especially across different trees in the GBDT model). Loose sensitivity bounds lead to more noise to obtain a fixed privacy level. Ineffective privacy budget allocations worsen the accuracy loss especially when the number of trees is large. Therefore, we propose a new GBDT training algorithm that achieves tighter sensitivity bounds and more effective noise allocations. Specifically, by investigating the property of gradient and the contribution of each tree in GBDTs, we propose to adaptively control the gradients of training data for each iteration and leaf node clipping in order to tighten the sensitivity bounds. Furthermore, we design a novel boosting framework to allocate the privacy budget between trees so that the accuracy loss can be reduced. Our experiments show that our approach can achieve much better model accuracy than other baselines.

We analyze the trade-off between model complexity and accuracy for random forests by breaking the trees up into individual classification rules and selecting a subset of them. We show experimentally that already a few rules are sufficient to achieve an acceptable accuracy close to that of the original model. Moreover, our results indicate that in many cases, this can lead to simpler models that clearly outperform the original ones.

Gradient Boosting Decision Trees (GBDTs) have become very successful in recent years, with many awards in machine learning and data mining competitions. There have been several recent studies on how to train GBDTs in the federated learning setting. In this paper, we focus on horizontal federated learning, where data samples with the same features are distributed among multiple parties. However, existing studies are not efficient or effective enough for practical use. They suffer either from the inefficiency due to the usage of costly data transformations such as secure sharing and homomorphic encryption, or from the low model accuracy due to differential privacy designs. In this paper, we study a practical federated environment with relaxed privacy constraints. In this environment, a dishonest party might obtain some information about the other parties' data, but it is still impossible for the dishonest party to derive the actual raw data of other parties. Specifically, each party boosts a number of trees by exploiting similarity information based on locality-sensitive hashing. We prove that our framework is secure without exposing the original record to other parties, while the computation overhead in the training process is kept low. Our experimental studies show that, compared with normal training with the local data of each owner, our approach can significantly improve the predictive accuracy, and achieve comparable accuracy to the original GBDT with the data from all parties.

Let's start by understanding what decision trees are because they are the fundamental units of a random forest classifier. At a high level, decision trees can be viewed as a machine learning construct used to perform either classification or regression on some data in a hierarchical structure. In this article, I will only discuss the use of decision trees for classification. Decision trees use machine learning to identify key differentiating factors between the different classes of our data. By doing so, decision trees can take some input data and predict a class by running the data through a set of differentiating questions that it forms using machine learning.

Classification is the method of predicting the class of a given input data point. Classification problems are common in machine learning and they fall under the Supervised learning method.

Tens of millions of women suffer from infertility worldwide each year. In vitro fertilization (IVF) is the best choice for many such patients. However, IVF is expensive, time-consuming, and both physically and emotionally demanding. The first question that a patient usually asks before the IVF is how likely she will conceive, given her basic medical examination information. This paper proposes three approaches to predict the cumulative pregnancy rate after multiple oocyte pickup cycles. Experiments on 11,190 patients showed that first clustering the patients into different groups and then building a support vector machine model for each group can achieve the best overall performance. Our model could be a quick and economic approach for reliably estimating the cumulative pregnancy rate for a patient, given only her basic medical examination information, well before starting the actual IVF procedure. The predictions can help the patient make optimal decisions on whether to use her own oocyte or donor oocyte, how many oocyte pickup cycles she may need, whether to use embryo frozen, etc. They will also reduce the patient's cost and time to pregnancy, and improve her quality of life.

This is most apparent when auto-encoders are trained, where a network is trained to map the input data upon itself but is forced to project them into a lower-dimensional embedding space on the way (Vincent et al., 2010). In addition to the conventional fully connected layers, there are various special types of network connections. For example, in computer vision, convolu-tional layers are commonly used, which train multiple sliding windows that move over the image data and process just a part of the image at a time, thereby learning to recognize local features. These layers are subsequently abstracted into more and more complex visual patterns (Krizhevsky et al., 2017). For temporal data, one can use recurrent neural networks, which do not make predictions for individual input vectors, but for a sequence of input vectors. To do so, they allow feeding abstracted information from previous data points forward to the next layers.

This paper presents a detailed comparison of a recently proposed algorithm for optimizing decision trees, tree alternating optimization (TAO), with other popular, established algorithms, such as CART and C5.0. We compare their performance on a number of datasets of different size, dimensionality and number of classes, across different performance factors: accuracy and tree size (in terms of the number of leaves or the depth of the tree). We find that TAO achieves higher accuracy in every single dataset, often by a large margin.

In this paper we adopted state-of-the-art machine learning algorithms, namely: random forest (RF) and least squares boosting, to model crash data and identify the optimum model to study the impact of narrow lanes on the safety of arterial roads. Using a ten-year crash dataset in four cities in Nebraska, two machine learning models were assessed based on the prediction error. The RF model was identified as the best model. The RF was used to compute the importance of the lane width predictors in our regression model based on two different measures. Subsequently, the RF model was used to simulate the crash rate for different lane widths. The Kruskal-Wallis test, was then conducted to determine if simulated values from the four lane width groups have equal means. The test null hypothesis of equal means for simulated values from the four lane width groups was rejected. Consequently, it was concluded that the crash rates from at least one lane width group was statistically different from the others. Finally, the results from the pairwise comparisons using the Tukey and Kramer test showed that the changes in crash rates between any two lane width conditions were statistically significant.