Random Subspace Ensemble is a machine learning algorithm that combines the predictions from multiple decision trees trained on different subsets of columns in the training dataset. Randomly varying the columns used to train each contributing member of the ensemble has the effect of introducing diversity into the ensemble and, in turn, can lift performance over using a single decision tree. It is related to other ensembles of decision trees such as bootstrap aggregation (bagging) that creates trees using different samples of rows from the training dataset, and random forest that combines ideas from bagging and the random subspace ensemble. Although decision trees are often used, the general random subspace method can be used with any machine learning model whose performance varies meaningfully with the choice of input features. In this tutorial, you will discover how to develop random subspace ensembles for classification and regression.

A decision tree is one of the supervised machine learning algorithms. This algorithm can be used for regression and classification problems -- yet, is mostly used for classification problems. A decision tree follows a set of if-else conditions to visualize the data and classify it according to the conditions. Before we dive deep into the working principle of the decision tree's algorithm you need to know a few keywords related to it. Attribute Subset Selection Measure is a technique used in the data mining process for data reduction.

We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing generalization error while retaining the interpretability of a tree. This is achieved by learning a weighted functional $L^{2}$ space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the input functions, in order to determine the binary split for each internal node of the tree. The approach is designed to manage multiple functional inputs and/or outputs, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with scalar and categorical data, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar-valued functional inputs defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real world applications.

Uplift is a particular case of individual treatment effect modeling. Such models deal with cause-and-effect inference for a specific factor, such as a marketing intervention. In practice, these models are built on customer data who purchased products or services to improve product marketing. Uplift is estimated using either i) conditional mean regression or ii) transformed outcome regression. Most existing approaches are adaptations of classification and regression trees for the uplift case. However, in practice, these conventional approaches are prone to overfitting. Here we propose a new method using neural networks. This representation allows to jointly optimize the difference in conditional means and the transformed outcome losses. As a consequence, the model not only estimates the uplift, but also ensures consistency in predicting the outcome. We focus on fully randomized experiments, which is the case of our data. We show our proposed method improves the state-of-the-art on synthetic and real data.

Explicit and implicit bias clouds human judgement, leading to discriminatory treatment of minority groups. A fundamental goal of algorithmic fairness is to avoid the pitfalls in human judgement by learning policies that improve the overall outcomes while providing fair treatment to protected classes. In this paper, we propose a causal framework that learns optimal intervention policies from data subject to fairness constraints. We define two measures of treatment bias and infer best treatment assignment that minimizes the bias while optimizing overall outcome. We demonstrate that there is a dilemma of balancing fairness and overall benefit; however, allowing preferential treatment to protected classes in certain circumstances (affirmative action) can dramatically improve the overall benefit while also preserving fairness. We apply our framework to data containing student outcomes on standardized tests and show how it can be used to design real-world policies that fairly improve student test scores. Our framework provides a principled way to learn fair treatment policies in real-world settings.

We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm using the training data. Since the validation of machine learning algorithms must always be explainable, we perform our experiments with the kNN algorithm as well as with an algorithm based on conditional probabilities, which is proposed in this work. For the evaluation of our approach, three publicly available data sets were used and three classification and two regression problems were evaluated. The presented algorithm based on conditional probabilities is also online capable and requires only a fraction of memory compared to the kNN algorithm.

In this chapter we will show you how to make a "Decision Tree". A Decision Tree is a Flow Chart, and can help you make decisions based on previous experience. In the example, a person will try to decide if he/she should go to a comedy show or not. Luckily our example person has registered every time there was a comedy show in town, and registered some information about the comedian, and also registered if he/she went or not. Now, based on this data set, Python can create a decision tree that can be used to decide if any new shows are worth attending to.

Formally a decision tree is a graphical representation of all possible solutions to a decision. These days, tree-based algorithms are the most commonly used algorithms in case of supervised learning scenarios. They are easier to interpret and visualize with great adaptability. We can use tree-based algorithms for both regression and classification problems, However, most of the time they are used for classification problem. Let's understand a decision tree from an example: Yesterday evening, I skipped dinner at my usual time because I was busy taking care of some stuff. Later in the night, I felt butterflies in my stomach.

A sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulations codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g. yield, shape) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield such as picket power and laser energy, variables that represent a dramatic change of the ICF design such as number of pulse steps are also very important. The obtained sparse components are then used to train a random forest (RF) surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF surrogate trained using all design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulations results.

Machine learning with application to questions in the physical sciences has become a widely used tool, successfully applied to classification, regression and optimization tasks in many areas. Research focus mostly lies in improving the accuracy of the machine learning models in numerical predictions, while scientific understanding is still almost exclusively generated by human researchers analysing numerical results and drawing conclusions. In this work, we shift the focus on the insights and the knowledge obtained by the machine learning models themselves. In particular, we study how it can be extracted and used to inspire human scientists to increase their intuitions and understanding of natural systems. We apply gradient boosting in decision trees to extract human interpretable insights from big data sets from chemistry and physics. In chemistry, we not only rediscover widely know rules of thumb but also find new interesting motifs that tell us how to control solubility and energy levels of organic molecules. At the same time, in quantum physics, we gain new understanding on experiments for quantum entanglement. The ability to go beyond numerics and to enter the realm of scientific insight and hypothesis generation opens the door to use machine learning to accelerate the discovery of conceptual understanding in some of the most challenging domains of science.