# Diagnosis

### Understanding Decision Tree Classification with Scikit-Learn

Gini Impurity is named after the Italian statistician Corrado Gini. Gini impurity can be understood as a criterion to minimize the probability of misclassification. To understand the definition (as shown in the figure) and exactly how we can build up a decision tree, let's get started with a very simple data-set, where depending on various weather conditions, we decide whether to play an outdoor game or not. From the definition, a data-set containing only one class will have 0 Gini Impurity. In building up the decision tree our idea is to choose the feature with least Gini Impurity as root node and so on... Let's get started with the simple data-set -- Here we see that depending on 4 features (Outlook, Temperature, Humidity, Wind), decision is made on whether to play tennis or not.

### Learning Partially Observable Models Using Temporally Abstract Decision Trees

This paper introduces timeline trees, which are partial models of partially observable environments. Timeline trees are given some specific predictions to make and learn a decision tree over history. The main idea of timeline trees is to use temporally abstract features to identify and split on features of key events, spread arbitrarily far apart in the past (whereas previous decision-tree-based methods have been limited to a finite suffix of history). Experiments demonstrate that timeline trees can learn to make high quality predictions in complex, partially observable environments with high-dimensional observations (e.g. an arcade game). Papers published at the Neural Information Processing Systems Conference.

### Efficient Identification in Linear Structural Causal Models with Instrumental Cutsets

One of the most common mistakes made when performing data analysis is attributing causal meaning to regression coefficients. Formally, a causal effect can only be computed if it is identifiable from a combination of observational data and structural knowledge about the domain under investigation (Pearl, 2000, Ch. 5). Building on the literature of instrumental variables (IVs), a plethora of methods has been developed to identify causal effects in linear systems. Almost invariably, however, the most powerful such methods rely on exponential-time procedures. In this paper, we investigate graphical conditions to allow efficient identification in arbitrary linear structural causal models (SCMs).

### The Case for Evaluating Causal Models Using Interventional Measures and Empirical Data

Causal inference is central to many areas of artificial intelligence, including complex reasoning, planning, knowledge-base construction, robotics, explanation, and fairness. An active community of researchers develops and enhances algorithms that learn causal models from data, and this work has produced a series of impressive technical advances. However, evaluation techniques for causal modeling algorithms have remained somewhat primitive, limiting what we can learn from experimental studies of algorithm performance, constraining the types of algorithms and model representations that researchers consider, and creating a gap between theory and practice. We argue for more frequent use of evaluation techniques that examine interventional measures rather than structural or observational measures, and that evaluate those measures on empirical data rather than synthetic data. We survey the current practice in evaluation and show that the techniques we recommend are rarely used in practice.

### Learning and Testing Causal Models with Interventions

We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009). Given a causal Bayesian network M on a graph with n discrete variables and bounded in-degree and bounded confounded components'', we show that O(log n) interventions on an unknown causal Bayesian network X on the same graph, and O(n/epsilon 2) samples per intervention, suffice to efficiently distinguish whether X M or whether there exists some intervention under which X and M are farther than epsilon in total variation distance. We also obtain sample/time/intervention efficient algorithms for: (i) testing the identity of two unknown causal Bayesian networks on the same graph; and (ii) learning a causal Bayesian network on a given graph. Although our algorithms are non-adaptive, we show that adaptivity does not help in general: Omega(log n) interventions are necessary for testing the identity of two unknown causal Bayesian networks on the same graph, even adaptively. Our algorithms are enabled by a new subadditivity inequality for the squared Hellinger distance between two causal Bayesian networks.

### Optimal Sparse Decision Trees

Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of optimality, or lack of guarantees of closeness to optimality: decision tree algorithms are often greedy or myopic, and sometimes produce unquestionably suboptimal models. Hardness of decision tree optimization is both a theoretical and practical obstacle, and even careful mathematical programming approaches have not been able to solve these problems efficiently. This work introduces the first practical algorithm for optimal decision trees for binary variables. The algorithm is a co-design of analytical bounds that reduce the search space and modern systems techniques, including data structures and a custom bit-vector library.

### Multi-Layered Gradient Boosting Decision Trees

Multi-layered distributed representation is believed to be the key ingredient of deep neural networks especially in cognitive tasks like computer vision. While non-differentiable models such as gradient boosting decision trees (GBDTs) are still the dominant methods for modeling discrete or tabular data, they are hard to incorporate with such representation learning ability. In this work, we propose the multi-layered GBDT forest (mGBDTs), with an explicit emphasis on exploring the ability to learn hierarchical distributed representations by stacking several layers of regression GBDTs as its building block. The model can be jointly trained by a variant of target propagation across layers, without the need to derive backpropagation nor differentiability. Experiments confirmed the effectiveness of the model in terms of performance and representation learning ability.

### Optimal Decision Tree with Noisy Outcomes

A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis).

### LightGBM: A Highly Efficient Gradient Boosting Decision Tree

Gradient Boosting Decision Tree (GBDT) is a popular machine learning algorithm, and has quite a few effective implementations such as XGBoost and pGBRT. Although many engineering optimizations have been adopted in these implementations, the efficiency and scalability are still unsatisfactory when the feature dimension is high and data size is large. A major reason is that for each feature, they need to scan all the data instances to estimate the information gain of all possible split points, which is very time consuming. To tackle this problem, we propose two novel techniques: \emph{Gradient-based One-Side Sampling} (GOSS) and \emph{Exclusive Feature Bundling} (EFB). With GOSS, we exclude a significant proportion of data instances with small gradients, and only use the rest to estimate the information gain.

### Efficient Non-greedy Optimization of Decision Trees

Decision trees and randomized forests are widely used in computer vision and machine learning. This greedy procedure often leads to suboptimal trees. In this paper, we present an algorithm for optimizing the split functions at all levels of the tree jointly with the leaf parameters, based on a global objective. We show that the problem of finding optimal linear-combination (oblique) splits for decision trees is related to structured prediction with latent variables, and we formulate a convex-concave upper bound on the tree's empirical loss. Computing the gradient of the proposed surrogate objective with respect to each training exemplar is O(d 2), where d is the tree depth, and thus training deep trees is feasible.