Recently, there has been a growing interest in creating synergies between Combinatorial Optimization (CO) and Machine Learning (ML), and vice-versa. This is a natural connection since ML algorithms can be seen in essence as optimization algorithms that try to minimize prediction error. In this paper, we focus on how CO techniques can be applied to improve decision tree classifiers in ML. A decision tree classifier is a supervised ML technique that builds a tree-structured classifier, where internal nodes represent the features of a dataset, branches represent the decision rules and each leaf node represents the outcome. In essence, every path from the root to a leaf is a classification rule that determines to which class belongs the input query.

Isolation forest or "iForest" is an intuitive and widely used algorithm for anomaly detection that follows a simple yet effective idea: in a given data distribution, if a threshold (split point) is selected uniformly at random within the range of some variable and data points are divided according to whether they are greater or smaller than this threshold, outlier points are more likely to end up alone or in the smaller partition. The original procedure suggested the choice of variable to split and split point within a variable to be done uniformly at random at each step, but this paper shows that "clustered" diverse outliers - oftentimes a more interesting class of outliers than others - can be more easily identified by applying a non-uniformly-random choice of variables and/or thresholds. Different split guiding criteria are compared and some are found to result in significantly better outlier discrimination for certain classes of outliers.

Welcome to my new article series: Boosting algorithms in machine learning! This is Part 1 of the series. Here, I'll give you a short introduction to boosting, its objective, some key definitions and a list of boosting algorithms that we intend to cover in the next posts. You should be familiar with elementary tree-based machine learning models such as decision trees and random forests. In addition to that, it is recommended to have good knowledge of Python and its Scikit-learn library.

The efficacy of machine learning models is typically determined by computing their accuracy on test data sets. However, this may often be misleading, since the test data may not be representative of the problem that is being studied. With QuantifyML we aim to precisely quantify the extent to which machine learning models have learned and generalized from the given data. Given a trained model, QuantifyML translates it into a C program and feeds it to the CBMC model checker to produce a formula in Conjunctive Normal Form (CNF). The formula is analyzed with off-the-shelf model counters to obtain precise counts with respect to different model behavior. QuantifyML enables i) evaluating learnability by comparing the counts for the outputs to ground truth, expressed as logical predicates, ii) comparing the performance of models built with different machine learning algorithms (decision-trees vs. neural networks), and iii) quantifying the safety and robustness of models.

Loop closure detection is an essential tool of Simultaneous Localization and Mapping (SLAM) to minimize drift in its localization. Many state-of-the-art loop closure detection (LCD) algorithms use visual Bag-of-Words (vBoW), which is robust against partial occlusions in a scene but cannot perceive the semantics or spatial relationships between feature points. CNN object extraction can address those issues, by providing semantic labels and spatial relationships between objects in a scene. Previous work has mainly focused on replacing vBoW with CNN-derived features. In this paper, we propose SymbioLCD, a novel ensemble-based LCD that utilizes both CNN-extracted objects and vBoW features for LCD candidate prediction. When used in tandem, the added elements of object semantics and spatial-awareness create a more robust and symbiotic loop closure detection system. The proposed SymbioLCD uses scale-invariant spatial and semantic matching, Hausdorff distance with temporal constraints, and a Random Forest that utilizes combined information from both CNN-extracted objects and vBoW features for predicting accurate loop closure candidates. Evaluation of the proposed method shows it outperforms other Machine Learning (ML) algorithms - such as SVM, Decision Tree and Neural Network, and demonstrates that there is a strong symbiosis between CNN-extracted object information and vBoW features which assists accurate LCD candidate prediction. Furthermore, it is able to perceive loop closure candidates earlier than state-of-the-art SLAM algorithms, utilizing added spatial and semantic information from CNN-extracted objects.

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.