Traditional gradient boosting algorithms employ static tree structures with fixed splitting criteria that remain unchanged throughout training, limiting their ability to adapt to evolving gradient distributions and problem-specific characteristics across different learning stages. This work introduces MorphBoost, a new gradient boosting framework featuring self-organizing tree structures that dynamically morph their splitting behavior during training. The algorithm implements adaptive split functions that evolve based on accumulated gradient statistics and iteration-dependent learning pressures, enabling automatic adjustment to problem complexity. Key innovations include: (1) morphing split criterion combining gradient-based scores with information-theoretic metrics weighted by training progress; (2) automatic problem fingerprinting for intelligent parameter configuration across binary/multiclass/regression tasks; (3) vectorized tree prediction achieving significant computational speedups; (4) interaction-aware feature importance detecting multiplicative relationships; and (5) fast-mode optimization balancing speed and accuracy. Comprehensive benchmarking across 10 diverse datasets against competitive models (XGBoost, LightGBM, GradientBoosting, HistGradientBoosting, ensemble methods) demonstrates that MorphBoost achieves state-of-the-art performance, outperforming XGBoost by 0.84% on average. MorphBoost secured the overall winner position with 4/10 dataset wins (40% win rate) and 6/30 top-3 finishes (20%), while maintaining the lowest variance (σ=0.0948) and highest minimum accuracy across all models, revealing superior consistency and robustness. Performance analysis across difficulty levels shows competitive results on easy datasets while achieving notable improvements on advanced problems due to higher adaptation levels.

Decision trees and randomized forests are widely used in computer vision and machine learning.

Document retrieval is a core component of question-answering systems, as it enables conditioning answer generation on new and large-scale corpora. While effective, the standard practice of encoding documents into high-dimensional embeddings for similarity search entails large memory and compute footprints, and also makes it hard to inspect the inner workings of the system. In this paper, we propose a tree-based method for organizing and representing reference documents at various granular levels, which offers the flexibility to balance cost and utility, and eases the inspection of the corpus content and retrieval operations. Our method, called ReTreever, jointly learns a routing function per internal node of a binary tree such that query and reference documents are assigned to similar tree branches, hence directly optimizing for retrieval performance. Our evaluations show that ReTreever generally preserves full representation accuracy. Its hierarchical structure further provides strong coarse representations and enhances transparency by indirectly learning meaningful semantic groupings. Among hierarchical retrieval methods, ReTreever achieves the best retrieval accuracy at the lowest latency, proving that this family of techniques can be viable in practical applications.

In this paper we introduce Context-Sensitive Decision Forests - A new perspective to exploit contextual information in the popular decision forest framework for the object detection problem. They are tree-structured classifiers with the ability to access intermediate prediction (here: classification and regression) information during training and inference time. This intermediate prediction is available for each sample and allows us to develop context-based decision criteria, used for refining the prediction process. In addition, we introduce a novel split criterion which in combination with a priority based way of constructing the trees, allows more accurate regression mode selection and hence improves the current context information. In our experiments, we demonstrate improved results for the task of pedestrian detection on the challenging TUD data set when compared to state-ofthe-art methods.

Decision trees and randomized forests are widely used in computer vision and machine learning.

Decision Trees are accessible, interpretable, and well-performing classification models. A plethora of variants with increasing expressiveness has been proposed in the last forty years. We contrast the two families of univariate DTs, whose split functions partition data through axis-parallel hyperplanes, and multivariate DTs, whose splits instead partition data through oblique hyperplanes. The latter include the former, hence multivariate DTs are in principle more powerful. Surprisingly enough, however, univariate DTs consistently show comparable performances in the literature. We analyze the reasons behind this, both with synthetic and real-world benchmark datasets. Our research questions test whether the pre-processing phase of removing correlation among features in datasets has an impact on the relative performances of univariate vs multivariate DTs. We find that existing benchmark datasets are likely biased towards favoring univariate DTs.

When dealing with tabular data, models based on decision trees are a popular choice due to their high accuracy on these data types, their ease of application, and explainability properties. However, when it comes to graph-structured data, it is not clear how to apply them effectively, in a way that incorporates the topological information with the tabular data available on the vertices of the graph. To address this challenge, we introduce TREE-G. TREE-G modifies standard decision trees, by introducing a novel split function that is specialized for graph data. Not only does this split function incorporate the node features and the topological information, but it also uses a novel pointer mechanism that allows split nodes to use information computed in previous splits. Therefore, the split function adapts to the predictive task and the graph at hand. We analyze the theoretical properties of TREE-G and demonstrate its benefits empirically on multiple graph and vertex prediction benchmarks. In these experiments, TREE-G consistently outperforms other tree-based models and often outperforms other graph-learning algorithms such as Graph Neural Networks (GNNs) and Graph Kernels, sometimes by large margins. Moreover, TREE-Gs models and their predictions can be explained and visualized

Linear Regression is a seminal technique in statistics and machine learning, where the objective is to build linear predictive models between a response (i.e., dependent) variable and one or more predictor (i.e., independent) variables from a given dataset of n instances, where each instance is a set of values of the independent variables and the corresponding value of the dependent variable. One of the classical and widely used approaches is Ordinary Least Square Regression (OLS), where the objective is the minimize the average squared error between the predicted and actual value of the dependent variable. Another classical approach is Quantile Regression (QR), where the objective is to minimize the average weighted absolute error between the predicted and actual value of the dependent variable. QR (also known as "Median Regression" for the special case of the middle quantile), is less affected by outliers and thus statistically a more robust alternative to OLS [15, 18]. However, while there exist efficient algorithms for OLS, the state-of-art algorithms for QR require solving large linear programs with many variables and constraints. They can be solved using using interior point methods [24] which are weakly polynomial (i.e., in the arithmetic computation model the running time is polynomial in the number of bits required to represent the rational numbers in the input), or using Simplex-based exterior point methods which can have exponential time complexity in the worst case [10]. The main focus of our paper is an investigation of the computational complexity of Quantile Regression, and in particular, to design efficient strongly polynomial algorithms (i.e., in the arithmetic computation model the running time is polynomial in the number of rational numbers in the input) for various special cases of the problem.

The emergence of Quantum Machine Learning (QML) to enhance traditional classical learning methods has seen various limitations to its realisation. There is therefore an imperative to develop quantum models with unique model hypotheses to attain expressional and computational advantage. In this work we extend the linear quantum support vector machine (QSVM) with kernel function computed through quantum kernel estimation (QKE), to form a decision tree classifier constructed from a decision directed acyclic graph of QSVM nodes - the ensemble of which we term the quantum random forest (QRF). To limit overfitting, we further extend the model to employ a low-rank Nystr\"{o}m approximation to the kernel matrix. We provide generalisation error bounds on the model and theoretical guarantees to limit errors due to finite sampling on the Nystr\"{o}m-QKE strategy. In doing so, we show that we can achieve lower sampling complexity when compared to QKE. We numerically illustrate the effect of varying model hyperparameters and finally demonstrate that the QRF is able obtain superior performance over QSVMs, while also requiring fewer kernel estimations.

This article is for current and aspiring machine learning practitioners looking to implement solutions to real-world machine learning problems. It is an introductory article suitable for beginners with no previous knowledge of machine learning or artificial intelligence (AI). This is the first article on my series "Machine Learning with Python". I will introduce the fundamental concepts of Machine Learning, its applications and how to set up our working environment as well as a hands on practices on a simple project. Machine learning is a type of artificial intelligence (AI) that provides computers with the ability to learn without being explicitly programmed.