We consider training decision trees using noisily labeled data, focusing on loss functions that can lead to robust learning algorithms. Our contributions are threefold. First, we offer novel theoretical insights on the robustness of many existing loss functions in the context of decision tree learning. We show that some of the losses belong to a class of what we call conservative losses, and the conservative losses lead to an early stopping behavior during training and noise-tolerant predictions during testing. Second, we introduce a framework for constructing robust loss functions, called distribution losses. These losses apply percentile-based penalties based on an assumed margin distribution, and they naturally allow adapting to different noise rates via a robustness parameter. In particular, we introduce a new loss called the negative exponential loss, which leads to an efficient greedy impurity-reduction learning algorithm. Lastly, our experiments on multiple datasets and noise settings validate our theoretical insight and the effectiveness of our adaptive negative exponential loss.

Decision trees remain one of the most popular machine learning models today, largely due to their out-of-the-box performance and interpretability. In this work, we present a Bayesian approach to decision tree induction via maximum a posteriori inference of a posterior distribution over trees. We first demonstrate a connection between maximum a posteriori inference of decision trees and AND/OR search. Using this connection, we propose an AND/OR search algorithm, dubbed MAPTree, which is able to recover the maximum a posteriori tree. Lastly, we demonstrate the empirical performance of the maximum a posteriori tree both on synthetic data and in real world settings. On 16 real world datasets, MAPTree either outperforms baselines or demonstrates comparable performance but with much smaller trees. On a synthetic dataset, MAPTree also demonstrates greater robustness to noise and better generalization than existing approaches. Finally, MAPTree recovers the maxiumum a posteriori tree faster than existing sampling approaches and, in contrast with those algorithms, is able to provide a certificate of optimality. The code for our experiments is available at https://github.com/ThrunGroup/maptree.

The study explores the synergistic combination of Synthetic Aperture Radar (SAR) and Visible-Near Infrared-Short Wave Infrared (VNIR-SWIR) imageries for land use/land cover (LULC) classification. Image fusion, employing Bayesian fusion, merges SAR texture bands with VNIR-SWIR imageries. The research aims to investigate the impact of this fusion on LULC classification. Despite the popularity of random forests for supervised classification, their limitations, such as suboptimal performance with fewer features and accuracy stagnation, are addressed. To overcome these issues, ensembles of random forests (RFE) are created, introducing random rotations using the Forest-RC algorithm. Three rotation approaches: principal component analysis (PCA), sparse random rotation (SRP) matrix, and complete random rotation (CRP) matrix are employed. Sentinel-1 SAR data and Sentinel-2 VNIR-SWIR data from the IIT-Kanpur region constitute the training datasets, including SAR, SAR with texture, VNIR-SWIR, VNIR-SWIR with texture, and fused VNIR-SWIR with texture. The study evaluates classifier efficacy, explores the impact of SAR and VNIR-SWIR fusion on classification, and significantly enhances the execution speed of Bayesian fusion code. The SRP-based RFE outperforms other ensembles for the first two datasets, yielding average overall kappa values of 61.80% and 68.18%, while the CRP-based RFE excels for the last three datasets with average overall kappa values of 95.99%, 96.93%, and 96.30%. The fourth dataset achieves the highest overall kappa of 96.93%. Furthermore, incorporating texture with SAR bands results in a maximum overall kappa increment of 10.00%, while adding texture to VNIR-SWIR bands yields a maximum increment of approximately 3.45%.

We propose polar encoding, a representation of categorical and numerical $[0,1]$-valued attributes with missing values to be used in a classification context. We argue that this is a good baseline approach, because it can be used with any classification algorithm, preserves missingness information, is very simple to apply and offers good performance. In particular, unlike the existing missing-indicator approach, it does not require imputation, ensures that missing values are equidistant from non-missing values, and lets decision tree algorithms choose how to split missing values, thereby providing a practical realisation of the "missingness incorporated in attributes" (MIA) proposal. Furthermore, we show that categorical and $[0,1]$-valued attributes can be viewed as special cases of a single attribute type, corresponding to the classical concept of barycentric coordinates, and that this offers a natural interpretation of polar encoding as a fuzzified form of one-hot encoding. With an experiment based on twenty real-life datasets with missing values, we show that, in terms of the resulting classification performance, polar encoding performs better than the state-of-the-art strategies \e{multiple imputation by chained equations} (MICE) and \e{multiple imputation with denoising autoencoders} (MIDAS) and -- depending on the classifier -- about as well or better than mean/mode imputation with missing-indicators.

Machine Learning (ML) algorithms are powerful data-driven tools for approximating highdimensional or non-linear nuisance functions which are useful in practice because the true functional form of the predictors is ex-ante unknown. In this paper, we develop estimators of policy interventions from panel data which allow for non-linear effects of the confounding regressors, and investigate the performance of these estimators using three well-known ML algorithms, specifically, LASSO, classification and regression trees, and random forests. We use Double Machine Learning (DML) (Chernozhukov et al., 2018) for the estimation of causal effects of homogeneous treatments with unobserved individual heterogeneity (fixed effects) and no unobserved confounding by extending Robinson (1988)'s partially linear regression model. We develop three alternative approaches for handling unobserved individual heterogeneity based on extending the within-group estimator, first-difference estimator, and correlated random effect estimator (Mundlak, 1978) for non-linear models. Using Monte Carlo simulations, we find that conventional least squares estimators can perform well even if the data generating process is nonlinear, but there are substantial performance gains in terms of bias reduction under a process where the true effect of the regressors is non-linear and discontinuous. However, for the same scenarios, we also find - despite extensive hyperparameter tuning - inference to be problematic for both tree-based learners because these lead to highly non-normal estimator distributions and the estimator variance being severely under-estimated. This contradicts the performance of trees in other circumstances and requires further investigation. Finally, we provide an illustrative example of DML for observational panel data showing the impact of the introduction of the national minimum wage in the UK.

The Distributional Random Forest (DRF) is a recently introduced Random Forest algorithm to estimate multivariate conditional distributions. Due to its general estimation procedure, it can be employed to estimate a wide range of targets such as conditional average treatment effects, conditional quantiles, and conditional correlations. However, only results about the consistency and convergence rate of the DRF prediction are available so far. We characterize the asymptotic distribution of DRF and develop a bootstrap approximation of it. This allows us to derive inferential tools for quantifying standard errors and the construction of confidence regions that have asymptotic coverage guarantees. In simulation studies, we empirically validate the developed theory for inference of low-dimensional targets and for testing distributional differences between two populations.

Livestock feeding behavior is an influential research area for those involved in animal husbandry and agriculture. In recent years, there has been a growing interest in automated systems for monitoring the behavior of ruminants. Despite the developments accomplished in the last decade, there is still much to do and learn about the methods for measuring and analyzing livestock feeding behavior. Automated monitoring systems mainly use motion, acoustic, and image sensors to collect animal behavioral data. The performance evaluation of existing methods is a complex task and direct comparisons between studies are difficult. Several factors prevent a direct comparison, starting from the diversity of data and performance metrics used in the experiments. To the best of our knowledge, this work represents the first tutorial-style review on the analysis of the feeding behavior of ruminants, emphasizing the relationship between sensing methodologies, signal processing and computational intelligence methods. It assesses the main sensing methodologies (i.e. based on movement, sound, images/videos and pressure) and the main techniques to measure and analyze the signals associated with feeding behavior, evaluating their use in different settings and situations. It also highlights the potentiality of automated monitoring systems to provide valuable information that improves our understanding of livestock feeding behavior. The relevance of these systems is increasingly important due to their impact on production systems and research. Finally, the paper closes by discussing future challenges and opportunities in livestock feeding behavior monitoring.

Decision tree and random forest classification and regression are some of the most widely used in machine learning approaches. Binary decision tree implementations commonly use conditioning in the form 'feature $\leq$ (or $<$) threshold', with the threshold being the midpoint between two observed feature values. In this paper, we investigate the bias introduced by the choice of conditioning operator (an intrinsic property of implementations) in the presence of features with lattice characteristics. We propose techniques to eliminate this bias, requiring an additional prediction with decision trees and incurring no cost for random forests. Using 20 classification and 20 regression datasets, we demonstrate that the bias can lead to statistically significant differences in terms of AUC and $r^2$ scores. The proposed techniques successfully mitigate the bias, compared to the worst-case scenario, statistically significant improvements of up to 0.1-0.2 percentage points of AUC and $r^2$ scores were achieved and the improvement of 1.5 percentage points of $r^2$ score was measured in the most sensitive case of random forest regression. The implementation of the study is available on GitHub at the following repository: \url{https://github.com/gykovacs/conditioning_bias}.

Street-level bureaucrats interact directly with people on behalf of government agencies to perform a wide range of functions, including, for example, administering social services and policing. A key feature of street-level bureaucracy is that the civil servants, while tasked with implementing agency policy, are also granted significant discretion in how they choose to apply that policy in individual cases. Using that discretion could be beneficial, as it allows for exceptions to policies based on human interactions and evaluations, but it could also allow biases and inequities to seep into important domains of societal resource allocation. In this paper, we use machine learning techniques to understand street-level bureaucrats' behavior. We leverage a rich dataset that combines demographic and other information on households with information on which homelessness interventions they were assigned during a period when assignments were not formulaic. We find that caseworker decisions in this time are highly predictable overall, and some, but not all of this predictivity can be captured by simple decision rules. We theorize that the decisions not captured by the simple decision rules can be considered applications of caseworker discretion. These discretionary decisions are far from random in both the characteristics of such households and in terms of the outcomes of the decisions. Caseworkers typically only apply discretion to households that would be considered less vulnerable. When they do apply discretion to assign households to more intensive interventions, the marginal benefits to those households are significantly higher than would be expected if the households were chosen at random; there is no similar reduction in marginal benefit to households that are discretionarily allocated less intensive interventions, suggesting that caseworkers are improving outcomes using their knowledge.

Random Forest is a machine learning method that offers many advantages, including the ability to easily measure variable importance. Class balancing technique is a well-known solution to deal with class imbalance problem. However, it has not been actively studied on RF variable importance. In this paper, we study the effect of class balancing on RF variable importance. Our simulation results show that over-sampling is effective in correctly measuring variable importance in class imbalanced situations with small sample size, while under-sampling fails to differentiate important and non-informative variables. We then propose a variable selection algorithm that utilizes RF variable importance and its confidence interval. Through an experimental study using many real and artificial datasets, we demonstrate that our proposed algorithm efficiently selects an optimal feature set, leading to improved prediction performance in class imbalance problem.