Decision trees are powerful for predictive modeling but often suffer from high variance when modeling continuous relationships. While algorithms like Multivariate Adaptive Regression Splines (MARS) excel at capturing such continuous relationships, they perform poorly when modeling discontinuities. To address the limitations of both approaches, we introduce Spline-based Multivariate Adaptive Regression Trees (SMART), which uses a decision tree to identify subsets of data with distinct continuous relationships and then leverages MARS to fit these relationships independently. Unlike other methods that rely on the tree structure to model interaction and higher-order terms, SMART leverages MARS's native ability to handle these terms, allowing the tree to focus solely on identifying discontinuities in the relationship. We test SMART on various datasets, demonstrating its improvement over state-of-the-art methods in such cases. Additionally, we provide an open-source implementation of our method to be used by practitioners.

Climate models are critical tools for developing strategies to manage the risks posed by sea-level rise to coastal communities. While these models are necessary for understanding climate risks, there is a level of uncertainty inherent in each parameter in the models. This model parametric uncertainty leads to uncertainty in future climate risks. Consequently, there is a need to understand how those parameter uncertainties impact our assessment of future climate risks and the efficacy of strategies to manage them. Here, we use random forests to examine the parametric drivers of future climate risk and how the relative importances of those drivers change over time. We find that the equilibrium climate sensitivity and a factor that scales the effect of aerosols on radiative forcing are consistently the most important climate model parametric uncertainties throughout the 2020 to 2150 interval for both low and high radiative forcing scenarios. The near-term hazards of high-end sea-level rise are driven primarily by thermal expansion, while the longer-term hazards are associated with mass loss from the Antarctic and Greenland ice sheets. Our results highlight the practical importance of considering time-evolving parametric uncertainties when developing strategies to manage future climate risks.

Did you ever wonder how credit card fraud detection is caught in real-time? Do you want to know how to catch an intruder program if it is trying to access your system? This is all possible by the application of the anomaly detection machine learning model. Anomaly detection is one of the most popular machine learning techniques. In this article, we will learn concepts related to anomaly detection and how to implement it as a machine learning model.

Ensemble methods is a machine learning technique that combines several base models in order to produce one optimal predictive model. There are various ensemble methods such as stacking, blending, bagging, and boosting. Gradient Boosting, as the name suggests is a boosting method. Boosting is loosely-defined as a strategy that combines multiple simple models into a single composite model. With the introduction of more simple models, the overall model becomes a stronger predictor.

There is a growing desire in the field of reinforcement learning (and machine learning in general) to move from black-box models toward more "interpretable AI." We improve interpretability of reinforcement learning by increasing the utility of decision tree policies learned via reinforcement learning. These policies consist of a decision tree over the state space, which requires fewer parameters to express than traditional policy representations. Existing methods for creating decision tree policies via reinforcement learning focus on accurately representing an action-value function during training, but this leads to much larger trees than would otherwise be required. To address this shortcoming, we propose a novel algorithm which only increases tree size when the estimated discounted future reward of the overall policy would increase by a sufficient amount. Through evaluation in a simulated environment, we show that its performance is comparable or superior to traditional tree-based approaches and that it yields a more succinct policy. Additionally, we discuss tuning parameters to control the tradeoff between optimizing for smaller tree size or for overall reward.

Ensemble methods are among the state-of-the-art predictive modeling approaches. Applied to modern big data, these methods often require a large number of sub-learners, where the complexity of each learner typically grows with the size of the dataset. This phenomenon results in an increasing demand for storage space, which may be very costly. This problem mostly manifests in a subscriber based environment, where a user-specific ensemble needs to be stored on a personal device with strict storage limitations (such as a cellular device). In this work we introduce a novel method for lossless compression of tree-based ensemble methods, focusing on random forests. Our suggested method is based on probabilistic modeling of the ensemble's trees, followed by model clustering via Bregman divergence. This allows us to find a minimal set of models that provides an accurate description of the trees, and at the same time is small enough to store and maintain. Our compression scheme demonstrates high compression rates on a variety of modern datasets. Importantly, our scheme enables predictions from the compressed format and a perfect reconstruction of the original ensemble. In addition, we introduce a theoretically sound lossy compression scheme, which allows us to control the trade-off between the distortion and the coding rate.

I recently participated in this Kaggle competition (WIDS Datathon by Stanford) where I was able to land up in Top 10 using various boosting algorithms. Since then, I have been very curious about the fine workings of each model including parameter tuning, pros and cons and hence decided to write this blog. Despite the recent re-emergence and popularity of neural networks, I am focusing on boosting algorithms because they are still more useful in the regime of limited training data, little training time and little expertise for parameter tuning. Since XGBoost (often called GBM Killer) has been in the machine learning world for a longer time now with lots of articles dedicated to it, this post will focus more on CatBoost & LGBM. LightGBM uses a novel technique of Gradient-based One-Side Sampling (GOSS) to filter out the data instances for finding a split value while XGBoost uses pre-sorted algorithm & Histogram-based algorithm for computing the best split.

I recently participated in this Kaggle competition (WIDS Datathon by Stanford) where I was able to land up in Top 10 using various boosting algorithms. Since then, I have been very curious about the fine workings of each model including parameter tuning, pros and cons and hence decided to write this blog. Despite the recent re-emergence and popularity of neural networks, I am focusing on boosting algorithms because they are still more useful in the regime of limited training data, little training time and little expertise for parameter tuning. Since XGBoost (often called GBM Killer) has been in the machine learning world for a longer time now with lots of articles dedicated to it, this post will focus more on CatBoost & LGBM. LightGBM uses a novel technique of Gradient-based One-Side Sampling (GOSS) to filter out the data instances for finding a split value while XGBoost uses pre-sorted algorithm & Histogram-based algorithm for computing the best split.