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In this paper we propose a synergistic melting of neural networks and decision trees (DT) we call neural decision trees (NDT). NDT is an architecture a la decision tree where each splitting node is an independent multilayer perceptron…

Mixed-integer programming (MIP) has emerged as a powerful framework for learning optimal decision trees. Yet, existing MIP approaches for regression tasks are either limited to purely binary features or become computationally intractable…

Prompt learning has become a prevalent strategy for adapting vision-language foundation models to downstream tasks. As large language models (LLMs) have emerged, recent studies have explored the use of category-related descriptions as input…

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…

Transformer architectures have achieved state-of-the-art performance across natural language tasks, yet they fundamentally misrepresent the hierarchical nature of human language by processing text as flat token sequences. This results in…

Decision Trees (DTs) are widely used in safety-critical domains such as medical diagnosis, valued for their interpretability and effectiveness on tabular data. However, training accurate oblique DTs is challenging due to complex…

We present Lower Bound Tree-RRT (LBT-RRT), a single-query sampling-based algorithm that is asymptotically near-optimal. Namely, the solution extracted from LBT-RRT converges to a solution that is within an approximation factor of 1+epsilon…

In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…

Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a…

Gradient boosting is widely popular due to its flexibility and predictive accuracy. However, statistical inference and uncertainty quantification for gradient boosting remain challenging and under-explored. We propose a unified framework…

The global optimization literature places large emphasis on reducing intractable optimization problems into more tractable structured optimization forms. In order to achieve this goal, many existing methods are restricted to optimization…

The scaling of Large Multimodal Models (LMMs) is constrained by the quality-quantity trade-off inherent in synthetic data. Previous approaches, such as LLM-as-a-Judge, have proven their effectiveness in addressing this but suffer from…

In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative…

In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…

In this paper, we focus our attention on the high-dimensional double sparse linear regression, that is, a combination of element-wise and group-wise sparsity. To address this problem, we propose an IHT-style (iterative hard thresholding)…

As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely…

In this paper, we propose a gradient boosting algorithm for large-scale regression problems called \textit{Gradient Boosted Binary Histogram Ensemble} (GBBHE) based on binary histogram partition and ensemble learning. From the theoretical…

Predictive clustering trees (PCTs) are a well established generalization of standard decision trees, which can be used to solve a variety of predictive modeling tasks, including structured output prediction. Combining them into ensembles…

Boosting is a learning scheme that combines weak prediction rules to produce a strong composite estimator, with the underlying intuition that one can obtain accurate prediction rules by combining "rough" ones. Although boosting is proved to…

In this paper, we present Batch Informed Trees (BIT*), a planning algorithm based on unifying graph- and sampling-based planning techniques. By recognizing that a set of samples describes an implicit random geometric graph (RGG), we are…