Neural Information Processing Systems http://nips.cc/

Interval-valued outputs arise naturally in fields such as computational biology and survival analysis. In the latter setting, one is interested in predicting the time until some adverse event, such as death, occurs.

Scaling up model sizes can lead to fundamentally new capabilities in many machine learning (ML) tasks. However, training big models requires strong distributed system expertise to carefully design model-parallel execution strategies that suit the model architectures and cluster setups.

Diffusion trajectory distillation methods aim to accelerate sampling in diffusion models, which produce high-quality outputs but suffer from slow sampling speeds. These methods train a student model to approximate the multi-step denoising process of a pretrained teacher model in a single step, enabling one-shot generation. However, theoretical insights into the trade-off between different distillation strategies and generative quality remain limited, complicating their optimization and selection. In this work, we take a first step toward addressing this gap. Specifically, we reinterpret trajectory distillation as an operator merging problem in the linear regime, where each step of the teacher model is represented as a linear operator acting on noisy data. These operators admit a clear geometric interpretation as projections and rescalings corresponding to the noise schedule. During merging, signal shrinkage occurs as a convex combination of operators, arising from both discretization and limited optimization time of the student model. We propose a dynamic programming algorithm to compute the optimal merging strategy that maximally preserves signal fidelity. Additionally, we demonstrate the existence of a sharp phase transition in the optimal strategy, governed by data covariance structures. Our findings enhance the theoretical understanding of diffusion trajectory distillation and offer practical insights for improving distillation strategies.

We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function.

Additional Feedback: Post feedback response: I appreciate the author feedback. One item I want to flag, though. The feedback said (of one of the reviews): "We are grateful to the reviewer for providing a comprehensive list of papers on non-Markovian reward". I do not think the list is at all "comprehensive". It represents a number of very relevant and very significant papers, but there are others in this area.

Binary segmentation is the classic greedy algorithm which recursively splits a sequential data set by optimizing some loss or likelihood function. Binary segmentation is widely used for changepoint detection in data sets measured over space or time, and as a sub-routine for decision tree learning. In theory it should be extremely fast for $N$ data and $K$ splits, $O(N K)$ in the worst case, and $O(N \log K)$ in the best case. In this paper we describe new methods for analyzing the time and space complexity of binary segmentation for a given finite $N$, $K$, and minimum segment length parameter. First, we describe algorithms that can be used to compute the best and worst case number of splits the algorithm must consider. Second, we describe synthetic data that achieve the best and worst case and which can be used to test for correct implementation of the algorithm. Finally, we provide an empirical analysis of real data which suggests that binary segmentation is often close to optimal speed in practice.

Neural Information Processing Systems http://nips.cc/

Learning a regression function using censored or interval-valued output data is an important problem in fields such as genomics and medicine. The goal is to learn a real-valued prediction function, and the training output labels indicate an interval of possible values. Whereas most existing algorithms for this task are linear models, in this paper we investigate learning nonlinear tree models. We propose to learn a tree by minimizing a margin-based discriminative objective function, and we provide a dynamic programming algorithm for computing the optimal solution in log-linear time. We show empirically that this algorithm achieves state-of-the-art speed and prediction accuracy in a benchmark of several data sets.