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We present a new connection between self-adjusting binary search trees (BSTs) and heaps, two fundamental, extensively studied, and practically relevant families of data structures. Roughly speaking, we map an arbitrary heap algorithm within…
We establish finite-sample guarantees for efficient proper learning of bounded-degree polytrees, a rich class of high-dimensional probability distributions and a subclass of Bayesian networks, a widely-studied type of graphical model.…
This paper presents a general framework for generating greedy algorithms for solving convex constraint satisfaction problems for sparse solutions by mapping the satisfaction problem into one of graph traversal on a rooted tree of unknown…
Regression trees and their ensemble methods are popular methods for nonparametric regression: they combine strong predictive performance with interpretable estimators. To improve their utility for locally smooth response surfaces, we study…
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph…
We propose a randomized greedy search algorithm to find a point estimate for a random partition based on a loss function and posterior Monte Carlo samples. Given the large size and awkward discrete nature of the search space, the…
Binary search trees (BSTs) with rotations can adapt to various kinds of structure in search sequences, achieving amortized access times substantially better than the Theta(log n) worst-case guarantee. Classical examples of structural…
In this work, we study Bayesian quantum parameter estimation given a finite number of uses of the process encoding one or more unknown physical quantities. For multiple uses, it is conventional to classify quantum metrological protocols as…
We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$…
In this paper, we revisit the problem of sampling edges in an unknown graph $G = (V, E)$ from a distribution that is (pointwise) almost uniform over $E$. We consider the case where there is some a priori upper bound on the arboriciy of $G$.…
In recent years, network embedding methods have garnered increasing attention because of their effectiveness in various information retrieval tasks. The goal is to learn low-dimensional representations of vertexes in an information network…
This paper proposes a new algorithm for multiple sparse regression in high dimensions, where the task is to estimate the support and values of several (typically related) sparse vectors from a few noisy linear measurements. Our algorithm is…
Bayesian Reinforcement Learning (RL) is capable of not only incorporating domain knowledge, but also solving the exploration-exploitation dilemma in a natural way. As Bayesian RL is intractable except for special cases, previous work has…
We propose a simple generalization of standard and empirically successful decision tree learning algorithms such as ID3, C4.5, and CART. These algorithms, which have been central to machine learning for decades, are greedy in nature: they…
SEATER is a generative retrieval model that improves recommendation inference efficiency and retrieval quality by utilizing balanced tree-structured item identifiers and contrastive training objectives. We reproduce and validate SEATER's…
Sequence models are a critical component of modern NLP systems, but their predictions are difficult to explain. We consider model explanations though rationales, subsets of context that can explain individual model predictions. We find…
Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high…
High dimensional integration is essential to many areas of science, ranging from particle physics to Bayesian inference. Approximating these integrals is hard, due in part to the difficulty of locating and sampling from regions of the…
We study the problem of how well a tree metric is able to preserve the sum of pairwise distances of an arbitrary metric. This problem is closely related to low-stretch metric embeddings and is interesting by its own flavor from the line of…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…