相关论文: Optimal Query Complexities for Dynamic Trace Estim…

Quantum kernel methods are among the leading candidates for achieving quantum advantage in supervised learning. A key bottleneck is the cost of inference: evaluating a trained model on new data requires estimating a weighted sum…

Motion planning under differential constraints is a classic problem in robotics. To date, the state of the art is represented by sampling-based techniques, with the Rapidly-exploring Random Tree algorithm as a leading example. Yet, the…

The Euclidean Steiner tree problem asks to find a min-cost metric graph that connects a given set of \emph{terminal} points $X$ in $\mathbb{R}^d$, possibly using points not in $X$ which are called Steiner points. Even though near-linear…

There are many approaches for training decision trees. This work introduces a novel gradient-based method for constructing decision trees that optimize arbitrary differentiable loss functions, overcoming the limitations of heuristic…

Tree-based models are widely recognized for their interpretability and have proven effective in various application domains, particularly in high-stakes domains. However, learning decision trees (DTs) poses a significant challenge due to…

The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…

We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that…

This paper investigates the optimal signal detection problem with a particular interest in large-scale multiple-input multiple-output (MIMO) systems. The problem is NP-hard and can be solved optimally by searching the shortest path on the…

A tremendous range of design tasks in materials, physics, and biology can be formulated as finding the optimum of an objective function depending on many parameters without knowing its closed-form expression or the derivative. Traditional…

We study the query complexity of the metric Steiner Tree problem, where we are given an $n \times n$ metric on a set $V$ of vertices along with a set $T \subseteq V$ of $k$ terminals, and the goal is to find a tree of minimum cost that…

The classic exact pattern matching problem, given two strings -- a pattern $P$ of length $m$ and a text $T$ of length $n$ -- asks whether $P$ occurs as a substring of $T$. A property tester for the problem needs to distinguish (with high…

Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…

Decision tree optimization is notoriously difficult from a computational perspective but essential for the field of interpretable machine learning. Despite efforts over the past 40 years, only recently have optimization breakthroughs been…

Contextual MDPs are powerful tools with wide applicability in areas from biostatistics to machine learning. However, specializing them to offline datasets has been challenging due to a lack of robust, theoretically backed methods. Our work…

The implicit trace estimation problem asks for an approximation of the trace of a square matrix, accessed via matrix-vector products (matvecs). This paper designs new randomized algorithms, XTrace and XNysTrace, for the trace estimation…

We design and analyze a novel accelerated gradient-based algorithm for a class of bilevel optimization problems. These problems have various applications arising from machine learning and image processing, where optimal solutions of the two…

This work considers the sample complexity of obtaining an $\varepsilon$-optimal policy in an average reward Markov Decision Process (AMDP), given access to a generative model (simulator). When the ground-truth MDP is weakly communicating,…

Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…

Decision trees partition the feature space using hard binary thresholds, assigning identical confidence to instances far from a decision boundary and to those directly on it. We introduce ternary decision trees, which augment each split…

In this paper, we develop and analyze sub-sampled trust-region methods for solving finite-sum optimization problems. These methods employ subsampling strategies to approximate the gradient and Hessian of the objective function,…