相关论文: Distance Metric Ensemble Learning and the Andrews-…

The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…

To attain the best learning accuracy, people move on with difficulties and frustrations. Though one can optimize the empirical objective using a given set of samples, its generalization ability to the entire sample distribution remains…

We introduce the Binary Matrix Guessing Problem and provide two algorithms to solve this problem. The first algorithm we introduce is Elementwise Probing Algorithm (EPA) which is very fast under a score which utilizes Frobenius Distance.…

Complex scientific models where the likelihood cannot be evaluated present a challenge for statistical inference. Over the past two decades, a wide range of algorithms have been proposed for learning parameters in computationally feasible…

We extend the theoretical analysis of a recently proposed single subspace learning algorithm, called Dual Principal Component Pursuit (DPCP), to the case where the data are drawn from of a union of hyperplanes. To gain insight into the…

Recently, the alternating direction method of multipliers (ADMM) has found many efficient applications in various areas; and it has been shown that the convergence is not guaranteed when it is directly extended to the multiple-block case of…

The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…

Embedding-based representations in Euclidean space $\mathbb{R}^d$ are a cornerstone of modern machine learning, where a major goal is to use the \emph{smallest dimension} that faithfully captures data relations. In this work, we prove sharp…

We study learning under a two-step contrastive example oracle, as introduced by Mansouri et. al. (2025), where each queried (or sampled) labeled example is paired with an additional contrastive example of opposite label. While Mansouri et…

Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…

A new learning algorithm proposed by Brandt and Lin for neural network [1], [2] has been shown to be mathematically equivalent to the conventional back-propagation learning algorithm, but has several advantages over the backpropagation…

Machine unlearning -- efficiently removing the effect of a small "forget set" of training data on a pre-trained machine learning model -- has recently attracted significant research interest. Despite this interest, however, recent work…

Approximate near-neighbors search (\textsc{ANNS}) is a long-studied problem in computational geometry. %that has received considerable attention by researchers in the community. In this paper, we revisit the problem and propose the first…

In the advent of big data and machine learning, researchers now have a wealth of congressional candidate ideal point estimates at their disposal for theory testing. Weak relationships raise questions about the extent to which they capture a…

Probabilistic proofs of the Johnson-Lindenstrauss lemma imply that random projection can reduce the dimension of a data set and approximately preserve pairwise distances. If a distance being approximately preserved is called a success, and…

Top-down induction of decision trees has been observed to suffer from the inadequate functioning of the pruning phase. In particular, it is known that the size of the resulting tree grows linearly with the sample size, even though the…

Recent work has shown that models trained to the same objective, and which achieve similar measures of accuracy on consistent test data, may nonetheless behave very differently on individual predictions. This inconsistency is undesirable in…

The main motivation for this article is to explore the connections between the existence of certain combinatorial patterns (as in van der Corputs's theorem on arithmetic progressions of length $3$) with well-known tools and theorems for…

Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and…

Motivated by recent work on ordinal embedding (Kleindessner and von Luxburg, 2014), we derive large sample consistency results and rates of convergence for the problem of embedding points based on triple or quadruple distance comparisons.…