相关论文: Distance Metric Ensemble Learning and the Andrews-…
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary…
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by…
Evaluating the performance of clustering models is a challenging task where the outcome depends on the definition of what constitutes a cluster. Due to this design, current existing metrics rarely handle multiple clustering models with…
Graph theory is an interdisciplinary field of study that has various applications in mathematical modeling and computer science. Research in graph theory depends on the creation of not only theorems but also conjectures. Conjecture-refuting…
Motivated by nonconvex, inconsistent feasibility problems in imaging, the relaxed alternating averaged reflections algorithm, or relaxed Douglas-Rachford algorithm (DR$\lambda$), was first proposed over a decade ago. Convergence results for…
We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…
In this note we give an example application of a recently presented predictive learning method called Rule Ensembles. The application we present is the search for super-symmetric particles at the Large Hadron Collider. In particular, we…
We investigate ensemble methods for prediction in an online setting. Unlike all the literature in ensembling, for the first time, we introduce a new approach using a meta learner that effectively combines the base model predictions via…
We consider machine learning in a comparison-based setting where we are given a set of points in a metric space, but we have no access to the actual distances between the points. Instead, we can only ask an oracle whether the distance…
Distance metric learning has attracted a lot of interest for solving machine learning and pattern recognition problems over the last decades. In this work we present a simple approach based on concepts from statistical physics to learn…
Ensemble learning has had many successes in supervised learning, but it has been rare in unsupervised learning and dimensionality reduction. This study explores dimensionality reduction ensembles, using principal component analysis and…
This work focuses on active learning of distance metrics from relative comparison information. A relative comparison specifies, for a data point triplet $(x_i,x_j,x_k)$, that instance $x_i$ is more similar to $x_j$ than to $x_k$. Such…
The framework of postselection is becoming more and more important in various recent directions in Quantum Computation research. Postselection renders simple computational models able to perform general quantum computation. This was first…
Tree ensembles are one of the most widely used model classes. However, these models are susceptible to adversarial examples, i.e., slightly perturbed examples that elicit a misprediction. There has been significant research on designing…
Conducting text retrieval in a dense learned representation space has many intriguing advantages over sparse retrieval. Yet the effectiveness of dense retrieval (DR) often requires combination with sparse retrieval. In this paper, we…
Ensemble learning has been a focal point of machine learning research due to its potential to improve predictive performance. This study revisits the foundational work on ensemble error decomposition, historically confined to…
It is shown that the original Andrews--Curtis conjecture on balanced presentations of the trivial group is equivalent to its "cyclic" version in which, in place of arbitrary conjugations, one can use only cyclic permutations. This, in…
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms…
The seminal result of Johnson and Lindenstrauss on random embeddings has been intensively studied in applied and theoretical computer science. Despite that vast body of literature, we still lack of complete understanding of statistical…
A conjecture of Hopkins (2018) posits that for certain high-dimensional hypothesis testing problems, no polynomial-time algorithm can outperform so-called "simple statistics", which are low-degree polynomials in the data. This conjecture…