Related papers: Approximating Higher-Order Distances Using Random …
In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
Many mobile robots rely on 2D laser scanners for localization, mapping, and navigation. However, those sensors are unable to correctly provide distance to obstacles such as glass panels and tables whose actual occupancy is invisible at the…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, the similarity between two trajectories is quantified by means of heuristic…
The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…
There has been a great deal of recent interest in methods for performing lifted inference; however, most of this work assumes that the first-order model is given as input to the system. Here, we describe lifted inference algorithms that…
Modern large language models (LLMs) such as GPT, Claude, and Gemini have transformed the way we learn, work, and communicate. Yet, their ability to produce highly human-like text raises serious concerns about misinformation and academic…
A set of piecewise linear functions, called polylines, $P_1,\ldots,P_L$ each with at most $n$ vertices can be simplified into a polyline $M$ with $k$ vertices, such that the Fr\'echet distances $\epsilon_1,\ldots,\epsilon_L$ to each of…
For robots to operate robustly in the real world, they should be aware of their uncertainty. However, most methods for object pose estimation return a single point estimate of the object's pose. In this work, we propose two learned methods…
In dynamical system theory, the process of obtaining a reduced-order approximation of the high-order model is called model order reduction. The closeness of the reduced-order model to the original model is generally gauged by using system…
We develop a new class of distances for objects including lines, hyperplanes, and trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute,…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
Ordinal classification models assign higher penalties to predictions further away from the true class. As a result, they are appropriate for relevant diagnostic tasks like disease progression prediction or medical image grading. The…
Approximate K Nearest Neighbor (AKNN) search in high-dimensional spaces is a critical yet challenging problem. In AKNN search, distance computation is the core task that dominates the runtime. Existing approaches typically use approximate…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…
We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\leq p<\infty$) upper bound in weighted form under a class of stratified sampling. This result…
We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…
We provide algorithms for isotonic regression minimizing $L_0$ error (Hamming distance). This is also known as monotonic relabeling, and is applicable when labels have a linear ordering but not necessarily a metric. There may be…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…