A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Estimates latent positions in 1D torus from noisy pairwise affinities.
We describe pairs (p,n) such that n-dimensional affine space is fibered by pairwise skew p-dimensional affine subspaces. The problem is closely related with the theorem of Adams on vector fields on spheres and the Hurwitz-Radon theory of composition of quadratic forms.
MASC balances dataset representation using affinity clustering and distribution discrepancies.
Researchers extend parametrization of Margulis spacetimes using strip deformations.
A natural family of affine cubic surfaces arises from SL(2)-characters of the 4-holed sphere and the 1-holed torus. The ideal locus is a tritangent plane which is generic in the sense that the cubic curve at infinity consists of three lines pairwise intersecting in three double points. We show that every affine cubic s…
The performance of most the clustering methods hinges on the used pairwise affinity, which is usually denoted by a similarity matrix. However, the pairwise similarity is notoriously known for its vulnerability of noise contamination or the imbalance in samples or features, and thus hinders accurate clustering. To tackl…
For a topological space we study continuous maps such that images of every pairwise distinct points are affinely (linearly) independent. Such maps are called affinely (linearly) -regular embeddings. We investigate the cohomology obstructions to existence of regular embeddings and give …
Let F be R or C, d the dimension of F over R. Denote by P(F) either the affine plane A(F) or the hyperbolic plane H(F) over F. An arrangement L of k lines in P(F) (pairwise non-parallel in the hyperbolic case) has a link at infinity K(L) comprising k unknotted (d-1)-spheres in the (2d-1)-sphere, whose topology reflects…
New method models aptamer libraries as Boltzmann-weighted graph ensembles for better affinity predictions.
Spectral Clustering(SC) is a prominent data clustering technique of recent times which has attracted much attention from researchers. It is a highly data-driven method and makes no strict assumptions on the structure of the data to be clustered. One of the central pieces of spectral clustering is the construction of an…
NucleusDiff models atomic nuclei interactions to prevent separation violations in drug design.
For a half-translation surface (S,q), the associated saddle connection complex A(S,q) is the simplicial complex where vertices are the saddle connections on (S,q), with simplices spanned by sets of pairwise disjoint saddle connections. This complex can be naturally regarded as an induced subcomplex of the arc complex. …
Efficient superpixel method for real-time segmentation.
New algorithm estimates task affinities without repeated training, improving model performance and efficiency.
Doubly-stochastic normalization improves robustness to heteroskedastic noise.
The paper proposes a method to ensure fairness in machine learning models.
New method preserves distances in time series data.
Cross-domain visual data matching is one of the fundamental problems in many real-world vision tasks, e.g., matching persons across ID photos and surveillance videos. Conventional approaches to this problem usually involves two steps: i) projecting samples from different domains into a common space, and ii) computing (…
Identifying components and estimating mixing weights in unlabeled finite mixtures under marginal independence.
We study the problem of ranking from crowdsourced pairwise comparisons. Answers to pairwise tasks are known to be affected by the position of items on the screen, however, previous models for aggregation of pairwise comparisons do not focus on modeling such kind of biases. We introduce a new aggregation model factorBT …
Spectral clustering is a leading and popular technique in unsupervised data analysis. Two of its major limitations are scalability and generalization of the spectral embedding (i.e., out-of-sample-extension). In this paper we introduce a deep learning approach to spectral clustering that overcomes the above shortcoming…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group , non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided. Basic criteria for finding a nearest consistent pairwise comparisons matrix (extend…
Paper introduces differential pairwise privacy for secure metric learning.
Cross-entropy loss linked to metric learning, outperforming complex pairwise losses.
Develops a statistical framework to measure uncertainty in model rankings based on human preferences.
A marked surface is a compact oriented surface equipped with some pairwise disjoint arcs embedded in its boundary. In this paper, we extend the notion of character varieties to marked surfaces, in such a way that they have a nice behaviour for the operation of gluing two boundary arcs together. These stated character v…
As one of the most important types of (weaker) supervised information in machine learning and pattern recognition, pairwise constraint, which specifies whether a pair of data points occur together, has recently received significant attention, especially the problem of pairwise constraint propagation. At least two reaso…
Paper proposes Pcomp classification for binary classification with pairwise confidence comparisons.
Study on pairwise counter-monotonicity, a type of negative dependence.
Exemplar-based clustering methods have been shown to produce state-of-the-art results on a number of synthetic and real-world clustering problems. They are appealing because they offer computational benefits over latent-mean models and can handle arbitrary pairwise similarity measures between data points. However, when…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of objects can be identified by standard sorting methods using pairwise comparisons. We are interested in natural situations in which relationships among the o…
Conditions for curves on a torus with specific pairwise intersections.
Chemical representations derived from deep learning are emerging as a powerful tool in areas such as drug discovery and materials innovation. Currently, this methodology has three major limitations - the cost of representation generation, risk of inherited bias, and the requirement for large amounts of data. We propose…
In this paper we study the stability and its trade-off with optimization error for stochastic gradient descent (SGD) algorithms in the pairwise learning setting. Pairwise learning refers to a learning task which involves a loss function depending on pairs of instances among which notable examples are bipartite ranking,…
Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack theoretical guarantees, or depend heavily on their initialization. We present a novel …
Paper characterizes and represents pairwise causal background knowledge for improved causal inference.
Paper establishes statistical inference for pairwise comparison models.
Study variational problem on manifold with special distributions.
Proposes a novel tensor-based approach for multi-level link prediction.
Recent work by Locatello et al. (2018) has shown that an inductive bias is required to disentangle factors of interest in Variational Autoencoder (VAE). Motivated by a real-world problem, we propose a setting where such bias is introduced by providing pairwise ordinal comparisons between instances, based on the desired…
Almost Zoll affine surface found on cylinder.
We examine several aspects of explicability of a classification system built from neural networks. The first aspect is the pairwise explicability, which is the ability to provide the most accurate prediction when the range of possibilities is narrowed to just two. Next we consider explicability in development, which me…
Paper develops active learning for clustering unknown pairwise similarities.
We study affine maps between affine manifolds. Even when the fibers are compact and diffeomorphic, two of them can inherit different affine structures from the source space. This leads to a fixed linear holonomy deformation theory of the affine structure of an affine manifold. We found various conditions which make the…
We investigate a generic problem of learning pairwise exponential family graphical models with pairwise sufficient statistics defined by a global mapping function, e.g., Mercer kernels. This subclass of pairwise graphical models allow us to flexibly capture complex interactions among variables beyond pairwise product. …
New algorithm clusters data and learns kernels without relaxing constraints.
In this article, we propose the notion of the general -affine capacity and prove some basic properties for the general -affine capacity, such as affine invariance and monotonicity. The newly proposed general -affine capacity is compared with several classical geometric quantities, e.g., the volume, the -var…
In this paper, we show that a compact affine manifold endowed with an Affine Anosov transformation is finitely covered by a complete affine nilmanifold.