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.
A new ensemble method improves kNN performance by extending the neighborhood rule.
Method learns relational features for Gaifman models from knowledge bases.
New adaptive stepsize method for stochastic approximation converges to target point.
We present a strikingly simple proof that two rules are sufficient to automate gradient descent: 1) don't increase the stepsize too fast and 2) don't overstep the local curvature. No need for functional values, no line search, no information about the function except for the gradients. By following these rules, you get…
The problem of identifying geometric structure in heterogeneous, high-dimensional data is a cornerstone of representation learning. While there exists a large body of literature on the embeddability of canonical graphs, such as lattices or trees, the heterogeneity of the relational data typically encountered in practic…
Proposes a fuzzy rule-based method for data visualization.
SOCP uses SOM to find groups and local calibration buffers for better regional coverage.
Develops a robust hedging valuation adjustment measure for dynamic hedging under liquidity-demand stress.
Previously, we proposed a physically inspired rule to organize the data points in a sparse yet effective structure, called the in-tree (IT) graph, which is able to capture a wide class of underlying cluster structures in the datasets, especially for the density-based datasets. Although there are some redundant edges or…
Paper develops a robust HVA measure for dynamic hedging under liquidity stress.
We derive spectral sequences for the intersection homology of stratified fibrations and approximate tubular neighborhoods in manifold stratified spaces. These neighborhoods include regular neighborhoods in PL stratified spaces.
Making an adaptive prediction based on one's input is an important ability for general artificial intelligence. In this work, we step forward in this direction and propose a semi-parametric method, Meta-Neighborhoods, where predictions are made adaptively to the neighborhood of the input. We show that Meta-Neighborhood…
Framework detects out-of-distribution inputs in regression and survival analysis.
Data-driven neighborhood definitions and graph constructions are often used in machine learning and signal processing applications. k-nearest neighbor~(kNN) and -neighborhood methods are among the most common methods used for neighborhood selection, due to their computational simplicity. However, the choice of param…
Study geodesics entering a fixed cusp neighborhood multiple times.
Urban2Vec combines street view imagery and POIs for better urban neighborhood embeddings.
Skeleta and other pure subsets of manifold stratified spaces are shown to have neighborhoods which are teardrops of stratified approximate fibrations (under dimension and compactness assumptions). In general, the stratified approximate fibrations cannot be replaced by bundles, and the teardrops cannot be replaced by ma…
New framework distinguishes knots via neighborhood invariants.
This paper tackles selection bias in recommender systems by considering the neighborhood effect.
Maximally hyperbolic solutions contain future neighborhoods of intersecting hypersurfaces.
Many prediction problems can be phrased as inferences over local neighborhoods of graphs. The graph represents the interaction between entities, and the neighborhood of each entity contains information that allows the inferences or predictions. We present an approach for applying machine learning directly to such graph…
Proposes a new NMF method incorporating neighborhood structure for better anomaly detection.
Study on transverse knots and their neighborhoods, proving unique standard neighborhoods and destabilization results.
Revises GNN neighborhood aggregation for more accurate node classification.
The study proves a neighborhood theorem for mean curvature flow in higher dimensions.
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to th…
Recent innovations in Information and Communication Technologies (ICT) provide new opportunities and challenges for integration of distributed energy resources (DERs) into the energy supply system as active market players. By increasing integration of DERs, novel market platform should be designed for these new market …
Graph representation learning is of paramount importance for a variety of graph analytical tasks, ranging from node classification to community detection. Recently, graph convolutional networks (GCNs) have been successfully applied for graph representation learning. These GCNs generate node representation by aggregatin…
Neighborhood sampling affects graph neural network training outcomes.
In this paper, we consider recommender systems with side information in the form of graphs. Existing collaborative filtering algorithms mainly utilize only immediate neighborhood information and have a hard time taking advantage of deeper neighborhoods beyond 1-2 hops. The main caveat of exploiting deeper graph informa…
Introduces a new theoretical framework for exponential smoothing.
We introduce a variant of the -nearest neighbor classifier in which is chosen adaptively for each query, rather than supplied as a parameter. The choice of depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k…
Learning graph-structured data with graph neural networks (GNNs) has been recently emerging as an important field because of its wide applicability in bioinformatics, chemoinformatics, social network analysis and data mining. Recent GNN algorithms are based on neural message passing, which enables GNNs to integrate loc…
We present novel graph kernels for graphs with node and edge labels that have ordered neighborhoods, i.e. when neighbor nodes follow an order. Graphs with ordered neighborhoods are a natural data representation for evolving graphs where edges are created over time, which induces an order. Combining convolutional subgra…
We present a new construction of tubular neighborhoods in (possibly infinite dimensional) Riemannian manifolds M, which allows us to show that if G is an arbitrary group acting isometrically on M, then every G-invariant submanifold with locally trivial normal bundle has a G-invariant total tubular neighborhood. We appl…
t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of…
This article is one of three highly influential articles on the topology of manifolds written by Robert D. Edwards in the 1970's but never published. Organizers of the Workshops in Geometric Topology (http://www.uwm.edu/~craigg/workshopgtt.htm) with the support of the National Science Foundation have facilitated the pr…
TNC learns time series representations by leveraging temporal neighborhoods.
We consider discrete graphical models Markov with respect to a graph and propose two distributed marginal methods to estimate the maximum likelihood estimate of the canonical parameter of the model. Both methods are based on a relaxation of the marginal likelihood obtained by considering the density of the variable…
This paper sets a lower limit for the size of Weinstein's Lagrangian tubular neighborhoods.
Existing popular methods for semi-supervised learning with Graph Neural Networks (such as the Graph Convolutional Network) provably cannot learn a general class of neighborhood mixing relationships. To address this weakness, we propose a new model, MixHop, that can learn these relationships, including difference operat…
We develop a theory of tubular neighborhoods for the lower strata in manifold stratified spaces with two strata. In these topologically stratified spaces, manifold approximate fibrations and teardrops play the role that fibre bundles and mapping cylinders play in smoothly stratified spaces. Applications include the cla…
The -NN graph has played a central role in increasingly popular data-driven techniques for various learning and vision tasks; yet, finding an efficient and effective way to construct -NN graphs remains a challenge, especially for large-scale high-dimensional data. In this paper, we propose a new approach to const…
Motivated by an abstract notion of low-level edge detector filters, we propose a simple method of unsupervised feature construction based on pairwise statistics of features. In the first step, we construct neighborhoods of features by regrouping features that correlate. Then we use these subsets as filters to produce n…
Inspired by a work of Kapranov, we define the notion of Dolbeault complex of the formal neighborhood of a closed embedding of complex manifolds. This construction allows us to study coherent sheaves over the formal neighborhood via complex analytic approach, as in the case of usual complex manifolds and their Dolbeault…
Normal forms of almost complex structures in a neighborhood of pseudoholomorphic curve are considered. We define normal bundles of such curves and study the properties of linear bundle almost complex structures. We describe 1-jet of the almost complex structure along a curve in terms of its Nijenhuis tensor. For pseudo…
The estimation of optimal treatment regimes is of considerable interest to precision medicine. In this work, we propose a causal -nearest neighbor method to estimate the optimal treatment regime. The method roots in the framework of causal inference, and estimates the causal treatment effects within the nearest neig…
We characterize metric spaces whose hyperspaces or of non-empty closed (bounded) subsets, endowed with the Hausdorff metric, are absolute [neighborhood] retracts.