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.
Extends partitioned local depth concept with probabilistic considerations.
Locally isoperimetric partitions minimize perimeter in space.
The paper constructs Markov partitions for geodesic flow on hyperbolic surfaces.
BN refines local partition geometry in piecewise-affine networks during training.
MD-split+ creates locally valid prediction regions for complex data.
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition functi…
We study the localization of a cluster of activated vertices in a graph, from adaptively designed compressive measurements. We propose a hierarchical partitioning of the graph that groups the activated vertices into few partitions, so that a top-down sensing procedure can identify these partitions, and hence the activa…
Minimal partitions with minimal perimeter found in metric spaces.
This paper presents a new approach for Gaussian process (GP) regression for large datasets. The approach involves partitioning the regression input domain into multiple local regions with a different local GP model fitted in each region. Unlike existing local partitioned GP approaches, we introduce a technique for patc…
Space partitions of underlie a vast and important class of fast nearest neighbor search (NNS) algorithms. Inspired by recent theoretical work on NNS for general metric spaces [Andoni, Naor, Nikolov, Razenshteyn, Waingarten STOC 2018, FOCS 2018], we develop a new framework for building space partitions re…
LA-MCTS learns search space partition for black-box optimization using Monte Carlo Tree Search.
Localized transfer learning improves nonparametric regression performance.
Traditionally, an artificial neural network (ANN) is trained slowly by a gradient descent algorithm such as the backpropagation algorithm since a large number of hyperparameters of the ANN need to be fine-tuned with many training epochs. To highly speed up training, we created a novel shallow 4-layer ANN called "Pairwi…
We present a new way of constructing an ensemble classifier, named the Guided Random Forest (GRAF) in the sequel. GRAF extends the idea of building oblique decision trees with localized partitioning to obtain a global partitioning. We show that global partitioning bridges the gap between decision trees and boosting alg…
Develops an MS-inspired algorithm for regression mode finding and space partitioning.
A common divide-and-conquer approach for Bayesian computation with big data is to partition the data, perform local inference for each piece separately, and combine the results to obtain a global posterior approximation. While being conceptually and computationally appealing, this method involves the problematic need t…
Minimal networks minimize length and mass in certain configurations.
ParK efficiently solves kernel ridge regression for large datasets.
A novel non-supervised method detects anomalies in multivariate time series.
Hyperkahler quotients by non-free actions are typically highly singular, but are remarkably still partitioned into smooth hyperkahler manifolds. We show that these partitions are topological stratifications, in a strong sense. We also endow the quotients with global Poisson structures which induce the hyperkahler struc…
Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS and several algorithms including -ALSH, Sign-ALSH and Simple-LSH have been proposed. In this paper, we introduce the norm-range partition technique, which partitions the original dataset into sub-datasets containing items with similar 2-…
Region-specific linear models are widely used in practical applications because of their non-linear but highly interpretable model representations. One of the key challenges in their use is non-convexity in simultaneous optimization of regions and region-specific models. This paper proposes novel convex region-specific…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function is calculated via zeta-function regularization with special attention to its mo…
LDP speeds up causal discovery by partitioning, improving VAS recall and runtime.
We present graph partition neural networks (GPNN), an extension of graph neural networks (GNNs) able to handle extremely large graphs. GPNNs alternate between locally propagating information between nodes in small subgraphs and globally propagating information between the subgraphs. To efficiently partition graphs, we …
In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via clustering), and then computing a KRR estimate for each partition. The conquering s…
Enhances POU-Nets with probabilistic noise model for efficient spatial data clustering.
Study on optimal partitions and nodal solutions for the Yamabe equation.
Novel threefold partitioning of -spinor space on cone links.
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified and a novel rearrangement algorithm is proposed, which we show is strictly decreas…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local structure/consistency of GM have been investigated as popular choices in practice. Howev…
Enhances random forests by smoothing predictions for better performance.
The MBO scheme for data clustering is analyzed in the large data limit, proving convergence to optimal partition problems.
Paper studies Transformer learning theory for Euclidean and Riemannian domains.
Quantum dilogarithms help define invariants of 3-manifolds.
Let M be a complete n-dimensional Riemannian spin manifold, partitioned by q two-sided hypersurfaces which have a compact transverse intersection N and which in addition satisfy a certain coarse transversality condition. Let E be a Hermitean bundle with connection on M. We define a coarse multi-partitioned index of the…
In regression tasks the distribution of the data is often too complex to be fitted by a single model. In contrast, partition-based models are developed where data is divided and fitted by local models. These models partition the input space and do not leverage the input-output dependency of multimodal-distributed data,…
GADGET framework decomposes global feature effects using recursive partitioning.
Study of 5D SYM theory on toric surfaces yields refined Vafa-Witten invariants.
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
We define an invariant of graphs embedded in a three-manifold and a partition function for 2-complexes embedded in a triangulated four-manifold by specifying the values of variables in the Turaev-Viro and Crane-Yetter state sum models. In the case of the three-dimensional invariant, we prove a duality formula relating …
Anisotropic curvature flow studied for planar networks.
DMFAW improves multi-view clustering with adaptive weights and feature selection.
Given a subset S of vertices of an undirected graph G, the cut-improvement problem asks us to find a subset S that is similar to A but has smaller conductance. A very elegant algorithm for this problem has been given by Andersen and Lang [AL08] and requires solving a small number of single-commodity maximum flow comput…
A lens cluster minimizes perimeter in the plane with given area constraints.
This paper introduces the Partition Tree Weighting technique, an efficient meta-algorithm for piecewise stationary sources. The technique works by performing Bayesian model averaging over a large class of possible partitions of the data into locally stationary segments. It uses a prior, closely related to the Context T…
The paper calculates a formula for knot complements using holomorphic curves.
Greedy training of recursive partitioning estimators faces a computational barrier when the true function doesn't satisfy a specific property.