arXiv research

Divide-and-conquer method splits large data sets for efficient analysis.

Dividing local Gaussian processes improve real-time prediction efficiency.

The paper classifies all tight contact structures on a solid torus.

New divide with gleams method simplifies symmetric link representation.

The paper characterizes links in 3D from divides with cusps.

SwISS improves scalability of Bayesian inference for large datasets.

We prove that Dranishnikov's $k$-dimensional resolution $d_k\colon μ^k\to Q$ is a UV$^{n-1}$-divider of Chigogidze's $k$-dimensional resolution $c_k$. This fact implies that $d_k^{-1}$ preserves $Z$-sets. A further development of the concept of UV$^{n-1}$-dividers permits us to find sufficient conditions for $d_k^{-1}(…

Divide-and-conquer framework speeds up black-box inference for large data.

DiCoLa recursively decomposes causal structure learning for latent variables.

This paper reveals hidden hyperbolic structures in divide links.

We give a method for constructing a shadowed polyhedron from a divide. The 4-manifold reconstructed from a shadowed polyhedron admits the structure of a Lefschetz fibration if it satisfies a certain property, which we call the LF-property. We will show that the shadowed polyhedron constructed from a divide satisfies th…

Tuning parameter selection is of critical importance for kernel ridge regression. To this date, data driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large data sets. In this paper, by modifying the Generalized Cr…

Starting from a divide, i.e. a generic immersion of finitely many copies of the interval [0,1] in the disk, we construct a classical link in the 3-sphere. We prove that the link's complement fibers over the circle, if the divide is connected. Moreover, we compute the monodromy diffeomorphism from the combinatorics of t…

Twinning splits data into fast, statistically similar sets.

In this article, we advance divide-and-conquer strategies for solving the community detection problem in networks. We propose two algorithms which perform clustering on a number of small subgraphs and finally patches the results into a single clustering. The main advantage of these algorithms is that they bring down si…

New method to encode Weinstein 4-manifolds using multisections with divides.

Construct divide knots with specific genus properties.

New method for efficient inference in large datasets.

I present a formula for the Casson invariant of knots associated with divides. The formula is written in terms of Arnold's invariants of pieces of the divide. Various corollaries are discussed.

Divides help construct fibered links from singularities.

We improve kernel ridge regression for skewed responses using oversampling and adaptive partitioning.

In the present paper we determine the Thurston-Bennequin invariant of graph divide links, which include all closed positive braids, all divide links and certain negative twist knots. As a corollary of this and a result of P. Lisca and A.I. Stipsicz, we prove that the 3-manifold obtained from the 3-sphere by Dehn surger…

The paper parallelizes MCMC using random forests for big data Bayesian computation.

Constructs examples of domains divided by groups in dimensions 3 and above.

The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network. This paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DN…

The study describes handle decompositions and Kirby diagrams for line arrangements.

It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parame…

This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.

Study explores efficient data division for ICPs.

Active learning (AL) repeatedly trains the classifier with the minimum labeling budget to improve the current classification model. The training process is usually supervised by an uncertainty evaluation strategy. However, the uncertainty evaluation always suffers from performance degeneration when the initial labeled …

We give a complete characterization of a circle immersion that can be divided into two arc embeddings in terms of its chord diagram.

Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets that cannot be stored or processed on one machine. Another challenge one may encounter is the presence of outliers and contaminations that da…

Divide knots and links, defined by A'Campo in the singularity theory of complex curves, is a method to present knots or links by real plane curves. The present paper is a continuation of the author's previous result that every knot in the major subfamilies of Berge's lens space surgery (i.e., knots yielding a lens spac…

A divide on an orientable 2-orbifold gives rise to a fibration of the unit tangent bundle to the orbifold.We characterize the corresponding monodromies as exactly the products of a left-veering horizontal and a right-veering vertical antitwist with respect to a cylinder decomposition, where the notion of an antitwist i…

Dividing deep learning models for consistent anomaly detection in changing log data.

A divide is a relative generic immersion of a finite union of copies of the unit interval in the unit disk. A divide defines a classical link in the 3- sphere, which is a fibered link if the image of the immersion is connected. We prove in this paper, that the Lefschetz number of the monodromy is 0. This result was kno…

Open books constructed from Morse functions and divides are shown to be isotopic.

Decision tree is an important method for both induction research and data mining, which is mainly used for model classification and prediction. ID3 algorithm is the most widely used algorithm in the decision tree so far. In this paper, the shortcoming of ID3's inclining to choose attributes with many values is discusse…

In the 3-dimensional Riemannian geometry, contact structures equipped with an adapted Riemannian metric are divergence-free, nondegenerate eigenforms of the Laplace-Beltrami operator. We trace out a 2-d analogue of this fact: there is a close relationship between the topology of the contact structure on a convex surfac…

The study classifies rational isoparametric functions on Damek-Ricci spaces.

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are it…

We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a coll…

Infinite type surfaces can be perfectly divided into triangles.

The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any help is most welcome. We prove that the restriction of surface minority to fiber surfaces of divides is a well-quasi-order. Here surface min…

In Divide & Recombine (D&R), big data are divided into subsets, each analytic method is applied to subsets, and the outputs are recombined. This enables deep analysis and practical computational performance. An innovate D\&R procedure is proposed to compute likelihood functions of data-model (DM) parameters for big dat…

We provide a surprising new application of classical approximation theory to a fundamental asset-pricing model of mathematical finance. Specifically, we calculate an analytic value for the correlation coefficient between exponential Brownian motion and its time average, and we find the use of divided differences greatl…

Divide-and-conquer method speeds sparse factorization for large matrices.

An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have $C^1$ boundary, and have word hyperbolic divid…