arXiv research

New method for MAP inference using Benders' decomposition.

We introduce a novel mechanism to tighten the local polytope relaxation for MAP inference in Markov random fields with low state space variables. We consider a surjection of the variables to a set of hyper-variables and apply the local polytope relaxation over these hyper-variables. The state space of each individual h…

We propose a faster and more accurate method for learning classification trees.

In this paper, we study the dual representation for generalized multiple stopping problems, hence the pricing problem of general multiple exercise options. We derive a dual representation which allows for cashflows which are subject to volume constraints modeled by integer valued adapted processes and refraction period…

The free energy of a closed 3-manifold is a 2-parameter formal power series which encodes the perturbative Chern-Simons invariant (also known as the LMO invariant) of a closed 3-manifold with gauge group U(N) for arbitrary $N$. We prove that the free energy of an arbitrary closed 3-manifold is uniformly Gevrey-1. As a …

We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an implied volatility consistent with options priced with the model. The…

This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes. The non-arbitrage property is not excluded if the class $\mathcal{A}$ of admiss…

Tree ensemble models such as random forests and boosted trees are among the most widely used and practically successful predictive models in applied machine learning and business analytics. Although such models have been used to make predictions based on exogenous, uncontrollable independent variables, they are increas…

This paper studies the problem of optimally allocating a cash injection into a financial system in distress. Given a one-period borrower-lender network in which all debts are due at the same time and have the same seniority, we address the problem of allocating a fixed amount of cash among the nodes to minimize the wei…

In Bender and Dokuchaev (2013), we studied a control problem related to swing option pricing in a general non-Markovian setting. The main result there shows that the value process of this control problem can be uniquely characterized in terms of a first order backward SPDE and a pathwise differential inclusion. In the …

Paper proves convergence of Markovian iteration for FBSDEs with fully coupled drift and Z process.

Researchers describe and compare decompositions of Poincaré duality pairs.

The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.

The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.

We combine aspects of the notions of finite decomposition complexity and asymptotic property C into a notion that we call finite APC-decomposition complexity. Any space with finite decomposition complexity has finite APC-decomposition complexity and any space with asymptotic property C has finite APC-decomposition comp…

This paper generalizes octahedral decomposition to links in thickened surfaces.

Researchers compute Goeritz groups for all (1,1)-link decompositions.

Study concordance of decompositions from defining sequences in 3-sphere.

Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…

Study shows OAT decomposition generates unexplained profit and loss, while SU decompositions depend on risk factor order.

A new algorithm speeds up CP decomposition for large tensors.

Paper characterizes optimization landscape of Tucker decomposition.

A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and h…

Smooth 4-manifolds have simple horizontal decompositions.

Let $\mathcal{J}^1$ be the real form of a complex simple Jordan algebra such that the automorphism group is $\mathrm{F}_{4(-20)}$. By using some orbit types of $\mathrm{F}_{4(-20)}$ on $\mathcal{J}^1$, for $\mathrm{F}_{4(-20)}$, explicitly, we give the Iwasawa decomposition, the Oshima--Sekiguchi's $K_ε-$Iwasawa decomp…

We study the topological types of pants decompositions of a surface by associating to any pants decomposition $P,$ in a natural way its pants decomposition graph, $Γ(P).$ This perspective provides a convenient way to analyze the maximum distance in the pants complex of any pants decomposition to a pants decomposition c…

New method uses random decompositions for high-dimensional Bayesian optimization.

New varifold example shows decomposition failure.

Derive new Euler-Ramanujan-type identities and infinite decompositions for zero mean curvature graphs in various spaces.

Decompositions on manifolds appear in various geometric structures. Necessary and sufficient conditions for quotient spaces of decompositions to be manifolds are widely characterized. We characterize necessary and sufficient conditions to be $k$-manifolds $(k = 1, 2)$, which generalize characterizations in the codimens…

Short proof for ideal polygons with near optimal orthogeodesic decomposition.

Paper introduces a new principle for fair redistribution of insurance surplus.

The paper defines and proves the existence of decompositions of integral varifolds.

We give an example of two JSJ decompositions of a group that are not related by conjugation, conjugation of edge-inclusions, and slide moves. This answers the question of Rips and Sela stated in "Cyclic splittings of finitely presented groups and the canonical JSJ decomposition," Ann. of Math. 146 (1997), 53-109. On th…

We consider a union of two pants decompositions of the same orientable 2-dimensional surface of any genus g. Each pants decomposition corresponds to some handlebody bounded by this surface, so two pants decompositions correspond to a Heegaard splitting of a 3-manifold. We introduce a groupoid FT acting on double pants …

We present a novel nonnegative tensor decomposition method, called Legendre decomposition, which factorizes an input tensor into a multiplicative combination of parameters. Thanks to the well-developed theory of information geometry, the reconstructed tensor is unique and always minimizes the KL divergence from an inpu…

Handles decompositions reveal new open book structures.

The aim of this paper is to provide some new tools to aid the study of decomposition complexity, a notion introduced by Guentner, Tessera and Yu. In this paper, three equivalent definitions for decomposition complexity are established. We prove that metric spaces with finite hyperbolic dimension have finite (weak) deco…

Unified algorithm for tensor decomposition supports multiple loss functions and models.

The paper defines and proves stabilization for 3-manifold decompositions with multibranched surface intersections.

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictiona…

Analyzes canonical reductive decomposition of extrinsic homogeneous submanifolds.

Tensor decomposition methods are widely used for model compression and fast inference in convolutional neural networks (CNNs). Although many decompositions are conceivable, only CP decomposition and a few others have been applied in practice, and no extensive comparisons have been made between available methods. Previo…

Examines respectful decompositions of Lie algebras.

In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition…

Formula connects foliated simplicial volume with group cost.

The study examines how different interpolation methods affect the decomposition of life insurance surplus.

The paper uses tensor decompositions to improve neural network models for tree data.