arXiv research

Lasso method applied to polynomial models with hierarchy constraints.

We add a set of convex constraints to the lasso to produce sparse interaction models that honor the hierarchy restriction that an interaction only be included in a model if one or both variables are marginally important. We give a precise characterization of the effect of this hierarchy constraint, prove that hierarchy…

C-HMCNN(h) improves HMC classification by leveraging class hierarchy.

The modified Korteweg-de Vries hierarchy (mKdV) is derived by imposing isometry and isoenergy conditions on a moduli space of plane loops. The conditions are compared to the constraints that define Euler's elastica. Moreover, the conditions are shown to be constraints on the curvature and other invariants of the loops …

For two solutions of the WDVV equations that are related by the inversion symmetry, we show that the associated principal hierarchies of integrable systems are related by a reciprocal transformation, and the tau functions of the hierarchies are related by a Legendre type transformation. We also consider relationships b…

For two solutions of the WDVV equations that are related by two types of symmetries of the equations given by Dubrovin, we show that the associated principal hierarchies of integrable systems are related by certain reciprocal transformation, and the tau functions of the hierarchies are either identical or related by a …

We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators $L_m$, $m\geq -1$ of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau fu…

Metric learning is a key problem for many data mining and machine learning applications, and has long been dominated by Mahalanobis methods. Recent advances in nonlinear metric learning have demonstrated the potential power of non-Mahalanobis distance functions, particularly tree-based functions. We propose a novel non…

Proposes a hierarchical curriculum loss to improve model accuracy and interpretability.

A multilevel optimization method for constrained problems.

We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial structure. A key aspect here is that finding the optimal benchmark predictor (even in hi…

Proves a formula for Kontsevich-Witten tau-function using Schur Q-polynomials.

This paper proposes to learn hierarchical compositional AND-OR model for interpretable image synthesis by sparsifying the generator network. The proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in image representation. A scene has different types (i.e., OR) each of which consists of a number…

Adversarial MoE learns category-specific models for product search.

We extend to the context of Courant algebroids several hierarchies that can be constructed on Poisson-Nijenhuis manifolds. More precisely, we introduce several notions (Poisson-Nijenhuis, deformation-Nijenhuis and Nijenhuis pairs) that extend to Courant algebroids the notion of a Poisson-Nijenhuis manifold, by using th…

Proposes a method to improve hierarchical clustering using set-level structural priors.

New method optimizes hierarchical multi-label classification results.

Equations link metrics with tensors, revealing curvature constraints.

Novel approximation hierarchy for sparse quadratic programs.

Unified description of p-brane QP-manifolds connects two recent tensor hierarchy descriptions.

Proposes a new algorithm for efficient probabilistic reconciliation of forecasts.

The paper establishes a connection between force-free fields and conformally geodesic fields.

This work improves graph inference using the degree-4 sum-of-squares hierarchy.

HLTF generates chemically valid 3D molecules with improved topology control.

A new framework for information theory considers computational constraints.

New unknots with geometric constraints exist, proving a long-standing conjecture.

CoRe method improves time series forecasting coherency without strict constraints.

Specialized hierarchies improve decision-making by partitioning tasks.

Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.

SafeQ-Learning uses Wasserstein DRO to ensure safety in online learning.

Hierarchical clustering is a popular unsupervised data analysis method. For many real-world applications, we would like to exploit prior information about the data that imposes constraints on the clustering hierarchy, and is not captured by the set of features available to the algorithm. This gives rise to the problem …

FOSC-X: An extended framework for extracting multiple optimal flat clusterings from hierarchical cluster trees

We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough ($L^\infty$) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered through a decision/game theory formulation of the problems of (1) identifying restri…

Study identifies pitfalls in assessing hierarchies for multi-class classification.

Super tau-covers extend bihamiltonian hierarchies' symmetries.

Hydrodynamic hierarchy deformed using conservation laws.

Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints…

Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at least one or both associated main effects to be present in the model. Lately, thi…

The paper develops a method for forecasting power consumption at various levels of aggregation.

Legendre transformations link related integrable hierarchies.

Twisted $U$- and twisted $U/K$-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted $\frac {O(J,J)}{O(J)\times O(J)}$-hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…

Data aggregation improves HAC for resource-constrained systems.

Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two numbers from its children and produces one output. Since thinking about functions in …

We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra $\mathcal{A}_1$. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.

New metrics improve quantum ensemble learning efficiency and power.

Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…

New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.