arXiv research

MOCA-HESP optimizes high-dimensional combinatorial and mixed spaces using hyper-ellipsoid partitioning.

Bayesian optimization for high-dimensional combinatorial spaces using embeddings.

New method uses hyperbolic space for faster phylogenetic tree inference.

This paper focuses on Bayesian Optimization (BO) for objectives on combinatorial search spaces, including ordinal and categorical variables. Despite the abundance of potential applications of Combinatorial BO, including chipset configuration search and neural architecture search, only a handful of methods have been pro…

SCOPE-FE improves feature engineering efficiency for high-dimensional datasets.

We study the topology of moduli spaces of closed linkages in \R^d depending on a length vector \ell\in \R^n. In particular, we use equivariant Morse theory to obtain information on the homology groups of these spaces, which works best for odd d. In the case d=5 we calculate the Poincare polynomial in terms of combinato…

In graph theory there are intimate connections between the expansion properties of a graph and the spectrum of its Laplacian. In this paper we define a notion of combinatorial expansion for simplicial complexes of general dimension, and prove that similar connections exist between the combinatorial expansion of a compl…

Study tackles distribution shift in combinatorial settings using matrix completion techniques.

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as the source of randomness is suitably ergodic---it converges quickly enough to a …

New combinatorial structure for hierarchically hyperbolic spaces.

Advances combinatorial complexes for better modeling of hierarchical and set-type relations.

Novel theory combines combinatorial and topological elements.

New combinatorial method for sparse PCA works beyond spiked identity model.

A new method reduces both input and output dimensions for better goal-oriented analysis.

A new combinatorial approach groups regression coefficients for improved accuracy.

It follows implicitly from recent work in Heegaard Floer theory that lens spaces are homology cobordant exactly when they are oriented homeomorphic. We provide a new combinatorial proof using the Heegaard Floer d-invariants, which themselves may be defined combinatorially for lens spaces.

SA-FDR uses simulated annealing for feature selection in high-dimensional data.

In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of 3-manifolds with transitive cyclic symmetry can be generalised to an infinite fami…

Bayesian optimization adapted for discrete spaces using random mappings.

Novel U-learning method for predicting continuous outcomes from high-dimensional data.

New fractal spaces not quasisymmetric to Loewner spaces discovered.

HiSS sampling overcomes local mode traps in rugged discrete spaces.

We consider high-dimensional binary classification by sparse logistic regression. We propose a model/feature selection procedure based on penalized maximum likelihood with a complexity penalty on the model size and derive the non-asymptotic bounds for the resulting misclassification excess risk. The bounds can be reduc…

Bayesian optimization method tackles combinatorial spaces, scalable for large data.

This research connects combinatorial Teichmüller space geometry to Weil-Petersson geometry.

In this article we give combinatorial criteria to decide whether a transitive cyclic combinatorial d-manifold can be generalized to an infinite family of such complexes, together with an explicit construction in the case that such a family exists. In addition, we substantially extend the classification of combinatorial…

Efficient algorithms for planning in cooperative multi-agent reinforcement learning with combinatorial action spaces.

LGS-Net improves NCO performance on combinatorial optimization tasks.

We determine the topology of the moduli space of periodic tilings of the plane by parallelograms. To each such tiling, we associate combinatorial data via the zone curves of the tiling. We show that all tilings with the same combinatorial data form an open subset in a suitable Euclidean space that is homotopy equivalen…

New machine learning pipeline solves dynamic vehicle routing problems efficiently.

New combinatorial structures for Teichmüller spaces with Thurston's metric are explored.

Generative models enhance BO for large batch optimization.

New proof for discrete Morse theory using combinatorial construction.

The motivation of this work is to define cohomology classes in the space of knots that are both easy to find and to evaluate, by reducing the problem to simple linear algebra. We achieve this goal by defining a combinatorial graded cochain complex, such that the elements of an explicit submodule in the cohomology defin…

Unified framework for gradient estimation in combinatorial spaces.

Study introduces combinatorial criterion for quasi-isometry groups of Euclidean spaces.

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the actio…

In low-dimensional topology, many important decision algorithms are based on normal surface enumeration, which is a form of vertex enumeration over a high-dimensional and highly degenerate polytope. Because this enumeration is subject to extra combinatorial constraints, the only practical algorithms to date have been v…

The homotopy theory of gauge groups has received considerable attention in recent decades. In this work, we study the homotopy theory of gauge groups over some high dimensional manifolds. To be more specific, we study gauge groups of bundles over $(n-1)$-connected closed $2n$-manifolds, the classification of which was …

For triangulated surfaces locally embedded in the standard hyperbolic space, we introduce combinatorial Calabi flow as the negative gradient flow of combinatorial Calabi energy. We prove that the flow produces solutions which converge to ZCCP-metric (zero curvature circle packing metric) if the initial energy is small …

New algorithm reduces regret in both adversarial and stochastic contexts.

We provide bounds for kernel matrices and new approximations for high-dimensional data.

The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evaluations pose challenges for current techniques in discrete optimization and machine …

Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.

GFlowNets improve combinatorial optimization by efficiently sampling from solution spaces.

In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial Yamabe flow on the space of all piecewise flat metrics associated to a triangul…

New proof for hyperbolic groups using contracting boundaries of cusped spaces.

Two triples of triangles having pairwise disjoint outlines in 3-space are called combinatorially isotopic if one triple can be obtained from the other by a continuous motion during which the outlines of the triangles remain pairwise disjoint. We conjecture that it can be algorithmically checked if an (ordered or unorde…