For a Legendrian torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed exact Lagrangian fillings, where is the -th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we com…
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48 results for “Exact Computation”
Exact Bayesian inference for discrete models using probability generating functions.
problem Discrete statistical models with infinite support and continuous priors.
method Probabilistic programming language with automatic differentiation and probability generating functions.
result Genfer tool provides exact solutions for a wide range of inference problems.
Gaussian processes (GPs) are flexible non-parametric models, with a capacity that grows with the available data. However, computational constraints with standard inference procedures have limited exact GPs to problems with fewer than about ten thousand training points, necessitating approximations for larger datasets. …
Exact second-order optimization for deep learning reduces computational cost and improves performance.
problem Inadequate use of second-order optimization methods in deep learning due to high computational cost and non-convexity.
method Developed an exact stochastic second-order Newton method that addresses the non-convexity issue and provides an expression for the stochastic Hessian.
result Exact second-order Newton direction formula and its application in deep learning datasets.
Paper computes a specific term of knot homology for 3-braids.
problem Computing a specific term in knot homology for 3-braids.
method Used skein exact sequence and Xu's classification.
result Computed the second-to-top term of HFK for closed 3-braids.
The celebrated Monte Carlo method estimates an expensive-to-compute quantity by random sampling. Bandit-based Monte Carlo optimization is a general technique for computing the minimum of many such expensive-to-compute quantities by adaptive random sampling. The technique converts an optimization problem into a statisti…
Federated learning supports exact support recovery with minimal communication.
problem Learning the exact support of sparse linear regression in federated learning.
method One-shot communication algorithm for exact support recovery without optimization.
result Polynomial sample complexity and logarithmic number of clients required.
Exact Gaussian Processes for Massive Datasets via Non-Stationary Sparsity-Discovering Kernelsstat.ML
Exact Gaussian Processes for massive datasets using non-stationary sparsity-discovering kernels.
problem High computational and storage costs for exact GPs in large datasets.
method Develop non-stationary kernels that allow the GP to discover sparse structure naturally.
result Exact Gaussian Processes scalable to over 5 million data points.
For a smooth family of exact forms on a smooth manifold, an algorithm for computing a primitive family smoothly dependent on parameters is given. The algorithm is presented in the context of a diagram chasing argument in the Čech-de Rham complex. In addition, explicit formulas for such primitive family are presented.
This paper explores the computational hardness of generating latent vectors for generative models.
problem Computational hardness of generating latent vectors for generative models.
method Established lower bounds for exact and approximate model inversion under strong exponential time hypothesis (SETH) and exponential time hypothesis (ETH).
result Lower bounds for computational complexity of exact and approximate model inversion.
Stable Torsion Lengthmath.GR
Study on stable torsion length in groups, showing it vanishes in crystallographic groups and providing algorithms for computation.
problem Understanding the stable torsion length in groups, especially in crystallographic and free products of groups.
method Developed linear programming and exact algorithms to compute stable torsion length in free products of groups and finite groups.
result Showed that stable torsion length vanishes in crystallographic groups and provided exact computations for nontrivial examples.
W. Thurston suggested a method for computing hyperbolic volume of hyperbolic 3-manifolds, based on a triangulation of the manifold. The method was implemented by J. Weeks in the program SnapPea, which produces a decimal approximation as a result. For hyperbolic 2-bridge links, we give formulae that allow one to find th…
In this paper, using similar idea as in Fukaya-Oh's work ([9]), we devise a method to compute the Fukaya category of certain exact symplectic manifolds by reducing it to the corresponding Morse category of non-Hausdorff manifold as perturbation of the Lagrangian skeleton of the exact symplectic manifold.
We show a connection between a surgery exact sequence in knot Floer homology and the sequence derived in [18]. As a consequence of this relationship we see that the exact sequence in [18] also works with coherent orientations and admits refinements with respect to spinc-structures. As an application of this discussion,…
Wasserstein distance plays increasingly important roles in machine learning, stochastic programming and image processing. Major efforts have been under way to address its high computational complexity, some leading to approximate or regularized variations such as Sinkhorn distance. However, as we will demonstrate, regu…
By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds for the comp…
PixelCNN models can achieve state-of-the-art results on CIFAR-10 with exact likelihood computation.
problem Dequantization gap in modeling discrete data like images.
method Introducing subset flows to allow exact computation of likelihoods for discrete data.
result PixelCNN models trained with exact likelihood computation achieve state-of-the-art results on CIFAR-10.
SPPL simplifies probabilistic programming for exact inference.
problem Efficient exact inference in probabilistic models.
method SPPL translates probabilistic programs into sum-product expressions, leveraging new techniques for scalability.
result SPPL achieves up to 3500x speedups in exact inference.
Paper explores limits of exact inference in structured prediction models.
problem Exact recovery of true labels in graph-based structured prediction models.
method Analyzes necessary and sufficient conditions for exact recovery using maximum likelihood estimation.
result Derives tight conditions for exact recovery, revealing a gap with computationally tractable methods.
GPU speeds up derivatives sensitivity computation for Heston model options.
problem Efficient computation of option Greeks under the Heston model.
method Implemented exact simulation and novel Milstein discretisation methods on GPU.
result GPU speeds up Greeks computation up to 200x compared to CPU methods.
Taking advantage of the recent litterature on exact simulation algorithms (Beskos, Papaspiliopoulos and Roberts) and unbiased estimation of the expectation of certain fonctional integrals (Wagner, Beskos et al. and Fearnhead et al.), we apply an exact simulation based technique for pricing continuous arithmetic average…
The article provides obstructions for exact submanifolds in symplectic applications.
problem Existence of exact submanifolds with specific homology classes.
method Study of formal deformations of the de Rham complex to compute obstructions.
result Symplectic manifolds like Kähler and Kodaira-Thurston admit no non-separating exact hypersurfaces.
Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transf…
Exact minibatch MH method improves scalability for large datasets.
problem Inexactness in minibatch MH methods causes inference errors.
method TunaMH proposes an exact minibatch MH method with a tunable batch size.
result TunaMH is asymptotically optimal in terms of batch size.
Differentiable Expected Hypervolume Improvement for Parallel Multi-Objective Bayesian Optimizationstat.ML
A new parallel BO method with exact gradients for multi-objective optimization.
problem Efficiently optimizing multiple objectives in a sample-efficient manner.
method Derive q-Expected Hypervolume Improvement (qEHVI) for parallel, constrained evaluation.
result qEHVI is computationally tractable and outperforms state-of-the-art methods.
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c >= rank(A) columns depend on the right singular vector matrix of A. For a Monte-…
Proves exact triangle linking knot instanton Floer homology to surgeries.
problem Relating knot instanton Floer homology to surgeries.
method Proves an exact triangle using integer coefficients.
result Poincaré Homology Sphere is not an instanton L-space with integer coefficients.
Extends cobordism groups of immersions to projections with new results.
problem Understanding cobordism groups of projected immersions.
method Classifying space construction by Szűcs and Terpai, Salomonsen's exact sequence.
result Obtains results on cobordism groups in small and large codimensional cases.
Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.
problem Computational challenges in high-dimensional penalized quantile regression.
method Pathwise coordinate descent algorithm to solve exact coordinatewise minimum of the nonsmooth loss function.
result Algorithm runs faster than existing alternatives and maintains estimation accuracy.
In graph-based active learning, algorithms based on expected error minimization (EEM) have been popular and yield good empirical performance. The exact computation of EEM optimally balances exploration and exploitation. In practice, however, EEM-based algorithms employ various approximations due to the computational ha…
This work extends knot homology theory to links, proving exact triangles and categorifying link signatures.
problem Extending knot homology theory to links and proving exact triangles.
method Equivariant singular instanton Floer theory, circle-equivariant Morse-Floer theory, cobordism constructions.
result Established unoriented skein exact triangles and categorified link signatures.
Exact computation of posterior distribution of mixture weights in hierarchical Bayesian modelsstat.ME
This paper computes exact posterior distributions of mixture weights in hierarchical Bayesian models.
problem Uncertainty in class membership or data-generating processes in heterogeneous data.
method Exact marginalization of mixture weights using dynamic programming and FFT for two components, and joint dynamic program for K >= 3 components.
result Exact posterior distributions of mixture weights are finite mixtures of Beta distributions, providing credible intervals and per-observation local false-discovery rates.
In this paper we address some problems concerning an approximate Dirichlet domain. We show that under some assumptions the approximate Dirichlet domain can work equally well as an exact Dirichlet domain. In particular, we consider a problem of tiling a hyperbolic ball with copies of the Dirichlet domain. This problem a…
TERA method speeds up derivative Gaussian processes in high dimensions.
problem High-dimensional function evaluations and gradient computations are computationally expensive.
method TERA uses exact gradient reduction to decouple and from the computational cost.
result TERA achieves state-of-the-art predictive accuracy with orders of magnitude faster computation.
The exact nonnegative matrix factorization (exact NMF) problem is the following: given an -by- nonnegative matrix and a factorization rank , find, if possible, an -by- nonnegative matrix and an -by- nonnegative matrix such that . In this paper, we propose two heuristics for exac…
Cardinality potentials are a generally useful class of high order potential that affect probabilities based on how many of D binary variables are active. Maximum a posteriori (MAP) inference for cardinality potential models is well-understood, with efficient computations taking O(DlogD) time. Yet efficient marginalizat…
New kernel enables exact GP analysis of massive datasets.
problem Limited scalability and flexibility of traditional GPs for large data sets.
method Explicitly derived nonstationary kernel for large-scale GP analysis.
result Novel kernel outperforms existing methods in synthetic and real-world applications.
Determinantal point processes (DPPs) enable the modeling of repulsion: they provide diverse sets of points. The repulsion is encoded in a kernel that can be seen as a matrix storing the similarity between points. The diversity comes from the fact that the inclusion probability of a subset is equal to the determinan…
Exact causal network discovery is polynomial for sparse networks.
problem Finding the optimal causal Bayesian network from data is computationally hard.
method Pruning the search space using network properties, combined with dynamic programming and shortest-path searches.
result Exact discovery is polynomial for sparse causal Bayesian networks.
We study the maps induced on link Floer homology by elementary decorated link cobordisms. We compute these for births, deaths, stabilizations, and destabilizations, and show that saddle cobordisms can be computed in terms of maps in a decorated skein exact triangle that extends the oriented skein exact triangle in knot…
TDS provides exact samples for conditional distributions in diffusion models.
problem Lack of exact sampling methods for diffusion models.
method Sequential Monte Carlo (SMC) algorithm with twisting technique.
result TDS offers more accurate approximations with fewer particles compared to heuristics.
We introduce a new method for computing triply graded link homology, which is particularly well-adapted to torus links. Our main application is to the (n,n)-torus links, for which we give an exact answer for all n. In several cases, our computations verify conjectures of Gorsky et al relating homology of torus links wi…
The graph complexity of a compact 3-manifold is defined as the minimum order among all 4-colored graphs representing it. Exact calculations of graph complexity have been already performed, through tabulations, for closed orientable manifolds (up to graph complexity 32) and for compact orientable 3-manifolds with toric …
We propose Kernel Hamiltonian Monte Carlo (KMC), a gradient-free adaptive MCMC algorithm based on Hamiltonian Monte Carlo (HMC). On target densities where classical HMC is not an option due to intractable gradients, KMC adaptively learns the target's gradient structure by fitting an exponential family model in a Reprod…
Topological group cohomology of Lie groups and Chern-Weil theory for compact symmetric spacesmath.AT
In this paper we analyse the topological group cohomology of finite-dimensional Lie groups. We introduce a technique for computing it (as abelian groups) for torus coefficients by the naturally associated long exact sequence. The upshot in there is that certain morphisms in this long exact coefficient sequence can be a…
Algorithm samples from Bingham distribution efficiently.
problem Sampling from the Bingham distribution on a sphere.
method Rejection sampling with polynomial approximation.
result Exact samples from Bingham distribution in polynomial time.
In this paper, we first define the equivariant infinitesimal -form, then we compare it with the equivariant -form, modulo exact forms, by a locally computable form. As a consequence, we obtain the singular behavior of the equivariant -form, modulo exact forms, as a function on the acting Lie group. This result…
A scalable Bayesian additive model for stellar flare detection using Gaussian process inference and hidden Markov models.
problem Bayesian time-series modeling for astronomical datasets
method Generative surrogate framework with Variational Autoencoder and neural network forward pass
result Significant reduction in computational time for stellar flare detection