New sampling method improves search efficiency in machine learning.
problem Efficiently sampling effective solutions from large search spaces.
method Developed a parameterized family of coverage-based designs and algorithms for effective synthesis.
result Consistently outperforms existing exploratory sampling methods in sample mining and hyper-parameter optimization.
The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we prove that such repulsive sampling schemes lowers the variance of the gradient est…
We define a Poisson Algebra called the {\em swapping algebra} using the intersection of curves in the disk. We interpret a subalgebra of the fraction algebra of the swapping algebra -- called the {\em algebra of multifractions} -- as an algebra of functions on the space of cross ratios and thus as an algebra of functio…
The {\em rank n swapping algebra} is a Poisson algebra defined on the set of ordered pairs of points of the circle using linking numbers, whose geometric model is given by a certain subspace of (Kn×Kn∗)r/GL(n,K). For any ideal triangulation of Dk---a disk wit…
The paper constructs a noncommutative bracket on surface groups and proves it's Hamiltonian.
problem Noncommutative Hamiltonian structures on surface groups.
method Double quasi Poisson bracket construction and noncommutative r-matrix formalism. result Noncommutative Hamiltonian structures on cyclic spaces of unbased loops.
Paper addresses class imbalance in disk SMART dataset using GANs and genetic algorithms.
problem Class imbalance in disk SMART dataset.
method Data synthesised by multivariate GANs mixed with genetic algorithms.
result Higher disk fault classification prediction accuracy.
Solves the Poisson problem for elastic plates with specific boundary conditions.
problem Finding an immersed surface minimizing Germain's elastic energy.
method Minimizes total curvature energy E(Σ) variationally. result The minimum is an immersed disk with branch points, extending to a C0,α Gauss map. Paper tackles Bayesian image restoration in low-photon Poisson imaging problems.
problem Bayesian inference in challenging low-photon Poisson imaging problems.
method Plug-and-play (PnP) Langevin sampling strategies with accelerated methods and mirror sampling.
result Effective PnP Langevin sampling methods for low-photon Poisson imaging problems.
Paper proposes a method to predict disk failures using multi-layer domain adaptive learning.
problem Traditional machine learning models struggle to predict disk failures due to limited data.
method Multi-layer domain adaptive learning with source and target domains.
result The proposed method improves failure prediction accuracy on disk data with few failure samples.
RODMAN improves ML-based disk failure prediction accuracy in cloud environments.
problem Imperfect data quality in real-world cloud environments degrades ML-based disk failure prediction accuracy.
method RODMAN uses three data preprocessing techniques: failure-type filtering, spline-based data filling, and automated pre-failure backtracking.
result RODMAN significantly improves prediction accuracy compared to no preprocessing.
Formalizes quantum path integrals using groupoids and differential forms.
problem Formalizing Feynman's path integral in quantum mechanics.
method Shifted focus to pair groupoid, using van Est map and piecewise linear structures.
result Developed a coordinate-free approach to integration of differential forms.
This paper solves mapping problems with a novel Gibbs sampling method.
problem Mapping problems with uncertainties in data associations and landmark cardinality.
method Derives a hybrid Poisson, multi-Bernoulli mixture distribution using a conjugate prior and Poisson process prior. Uses Gibbs sampling to sample from the posterior.
result The proposed method outperforms state-of-the-art methods on synthetic data.
New method speeds up Gibbs sampling for large graphs.
problem Efficiently sampling from large graphical models.
method Poisson-minibatching Gibbs sampling.
result Theoretical convergence rate guarantees for Poisson-minibatching Gibbs.
Novel Bayesian framework for Poisson inverse problems using Bregman geometry.
problem Solving Poisson inverse problems with non-Euclidean geometry and positivity constraints.
method Develops a Monte Carlo sampling algorithm that accounts for Bregman geometry, data augmentations, and conditional conjugacy properties.
result Efficient sampling via Gibbs steps and Hessian Riemannian Langevin Monte Carlo (HRLMC) for positivity constraints.
New sampling methods improve classifier performance estimation.
problem Efficiently selecting data points to estimate classifier performance.
method Introduced and compared Importance Sampling and Poisson Sampling.
result Poisson Sampling outperforms Importance Sampling.
We investigate the class of σ-stable Poisson-Kingman random probability measures (RPMs) in the context of Bayesian nonparametric mixture modeling. This is a large class of discrete RPMs which encompasses most of the the popular discrete RPMs used in Bayesian nonparametrics, such as the Dirichlet process, Pitman-Yor p…
Disk surgery on primitive disks of genus-3 Heegaard splittings of 3-sphere yields no primitive disks.
problem Characterizing primitive disks in genus-3 Heegaard splittings of 3-sphere.
method Analyzing the effect of disk surgery on primitive disks in genus-3 Heegaard splittings of 3-sphere.
result Primitive disks in genus-3 Heegaard splittings of 3-sphere are not weakly closed under disk surgery.
Study of embedding spaces using homotopy theory and operads.
problem Understanding the stable homotopy type of embedding spaces.
method Analysis of cubes of framed configuration spaces, homotopy theory of presheaves, operadic structures.
result Induced action of the Poisson operad on the homology of configuration spaces is a homotopy invariant.
The kth-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of k; and by the absence of…
Note on connectedness of primitive disk complex.
problem Whether primitive disk complex is connected for genus > 3 Heegaard splittings.
method Defined and quotiented primitive disk complex to prove connectedness.
result Homotopy primitive disk complex is connected.
Let K be an unknot in 8-bridge position in the 3-sphere. We give an example of a pair of weak reducing disks D1 and D2 for K such that both disks obtained from Di (i=1,2) by a surgery along any outermost disk in D3−i, cut off by an outermost arc of Di∩D3−i in D3−i, are not wea…
Researchers determine Poisson boundary of relativistic Brownian motion.
problem Understanding the interplay between geometry and random paths in curved manifolds.
method Dévissage method applied to Lorentzian manifolds.
result Determined Poisson boundary for specific manifolds.
Modeling trading volume curves using hierarchical Poisson processes.
problem Predicting trading volume curves for financial instruments.
method Hierarchical Poisson process model based on hierarchical Dirichlet process with MCMC algorithm.
result Demonstrated scalability on NASDAQ stocks, including Apple.
The fundamental group of the 2-dimensional Linial-Meshulam random simplicial complex Y2(n,p) was first studied by Babson, Hoffman and Kahle. They proved that the threshold probability for simple connectivity of Y2(n,p) is about p≈n−1/2. In this paper, we show that this threshold probability is at mo…
Speeding up Markov Chain Monte Carlo (MCMC) for datasets with many observations by data subsampling has recently received considerable attention. A pseudo-marginal MCMC method is proposed that estimates the likelihood by data subsampling using a block-Poisson estimator. The estimator is a product of Poisson estimators,…
A deep Neyman-Scott process uses Poisson processes for efficient inference in complex point processes.
problem Efficient inference in complex hierarchical point processes.
method Developed an efficient posterior sampling via Markov chain Monte Carlo for likelihood-based inference.
result More hidden Poisson processes improve likelihood fitting and event prediction.
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random variable whose mean is a sparse linear superposition of known patterns. Unlike many co…
Estimates support in distributions with sampling artifacts and errors.
problem Support estimation in the presence of sampling artifacts and errors.
method Regularized weighted Chebyshev approximations with Touchard polynomials, discretized semi-infinte programming.
result Significant improvements over noiseless support estimation methods.
Persistent homology detects curvature from sampled points.
problem Understanding the geometric information encoded in short intervals of persistent homology.
method Persistent homology computations and average persistence landscapes.
result Persistent homology detects curvature of disks from sampled points.
New knots bound multiple non-isotopic ribbon disks.
problem Finding knots that bound multiple non-isotopic ribbon disks.
method Classification of fibered, homotopy-ribbon disks for generalized square knots.
result Infinitely many knots bound infinitely many pairwise non-isotopic ribbon disks.
We study cobordisms and cobordisms rel boundary of PL locally-flat disk knots $D^{n-2}\into D^n$. Cobordisms of disk knots that do not fix the boundary sphere knots are easily classified by the cobordism properties of these boundaries, and any two even-dimensional disk knots with isotopic boundary knots are cobordant r…
To infer a multilayer representation of high-dimensional count vectors, we propose the Poisson gamma belief network (PGBN) that factorizes each of its layers into the product of a connection weight matrix and the nonnegative real hidden units of the next layer. The PGBN's hidden layers are jointly trained with an upwar…
Two new coding schemes improve the efficient communication of noisy data.
problem Efficient communication of noisy data in machine learning.
method Ordered Random Coding (ORC) and Hybrid Coding Scheme.
result Improved coding schemes over existing approaches.
Khovanov homology fails to differentiate certain slice disks.
problem Differentiating roll-spun slice disks from trivial ones.
method Using Khovanov homology and Morse theory.
result Khovanov homology cannot distinguish roll-spun slice disks from trivial ones.
For a genus two Heegaard splitting of a lens space, the primitive disk complex is defined to be the full subcomplex of the disk complex for one of the handlebodies of the splitting spanned by all vertices of primitive disks. In this work, we describe the complete combinatorial structure of the primitive disk complex fo…
We study the classification of slice disks of knots up to isotopy and diffeomorphism using an invariant in knot Floer homology. We compute the invariant of a slice disk obtained by deform-spinning, and show that it can be effectively used to distinguish non-isotopic slice disks with diffeomorphic complements. Given a s…
Modified EAT method improves Poisson gradient estimation.
problem Challenging differentiation through Poisson-distributed latent variables.
method Exponential Arrival Time (EAT) simulation with modifications and Gumbel-SoftMax relaxation.
result Modified EAT method provides unbiased first moment and reduced second-moment bias.
A bandit problem with filtered Poisson process data.
problem Maximizing points revealed from a continuum action space.
method Upper confidence bound algorithm with data-adaptive discretisation.
result Regret bound of O(T^(2/3)) under Lipschitz assumption.
A criterion for Whitney disks connects intersections in 3-manifold homology.
problem Existence of Whitney disks in Heegaard Floer homology.
method Use Nielsen theory to establish a criterion.
result Simple criterion for the existence of Whitney disks.
Transformers solve Poisson means estimation via empirical Bayes.
problem Estimating Poisson means under empirical Bayes setting.
method Pre-trained transformer learns to adapt to unknown prior and do in-context learning.
result Transformers achieve vanishing regret with large models and outperform classical algorithms.
Balls-and-Bins sampling improves DP-SGD privacy and utility.
problem Improving privacy and utility in DP-SGD implementations.
method Introducing Balls-and-Bins sampling as an alternative to shuffling in DP-SGD.
result Balls-and-Bins sampling achieves utility comparable to shuffling while offering better privacy amplification.
New disks found with similar outer shapes.
problem Finding similar outer shapes for Lagrangian disks.
method Modified construction of Abe and Tange.
result Arbitrarily large families of disks found.
Poisson likelihood models have been prevalently used in imaging, social networks, and time series analysis. We propose fast, simple, theoretically-grounded, and versatile, optimization algorithms for Poisson likelihood modeling. The Poisson log-likelihood is concave but not Lipschitz-continuous. Since almost all gradie…
New method learns high-dimensional Poisson DAG models from observational data.
problem Learning high-dimensional Poisson DAG models from observational data without strong assumptions.
method Decouples ordering estimation and parent search using ℓ1-regularized regression and mean-variance relationship. result Sample size n=Ω(d2log9p) sufficient for polynomial time algorithm to recover true directed graph. We construct an infinite family of slice disks with the same exterior, which gives an affirmative answer to an old question asked by Hitt and Sumners in 1981. Furthermore, we prove that these slice disks are ribbon disks.
Disk Embeddings tackle embedding DAGs with exponential growth.
problem Embedding DAGs with exponentially increasing ancestors and descendants.
method Disk Embeddings framework for quasi-metric spaces, including Hyperbolic Disk Embeddings.
result Disk Embeddings outperform existing methods in complex DAGs.
New model estimates higher-order interactions in stochastic processes using lower-dimensional projections.
problem Estimating higher-order interaction effects in stochastic processes with limited data.
method Additive Poisson Process (APP) combines information geometry and generalized additive models to model intensity functions in lower dimensions.
result The model can estimate higher-order intensity functions with sparse data.
Study constructs disks with curved boundaries in a 3D ball.
problem Constructing non-planar free boundary disks in a unit ball.
method Infinite family of non-planar disks with non-positive Gaussian curvature.
result Constructs disks with curved boundaries in a unit ball.