arXiv research

Introduces a new theoretical framework for exponential smoothing.

Exponentially smoothed RNNs improve industrial forecasting.

Auto-regressive models improve smoothing efficiency with exponentially tapered windows.

Time series analysis is used to understand and predict dynamic processes, including evolving demands in business, weather, markets, and biological rhythms. Exponential smoothing is used in all these domains to obtain simple interpretable models of time series and to forecast future values. Despite its popularity, expon…

Improved Gibbs sampler speeds up Bayesian exponential smoothing model.

This paper extends exponential smoothing to distributional time series using Wasserstein distance.

Exponential smoothers are a simple and memory efficient way to compute running averages of time series. Here we define and describe practical properties of exponential smoothers for signals observed at constant and variable intervals.

Smooth solutions found for hydrodynamic equations.

Untuned SGD converges but with an exponential dependence on smoothness, adaptive methods prevent this.

In this paper, we examine the dependence of standard gluing process for pseudoholomorphic curves under the change of the length $T$ of the neck-region with respect to the cylindrical metrics associated to the given analytic coordinates near the punctures in the setting of bordered open Riemann surface with boundary pun…

Continuous control imitation learning fails if expert actions are smooth.

The paper extends properties of smooth functions to closed sets and maps.

We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on complex supermanifolds. Furthermore we discuss local actions associated to supe…

NSGD-M optimizes machine learning models without hyperparameter tuning, even under relaxed smoothness.

The COS method for European options pricing is improved with a new bound for the number of terms.

Study on focal locus of submanifolds in Finsler manifolds, showing regularity and smoothness.

This work improves polynomial approximations for functions with asymmetric behavior.

Paper explores robust estimators for kernel exponential families using smoothed total variation distances.

Quantifies polynomial approximation rates for smooth functions under various distributions.

Paper shows SVM can achieve super fast convergence rates.

Dropout improves regularization in flexible models for rare features.

We propose a Laplace approximation that creates a stochastic unit from any smooth monotonic activation function, using only Gaussian noise. This paper investigates the application of this stochastic approximation in training a family of Restricted Boltzmann Machines (RBM) that are closely linked to Bregman divergences.…

Given a pseudo-Riemannian metric of regularity $C^{1,1}$ on a smooth manifold, we prove that the corresponding exponential map is a bi-Lipschitz homeomorphism locally around any point. We also establish the existence of totally normal neighborhoods in an appropriate sense. The proofs are based on regularization, combin…

Smooth convergence shown for curve diffusion flows.

Adapts SGD to noise and problem specifics for faster convergence.

We introduce, for every $\mathbb{Z}$-graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new construction of a Fedosov type resolution of the algebra of smooth functions of $\mathbb{Z}$-graded manifolds and we extend the Emmrich--Wein…

This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.

Hybrid model combines LSTM and ETS for mid-term electric load forecasting.

We consider the smoothing probabilities of hidden Markov model (HMM). We show that under fairly general conditions for HMM, the exponential forgetting still holds, and the smoothing probabilities can be well approximated with the ones of double sided HMM. This makes it possible to use ergodic theorems. As an applicatio…

Study improves the exponential rate of metric difference in Higgs bundles.

On a complete non-compact gradient shrinking Ricci soliton, we prove the analyticity in time for smooth solutions of the heat equation with quadratic exponential growth in the space variable. This growth condition is sharp. As an application, we give a necessary and sufficient condition on the solvability of the backwa…

Price changes are induced by aggressive market orders in stock market. We introduce a bivariate marked Hawkes process to model aggressive market order arrivals at the microstructural level. The order arrival intensity is marked by an exogenous part and two endogenous processes reflecting the self-excitation and cross-e…

Frolicher spaces and smooth mappings form a cartesian closed category. It was shown in our previous paper [Far East Journal of Mathematical Sciences, 35 (2009), 211-233] that its full subcategory of Weil exponentiable Frolicher spaces is cartesian closed. By emancipating microlinearity from within a well-adapted model …

We study spaces with a cuspidal (or horn-like) singularity embedded in a smooth Riemannian manifold and analyze the geodesics in these spaces which start at the singularity. This provides a basis for understanding the intrinsic geometry of such spaces near the singularity. We show that these geodesics combine to natura…

Improved averaging method for noisy observations converges strongly.

This research improves LSTM for monthly electricity demand forecasting using pattern-based methods.

Study infinitesimal deformations of Lie algebroid pairs.

In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold $\mathcal{M}$ with a torsion-free affine connection the operator $\mathcal{E}_p(v)$ acting on the space $T_p\mathcal{M}$ is defined to be the composition of the differential …

A new method for efficiently computing derivatives of skew-symmetric matrix exponentials.

We propose networked exponential families to jointly leverage the information in the topology as well as the attributes (features) of networked data points. Networked exponential families are a flexible probabilistic model for heterogeneous datasets with intrinsic network structure. These models can be learnt efficient…

Study on controllability and groups of manifolds with boundaries.

The paper classifies flows of ancient curves in 2D space.

Using symplectic techniques and spectral analysis of smooth paths of self-adjoint operators, we characterize the set of conjugate instants along a geodesic in an infinite dimensional Riemannian Hilbert manifold.

This manuscript develops the theory of agglomerative clustering with Bregman divergences. Geometric smoothing techniques are developed to deal with degenerate clusters. To allow for cluster models based on exponential families with overcomplete representations, Bregman divergences are developed for nondifferentiable co…

Study controllability of diffeomorphisms of simple polytopes.

Annealed Entropic Allocation improves ranking and selection by mitigating hard switching and improving finite-budget discrimination.

We show that a smooth unknotted curve in R^3 satisfies an isoperimetric inequality that bounds the area of an embedded disk spanning the curve in terms of two parameters: the length L of the curve and the thickness r (maximal radius of an embedded tubular neighborhood) of the curve. For fixed length, the expression giv…

We prove polynomial and exponential decay at infinity of eigen-vectors of partial differential operators related to radiation problems for time-harmonic generalized Maxwell systems in an exterior domain with non-smooth inhomogeneous, anisotropic coefficients converging near infinity with a certain rate towards the iden…