A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The paper establishes bounds on the smoothness parameter in Gaussian process interpolation.
Smoothness analysis of adversarial training reveals constraints cause more non-smoothness.
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each subject as fixed during clustering, we measure the dissimilarity between subjec…
A flow defined by a nonsingular smooth vector field on a closed manifold is said to be parameter rigid if given any real valued smooth function on , there are a smooth funcion and a constant such that holds. We show that the parameter rigid flows on closed orientable 3-manifolds are sm…
NSGD-M optimizes machine learning models without hyperparameter tuning, even under relaxed smoothness.
Deep neural networks with specific parameter sets can approximate smooth functions efficiently.
In high-dimensional and/or non-parametric regression problems, regularization (or penalization) is used to control model complexity and induce desired structure. Each penalty has a weight parameter that indicates how strongly the structure corresponding to that penalty should be enforced. Typically the parameters are c…
A new method for efficient BNC parameter estimation outperforms HDP smoothing.
We propose an adaptive smoothing algorithm based on Nesterov's smoothing technique in \cite{Nesterov2005c} for solving "fully" nonsmooth composite convex optimization problems. Our method combines both Nesterov's accelerated proximal gradient scheme and a new homotopy strategy for smoothness parameter. By an appropriat…
Predictive models can be used on high-dimensional brain images for diagnosis of a clinical condition. Spatial regularization through structured sparsity offers new perspectives in this context and reduces the risk of overfitting the model while providing interpretable neuroimaging signatures by forcing the solution to …
A non-Bayesian, regression-based or generalized least squares (GLS)-based approach is formally proposed to estimate a class of time-varying AR parameter models. This approach has partly been used by Ito et al. (2014, 2016a,b), and is proven to be efficient because, unlike conventional methods, it does not require Kalma…
PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.
In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees -cohomology with $\C/\Z$-cohomology, for . Furthermore, they are shown to be rigid in a variation of paths (p…
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, -nets and conical…
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.
Efficient estimators for smooth Hilbert-valued parameters with theoretical guarantees.
New matching estimators correct bias in multivariate settings without smoothing parameters.
T-LoHo model detects structured sparsity and smoothness on graph data.
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning. We also show how to allow for non-Gaussian noise and outliers which are typical…
Improved regret bounds for structured linear contextual bandits with Gaussian noise.
Averaged SGD optimizes a smoothed objective, leading to better generalization.
Novel method for SDE calibration from sparse data using neural flows.
New magnetic flow rigidity theorem for negative curvatures.
Here, we study different update rules in stochastic gradient descent (SGD) for online forecasting problems. The selection of the learning rate parameter is critical in SGD. However, it may not be feasible to tune this parameter in online learning. Therefore, it is necessary to have an update rule that is not sensitive …
We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4-space with barrier 3-spheres. \par The existe…
Nonparametric tests via kernel embedding of distributions have witnessed a great deal of practical successes in recent years. However, statistical properties of these tests are largely unknown beyond consistency against a fixed alternative. To fill in this void, we study here the asymptotic properties of goodness-of-fi…
New law explains why deep learning models often have more parameters than needed.
A new federated learning algorithm improves on existing methods by exploiting data smoothness.
This work introduces two strategies for training network classifiers with heterogeneous agents. One strategy promotes global smoothing over the graph and a second strategy promotes local smoothing over neighbourhoods. It is assumed that the feature sizes can vary from one agent to another, with some agents observing in…
Untuned SGD converges but with an exponential dependence on smoothness, adaptive methods prevent this.
The paper proves weaker conditions for global smoothings of special Lagrangian submanifolds with conical singularities.
If the fundamental group of the complement of a smooth embedding f: S^2 \subset R^4 is a cyclic group, the map can be deformed to the standard embedding by a generic one-parameter family with at most cusp singularities. If two smooth embeddings are connected by such a deformation, they will be called cusp equivalent. W…
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its derivatives as a "non-smooth + non-smooth" optimization problem. Modern technique…
Multiple generalized additive models (GAMs) are a type of distributional regression wherein parameters of probability distributions depend on predictors through smooth functions, with selection of the degree of smoothness via regularization. Multiple GAMs allow finer statistical inference by incorporating explana…
We consider the combinatorial multi-armed bandit (CMAB) problem, where the reward function is nonlinear. In this setting, the agent chooses a batch of arms on each round and receives feedback from each arm of the batch. The reward that the agent aims to maximize is a function of the selected arms and their expectations…
Isothermic nets created from special maps for smooth surfaces.
We perform a geometric study of the equilibrium locus of the flow that models the diffusion process over a circular network of cells. We prove that when considering the set of all possible values of the parameters, the equilibrium locus is a smooth manifold with corners, while for a given value of the parameters, it is…
A neural network with a single hidden layer can't represent certain multivariable functions.
Dropout improves regularization in flexible models for rare features.
Study revisits AdaGrad convergence with relaxed noise assumptions.
We consider the non-parametric regression problem under Huber's -contamination model, in which an fraction of observations are subject to arbitrary adversarial noise. We first show that a simple local binning median step can effectively remove the adversary noise and this median estimator is minimax optimal up t…
Paper tackles private optimization for non-smooth objectives efficiently.
The study reveals a persistent bias in the distribution of holonomy on compact hyperbolic 3-manifolds.
This paper improves neural network approximation for analytic functions with adjustable depth and width.
Proposes a new method for estimating non-pathwise differentiable functional parameters.
Black-box variational inference tries to approximate a complex target distribution though a gradient-based optimization of the parameters of a simpler distribution. Provable convergence guarantees require structural properties of the objective. This paper shows that for location-scale family approximations, if the targ…
We present a 1-parameter family of finite action solutions to the Hitchin's equations and explore some of its basic properties. For a fixed value of the parameter, the solution is smooth. We conclude by showing a multi-particle generalization of our basic solutions.
New algorithms optimize without knowing problem parameters.