arXiv research

Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.

A new method calibrates value predictions in offline RL to improve reliability.

We study the problem of variable selection in convex nonparametric regression. Under the assumption that the true regression function is convex and sparse, we develop a screening procedure to select a subset of variables that contains the relevant variables. Our approach is a two-stage quadratic programming method that…

The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.

A new method approximates expected empirical loss for stochastic deep learning tasks.

We extend the Deep Image Prior (DIP) framework to one-dimensional signals. DIP is using a randomly initialized convolutional neural network (CNN) to solve linear inverse problems by optimizing over weights to fit the observed measurements. Our main finding is that properly tuned one-dimensional convolutional architectu…

Background: It is still an open research area to theoretically understand why Deep Neural Networks (DNNs)---equipped with many more parameters than training data and trained by (stochastic) gradient-based methods---often achieve remarkably low generalization error. Contribution: We study DNN training by Fourier analysi…

We present a new algorithm for boosting generalized additive models for location, scale and shape (GAMLSS) that allows to incorporate stability selection, an increasingly popular way to obtain stable sets of covariates while controlling the per-family error rate (PFER). The model is fitted repeatedly to subsampled data…

Push-forward models struggle to fit multimodal distributions due to high Lipschitz constants.

Study one-dimensional topological theories with linear generating functions.

Matrix Product States (MPS), also known as Tensor Train (TT) decomposition in mathematics, has been proposed originally for describing an (especially one-dimensional) quantum system, and recently has found applications in various applications such as compressing high-dimensional data, supervised kernel linear classifie…

Proposes an optimization framework for sparse robust subspace estimation.

Deep heteroskedastic models overfit, showing a phase transition with regularization strength.

This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduce a kind of Morse-Lyapunov function, called dynamically ordered, which fits well dynamics of diffeomorphism. The paper is devoted to finding…

We found a new simple family of Cantor sets whose projections are one-dimensional.

Study of one-dimensional non-Hausdorff manifolds and their quotient to CW complexes.

A new metric-based principal curve method learns 1D manifolds from spatial data.

Study reveals structure of local minima in GMMs, identifying key cluster centers.

We prove that for compact, non-contractible, one dimensional geodesic spaces, a version of the marked length spectrum conjecture holds. For a compact one dimensional geodesic space X, we define a subspace Conv(X). When X is non-contractible, we show that X deformation retracts to Conv(X). If two such spaces X, Y have t…

We present a novel Neural Embedding Spatio-Temporal (NEST) point process model for spatio-temporal discrete event data and develop an efficient imitation learning (a type of reinforcement learning) based approach for model fitting. Despite the rapid development of one-dimensional temporal point processes for discrete e…

This paper optimizes paths for generative models using kinetic energy.

One-dimensional crystals have convex shapes under certain conditions.

Smooth algebra analysis for one-dimensional singular foliations.

We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.

In this paper we focus on the problem of assigning uncertainties to single-point predictions. We introduce a cost function that encodes the trade-off between accuracy and reliability in probabilistic forecast. We derive analytic formula for the case of forecasts of continuous scalar variables expressed in terms of Gaus…

It is generally understood that a given one-dimensional diffusion may be transformed by Cameron-Martin-Girsanov measure change into another one-dimensional diffusion with the same volatility but a different drift. But to achieve this we have to know that the change-of-measure local martingale that we write down is a tr…

Proposes variance reduction techniques for sliced Wasserstein distance estimation.

We obtain a deterministic characterisation of the \emph{no free lunch with vanishing risk}, the \emph{no generalised arbitrage} and the \emph{no relative arbitrage} conditions in the one-dimensional diffusion setting and examine how these notions of no-arbitrage relate to each other.

In this paper we continue our studies of the one dimensional conformal metric flows, which were introduced in [8]. In this part we mainly focus on evolution equations involving fourth order derivatives. The global existence and exponential convergence of metrics for the 1-Q and 4-Q flows are obtained.

We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.

Geometric Occam's Razor shapes deep learning solutions.

Combines machine learning and convex limiting for accurate subgrid flux modeling in shallow-water equations.

Suppose that f and g are Markov surjections, each defined on a wedge of circles, each fixing the branch point and having the branch point as the only critical value. We show that if the points in the inverse limit spaces associated with f and g corresponding to the branch point are distinguished then these inverse limi…

In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topological Cayley graph? We answer this question in the positive and provide a combinatorial description of such an object.

Proposes a new regression method using $L_p$-norms for non-Gaussian noise.

Study shows one-dimensional location-scale-shape models are flat in Wasserstein geometry.

This paper optimizes Gaussian mixture model learning with optimal sampling complexity.

The paper analyzes how the one-dimensional Wasserstein distance captures pointwise density differences in finite samples.

Proposes a new method for two-dimensional data discretization.

Any two compact, complete, one-dimensional geodesic spaces with identical marked length spectrum have isometric $π_1$-hull. The present version contains errors, notably in Lemmas 2.2 and 2.3 (path cancellations can be more complicated), which then propagate through the paper. The main result is correct as stated, and a…

TRA detects causal direction from bivariate data using geometric shapes.

The paper explores global index formulas for one-dimensional holomorphic foliations.

We prove that every homomorphism from the fundamental group of a planar Peano continuum to the fundamental group of a planar or one-dimensional Peano continuum is induced by a continuous map up to conjugation. This is then used to provide a family of uncountable many planar Peano continua with pairwise non-isomorphic f…

We introduce a general notion of twistorial map and classify twistorial harmonic morphisms with one-dimensional fibres from self-dual four-manifolds. Such maps can be characterised as those which pull back Abelian monopoles to self-dual connections. In fact, the constructions involve solving a generalised monopole equa…

Study on the complexity of 1D ReLU neural networks, proving growth in linear regions.

Using the one dimensional free particle symmetries, the quantum finance symmetries are obtained. Namely, it is shown that Black-Scholes equation is invariant under Schrödinger group. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited. To get the Black-Scholes equati…

We assess cluster stability by trimming extreme points and tracking data range reduction.

Simplifies study of multivariate shortfall risk measures.