arXiv research

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

Study one-dimensional topological theories with linear generating functions.

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

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

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.

Neural autoregressive models are explicit density estimators that achieve state-of-the-art likelihoods for generative modeling. The D-dimensional data distribution is factorized into an autoregressive product of one-dimensional conditional distributions according to the chain rule. Data completion is a more involved ta…

New uniqueness concept for adversarial Bayes classifier.

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…

One-dimensional crystals have convex shapes under certain conditions.

Smooth algebra analysis for one-dimensional singular foliations.

We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curve…

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…

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.

Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying confidence intervals to multivariate data. In this paper we define confidence interval…

BFCR detects anomalies in 1D data efficiently.

CNNs outperform standard chemometric methods for spectral data classification.

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…

A new model clusters networks with community-specific submanifold structures.

Subspace clustering is the problem of partitioning unlabeled data points into a number of clusters so that data points within one cluster lie approximately on a low-dimensional linear subspace. In many practical scenarios, the dimensionality of data points to be clustered are compressed due to constraints of measuremen…

Method estimates multivariate counterfactual distributions efficiently and accurately.

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.

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

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.

Diffusion models improve creativity by smoothing the score function, leading to interpolated data.

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

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

Efficiently estimates common mean in high-dimensional data with noisy subset.

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

Generative adversarial networks (GANs) are an exciting alternative to algorithms for solving density estimation problems---using data to assess how likely samples are to be drawn from the same distribution. Instead of explicitly computing these probabilities, GANs learn a generator that can match the given probabilisti…

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…

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…

Simplifies study of multivariate shortfall risk measures.

Air quality forecasting has been regarded as the key problem of air pollution early warning and control management. In this paper, we propose a novel deep learning model for air quality (mainly PM2.5) forecasting, which learns the spatial-temporal correlation features and interdependence of multivariate air quality rel…

New method estimates SW distance using CDFs for scalable data parallelism.

Sliced Optimal Transport simplifies OT for fast computation.

Warped products over one-dimensional base spaces satisfy curvature-dimension condition under specific conditions.

We show that the Bruschlinsky group with the winding order is a homeomorphism invariant for a class of one-dimensional inverse limit spaces. In particular we show that if a presentation of an inverse limit space satisfies the Simplicity Condition, then the Bruschlinsky group with the winding order of the inverse limit …

The Brasselet number of a function $f$ with nonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, using the Brasselet number, we present several formulas for germs $f:(X, 0) \rightarrow (\mathbb{C}, 0)$ and $g : (X, 0)\rightarrow (\mathbb{C}, 0)$ in t…

CNN model predicts financial market movement with better performance.

Study proves existence and uniqueness for differential equations with non-Lipschitz coefficients.