arXiv research

The paper addresses bias amplification in prediction and decision-making using causal analysis.

Bubbles are essential in certain economic models with high growth and low interest rates.

Paper proposes forecast-necessity testing for accurate causal interpretation in nonlinear time-series models.

Unified feature importance for machine learning models tackles sufficiency and necessity limitations.

Paper presents a dynamic tail risk protection strategy using ML and econometrics.

Discussing rigidity in codimension 2, extending rigidity concepts.

Study on multiple linking numbers, extending Gauss diagram formulas.

Study finds cryptocurrency market diversity patterns inconsistent with neutral models.

We introduce an up-down coloring of a virtual-link diagram. The colorabilities give a lower bound of the minimum number of Reidemeister moves of type II which are needed between two 2-component virtual-link diagrams. By using the notion of a quandle cocycle invariant, we determine the necessity of Reidemeister moves of…

New DA method CIRM outperforms existing methods under structural causal model assumptions.

Transformers show strengths and weaknesses in complexity analysis.

AdaDKRR tackles data silos by combining autonomy, privacy, and collaboration.

Improved variational inequality algorithms using adaptive step sizes.

New algorithms improve boosting by optimizing chance-corrected measures.

Using powerful posterior distributions is a popular approach to achieving better variational inference. However, recent works showed that the aggregated posterior may fail to match unit Gaussian prior, thus learning the prior becomes an alternative way to improve the lower-bound. In this paper, for the first time in th…

In 2001, Oestlund conjectured that Reidemeister moves 1 and 3 are sufficient to describe a homotopy from any generic immersion from the circle into the plane to the standard embedding of the circle. We show that this conjecture is false.

The great success of deep learning poses urgent challenges for understanding its working mechanism and rationality. The depth, structure, and massive size of the data are recognized to be three key ingredients for deep learning. Most of the recent theoretical studies for deep learning focus on the necessity and advanta…

Paper proposes methods to learn accurate models from incomplete data without imputation.

Optimal machine learning requires interpolating training data in high-dimensional linear regression.

Using Jeff Holman's comments in Quantitative Finance to illustrate 4 critical errors students should learn to avoid: 1) Mistaking tails (4th moment) for volatility (2nd moment), 2) Missing Jensen's Inequality, 3) Analyzing the hedging wihout the underlying, 4) The necessity of a numeraire in finance.

We discuss general notions of metrics and of Finsler structures which we call weak metrics and weak Finsler structures. Any convex domain carries a canonical weak Finsler structure, which we call its tautological weak Finsler structure. We compute distances in the tautological weak Finsler structure of a domain and we …

DOODLER detects out-of-distribution inputs by reconstructing in-distribution data.

Tensoring $p$-weak differentiable structures preserves their properties.

New structures defined for studying contact foliations and their geometry.

The study examines conditions for weak nearly cosymplectic manifolds to split into products.

Subset selection improves weak supervision performance.

Defines weak geodesics on specific subsets of manifolds.

Study weak conjugacy in surface homeomorphisms.

New model shows weak teachers can help strong students learn even with imperfect labels.

Introduces weak $(p,k)$-Dirac structures in geometric settings.

RAVEN improves weak-to-strong generalization under distribution shifts.

Study weak $f$-K-contact manifolds, finding Einstein-type metrics and solitons.

Study the geometry of weak para-f-structures and subclasses.

We prove that every Kaehler solvmanifold has a finite covering whose holomorphic reduction is a principal bundle. An example is given that illustrates the necessity, in general, of passing to a proper covering. We also answer a stronger version of a question posed by Akhiezer for homogeneous spaces of nonsolvable algeb…

The study explores new metric structures on manifolds, linking them to Einstein metrics.

Study on Ricci solitons and Einstein metrics in weak β-Kenmotsu manifolds.

This paper studies properties of weak reducing pairs in critical Heegaard splittings.

We study weakened $f$-structures on manifolds, generalizing classical results.

Equivalent bicategories constructed from action Lie groupoids.

In this work we wish characterize the Einstein manifolds $(M,g)$, however without the necessity of hypothesis of compactness over $M$ and unitary volume of $g$, which are well known in many works. Our result says that if all eingenvalues $λ$ of $r_{g}$, with respect to $g$, satisfy $λ\geq \frac{1}{n}s_{g}$, then $(M,g)…

We deal with a notion of weak binormal and weak principal normal for non-smooth curves of the Euclidean space with finite total curvature and total absolute torsion. By means of piecewise linear methods, we first introduce the analogous notation for polygonal curves, where the polarity property is exploited, and then m…

New causal analysis reconciles predictive and statistical fairness.

Classifies compact spaces by shape, finite spaces by weak homotopy.

Optimal algorithm converts weak to strong learner with less data.

Formalizes weak and strong verification for LLMs, controlling errors without assumptions.

In this paper we discuss the possibility of using multilevel Monte Carlo (MLMC) methods for weak approximation schemes. It turns out that by means of a simple coupling between consecutive time discretisation levels, one can achieve the same complexity gain as under the presence of a strong convergence. We exemplify thi…

Random feature models can outperform a weak teacher with early stopping.

Paper establishes a general inequality for warped product CR-submanifolds in Kähler manifolds.