arXiv research

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.

Discussing rigidity in codimension 2, extending rigidity concepts.

Study on multiple linking numbers, extending Gauss diagram formulas.

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…

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

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.

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

Deep nets with massive data learn spatially sparse functions.

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

New causal analysis reconciles predictive and statistical fairness.

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)…

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

This is a survey on quaternion Hermitian Weyl (locally conformally quaternion Kähler) and hyperhermitian Weyl (locally conformally hyperkähler) manifolds. These geometries appear by requesting the compatibility of some quaternion Hermitian or hyperhermitian structure with a Weyl structure. The motivation for such a stu…

Proves a vanishing property for symplectic manifold cohomology.

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

Invariants defined for braid systems under Hurwitz equivalence.

This study evaluates the importance of design of experiments for PINN in physics-informed deep learning.

We discuss Russia's underlying motives for issuing its government-backed cryptocurrency, CryptoRuble, and the implications thereof and of other likely-soon-forthcoming government-issued cryptocurrencies to some stakeholders (populace, governments, economy, finance, etc.), existing decentralized cryptocurrencies (such a…

New framework for fairness in continuous protected attributes.

The study proves nearly Frobenius algebras over certain domains are Frobenius.

Value-function approximation methods that operate in batch mode have foundational importance to reinforcement learning (RL). Finite sample guarantees for these methods often crucially rely on two types of assumptions: (1) mild distribution shift, and (2) representation conditions that are stronger than realizability. H…

This paper is intended to explain, in simple terms, some of the mechanisms and agents common to multiagent financial market simulations. We first discuss the necessity to include an exogenous price time series ("the fundamental value") for each asset and three methods for generating that series. We then illustrate one …

We provide the first information theoretic tight analysis for inference of latent community structure given a sparse graph along with high dimensional node covariates, correlated with the same latent communities. Our work bridges recent theoretical breakthroughs in the detection of latent community structure without no…

We propose a quantum machine learning algorithm for efficiently solving a class of problems encoded in quantum controlled unitary operations. The central physical mechanism of the protocol is the iteration of a quantum time-delayed equation that introduces feedback in the dynamics and eliminates the necessity of interm…

Rogue is a famous dungeon-crawling video-game of the 80ies, the ancestor of its gender. Rogue-like games are known for the necessity to explore partially observable and always different randomly-generated labyrinths, preventing any form of level replay. As such, they serve as a very natural and challenging task for rei…

In real supervised learning scenarios, it is not uncommon that the training and test sample follow different probability distributions, thus rendering the necessity to correct the sampling bias. Focusing on a particular covariate shift problem, we derive high probability confidence bounds for the kernel mean matching (…

This paper studies robust forward investment and consumption preferences within a zero-volatility context. Different from previous works, we consider an incomplete financial market model due to general investment portfolio constraints. We provide a new PDE characterization and a novel semi-explicit saddle-point constru…

Deep learning models generalize by extending decision boundaries outside the convex hull of training data.

As machine learning is applied to an increasing variety of complex problems, which are defined by high dimensional and complex data sets, the necessity for task oriented feature learning grows in importance. With the advancement of Deep Learning algorithms, various successful feature learning techniques have evolved. I…

We prove that any mapping torus of a pseudo-Anosov mapping class with bounded normalized Weil-Petersson translation length contains a finite set of transverse and level closed curves, and drilling out this set of curves results in one of a finite number of cusped hyperbolic 3-manifolds. The number of manifolds in the f…

The increasing use of machine learning in practice and legal regulations like EU's GDPR cause the necessity to be able to explain the prediction and behavior of machine learning models. A prominent example of particularly intuitive explanations of AI models in the context of decision making are counterfactual explanati…

Asymptotic geodesics in convex polygons are convex for large distances.

The banking systems that deal with risk management depend on underlying risk measures. Following the Basel II accord, there are two separate methods by which banks may determine their capital requirement. The Value at Risk measure plays an important role in computing the capital for both approaches. In this paper we an…

We give a necessary and sufficient condition for a graph to have a right-angled Artin group as its braid group for braid index $\ge 5$. In order to have the necessity part, graphs are organized into small classes so that one of homological or cohomological characteristics of right-angled Artin groups can be applied. Fi…

New method uses momentum to converge in DC optimization with small batches.

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in open systems and its absence in closed ones, we prove sharp, state-independent i…

Due to recent advances - compute, data, models - the role of learning in autonomous systems has expanded significantly, rendering new applications possible for the first time. While some of the most significant benefits are obtained in the perception modules of the software stack, other aspects continue to rely on know…

Study proves Maximum Principles for unbounded Riemannian domains.

The complement of a non-separating planar graph contains a K_n minor.

Paper explores second-order optimization in first-order methods, proving and disproving the necessity of square root.

The paper extends fairness to hierarchical clustering, finding efficient algorithms with minimal loss.

Based on the tree architecture, the objective of this paper is to design deep neural networks with two or more hidden layers (called deep nets) for realization of radial functions so as to enable rotational invariance for near-optimal function approximation in an arbitrarily high dimensional Euclidian space. It is show…