arXiv research

New theory for nonsmooth systems helps optimize and control complex functions.

The paper simulates Lévy processes and their extremum and hitting time.

The relationship between price volatilty and a market extremum is examined using a fundamental economics model of supply and demand. By examining randomness through a microeconomic setting, we obtain the implications of randomness in the supply and demand, rather than assuming that price has randomness on an empirical …

Stochastic bridges are commonly used to impute missing data with a lower sampling rate to generate data with a higher sampling rate, while preserving key properties of the dynamics involved in an unbiased way. While the generation of Brownian bridges and Ornstein-Uhlenbeck bridges is well understood, unbiased generatio…

The paper finds extremum values for mixed Laplacian eigenvalues on triangles and trapezoids.

Survey about extremum of eigenvalues of geometric operators within a conformal class of a compact riemannian manifold.

In the theory of submanifolds, the following problem is fundamental: to establish simple relationships between the main intrinsic invariants and the main extrinsic invariants of the submanifolds.The basic relationships discovered until now [1, 2, 3, 4] are inequalities. To analyze these problems, we follow the idea of …

A neural framework corrects bias in estimating individual treatment effects.

For Hamiltonian flows we establish the existence of periodic orbits on a sequence of level sets approaching a Bott-nondegenerate symplectic extremum of the Hamiltonian. As a consequence, we show that a charge on a compact manifold with a nondegenerate (i.e. symplectic) magnetic field has periodic orbits on a sequence o…

Derives integral representations for a Lévy process and its extremum, hitting time, with fast evaluation.

Generalized Berwald manifolds are Finsler manifolds admitting linear connections such that the parallel transports preserve the Finslerian length of tangent vectors (compatibi\-li\-ty condition). By the fundamental result of the theory \cite{V5} such a linear connection must be metrical with respect to the averaged Rie…

Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the shortest closed geodesic among the Riemannian spheres with conical singularities of fixed area. We give an alternative proof of this theore…

Model selection is difficult to analyse yet theoretically and empirically important, especially for high-dimensional data analysis. Recently the least absolute shrinkage and selection operator (Lasso) has been applied in the statistical and econometric literature. Consis- tency of Lasso has been established under vario…

The paper evaluates functions of stable Lévy processes and their extrema efficiently.

Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.

Imagine that measurements are made at times $t_0$ and $t_1$ of the trajectory of a physical system whose governing laws are given approximately by a class ${\cal A}$ of so-called {\em prior vector fields}. Because the physical laws are not known precisely, it might be that the measurements are not realised by the integ…

Given a Laplace eigenfunction on a surface, we study the distribution of its extrema on the nodal domains. It is classically known that the absolute value of the eigenfunction is asymptotically bounded by the 4-th root of the eigenvalue. It turns out that the number of nodal domains where the eigenfunction has an extre…

New algorithm explains neural network extrema for better model generalization.

Have you ever felt miserable because of a sudden whipsaw in the price that triggered an unfortunate trade? In an attempt to remove this noise, technical analysts have used various types of moving averages (simple, exponential, adaptive one or using Nyquist criterion). These tools may have performed decently but we show…

Market impact has become a subject of increasing concern among academics and industry experts. We put forward a price impact model which considers the heteroscedasticity of price in the time dimension and dependency between permanent impact and temporary impact. We discuss and derive the extremum of the expectation of …

Much combinatorial optimisation problems constitute a non-polynomial (NP) hard optimisation problem, i.e., they can not be solved in polynomial time. One such problem is finding the shortest route between two nodes on a graph. Meta-heuristic algorithms such as $A^{*}$ along with mixed-integer programming (MIP) methods …

The paper derives formulas for option pricing and random walk expectations.

Are cryptocurrency traders driven by a desire to invest in a new asset class to diversify their portfolio or are they merely seeking to increase their levels of risk? To answer this question, we use individual-level brokerage data and study their behavior in stock trading around the time they engage in their first cryp…

As more and more people shift their movie watching online, competition between movie viewing websites are getting more and more intense. Therefore, it has become incredibly important to accurately predict a given user's watching list to maximize the chances of keeping the user on the platform. Recent studies have sugge…

Examines optimal risk sharing with realistic risk attitudes, finding risk seeking in certain subdomains.

Paper finds new criteria for conjugate points in fluid flows.

CPS solves inverse problems using forward passes and constrained particle seeking.

Controller seeks informative system observations to predict nonlinear dynamics.

The paper studies risk-sharing allocations for risk-seeking agents using a common distortion risk measure.

As humans we are driven by a strong desire for seeking novelty in our world. Also upon observing a novel pattern we are capable of refining our understanding of the world based on the new information---humans can discover their world. The outstanding ability of the human mind for discovery has led to many breakthroughs…

AutoDIME automates design of multi-agent environments for RL.

For Machine Learning (ML) classification problem, where a vector of $\mathbf{x}$--observations (values of attributes) is mapped to a single $y$ value (class label), a generalized Radon--Nikodym type of solution is proposed. Quantum--mechanics --like probability states $ψ^2(\mathbf{x})$ are considered and "Cluster Cente…

Let $(M,I)$ be an almost complex 6-manifold. The obstruction to integrability of almost complex structure (so-called Nijenhuis tensor) maps a 3-dimensional bundle to a 3-dimensional one. We say that Nijenhuis tensor is non-degenerate if it is an isomorphism. An almost complex manifold is called nearly Kaehler if it adm…

RiskMiner discovers formulaic alphas using MCTS for better performance.

Distributed strategic learning has been getting attention in recent years. As systems become distributed finding Nash equilibria in a distributed fashion is becoming more important for various applications. In this paper, we develop a distributed strategic learning framework for seeking Nash equilibria under stochastic…

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction e…

We study an adaptive source seeking problem, in which a mobile robot must identify the strongest emitter(s) of a signal in an environment with background emissions. Background signals may be highly heterogeneous and can mislead algorithms that are based on receding horizon control. We propose AdaSearch, a general algor…

Generative adversarial networks (GANs) are a learning framework that rely on training a discriminator to estimate a measure of difference between a target and generated distributions. GANs, as normally formulated, rely on the generated samples being completely differentiable w.r.t. the generative parameters, and thus d…

We introduce a copula mixture model to perform dependency-seeking clustering when co-occurring samples from different data sources are available. The model takes advantage of the great flexibility offered by the copulas framework to extend mixtures of Canonical Correlation Analysis to multivariate data with arbitrary c…

Challenge hides and seeks privacy in clinical time-series data.

Modes and ridges of the probability density function behind observed data are useful geometric features. Mode-seeking clustering assigns cluster labels by associating data samples with the nearest modes, and estimation of density ridges enables us to find lower-dimensional structures hidden in data. A key technical cha…

Hides the complexity of neural networks, making them more transparent.

We determine the optimal amount to invest in a Black-Scholes financial market for an individual who consumes at a rate equal to a constant proportion of her wealth and who wishes to minimize the expected time that her wealth spends in drawdown during her lifetime. Drawdown occurs when wealth is less than some fixed pro…

Universal AI seeks high-optionality states through empowerment and curiosity.

Optimal risk sharing found for heterogeneous risk attitudes using distortion risk measures.

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. …

Quantum algorithm finds extrema in discrete optimisation problems.

Study on RL on volatility surfaces, proving no free lunch for law-seeking methods.