相关论文: Biology-inspired geometric representation of proba…

Economic and financial theories and practice essentially deal with uncertain future. Humans encounter uncertainty in different kinds of activity, from sensory-motor control to dynamics in financial markets, what has been subject of…

We study computing geometric problems on uncertain points. An uncertain point is a point that does not have a fixed location, but rather is described by a probability distribution. When these probability distributions are restricted to a…

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

The geometric formulation of fiducial probability employed in this paper is an improvement over the usual pivotal quantity formulation. For a single parameter and single observation, the new formulation is based on the geometric properties…

The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…

This paper develops a geometric reinterpretation of probability in which expectation arises from averaging in probability coordinates rather than in value space. By interpreting the cumulative distribution functions as coordinate maps, a…

Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…

Current theories of perception suggest that the brain represents features of the world as probability distributions, but can such uncertain foundations provide the basis for everyday vision? Perceiving objects and scenes requires knowing…

In this paper, we introduce a deterministic formulation for the geometric programming problem, wherein the coefficients are represented as independent linear-normal uncertain random variables. To address the challenges posed by this…

Machine learning classifiers are probabilistic in nature, and thus inevitably involve uncertainty. Predicting the probability of a specific input to be correct is called uncertainty (or confidence) estimation and is crucial for risk…

We propose a structural framework for the geometry of financial order books in which liquidity, supply, and demand are treated as emergent observables rather than primitive economic variables. The market is modeled as an inflationary…

We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…

Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects…

Conventional and current wisdom assumes that the brain represents probability as a continuous number to many decimal places. This assumption seems implausible given finite and scarce resources in the brain. Quantization is an information…

Classical asset pricing relies on the risk-neutral measure $Q$ for valuation, yet its economic interpretation is typically anchored in a physical measure $P$. This creates an inherent asymmetry: pricing is governed by $Q$, while meaning…

Quantifying uncertainty in neural network predictions is essential for high-stakes domains such as autonomous driving, healthcare, and manufacturing. While existing approaches often depend on costly sampling or restrictive distributional…

Exploiting the geometric nature of statistical divergences, we devise a way to define associated induced uncertainty measures for discrete and finite probability distributions. We also report new uncertainty measures and discuss their…

Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem…

In this paper we will analyze discrete probability distributions in which probabilities of particular outcomes of some experiment (microstates) can be represented by the ratio of natural numbers (in other words, probabilities are…

Human cognition spans perception, memory, intuitive judgment, deliberative reasoning, action selection, and social inference, yet these capacities are often explained through distinct computational theories. Here we present a unified…