Related papers: A Framework for Analyzing Stochastic Jumps in Fina…
We develop the foundations of Algebraic Stochastic Calculus, with an aim to replacing what is typically referred to as Stochastic Calculus by a purely categorical version thereof. We first give a sheaf theoretic reinterpretation of…
Reliability analysis is a sub-field of uncertainty quantification that assesses the probability of a system performing as intended under various uncertainties. Traditionally, this analysis relies on deterministic models, where experiments…
Traditional logic-based belief revision research focuses on designing rules to constrain the behavior of revision operators. Frameworks have been proposed to characterize iterated revision rules, but they are often too loose, leading to…
While Large Language Models (LLMs) have found success in real-world applications, their underlying explanatory process is still poorly understood. This paper proposes IBE-Eval, a framework inspired by philosophical accounts on Inference to…
Many applications of intelligent systems require reasoning about the mental states of agents in the domain. We may want to reason about an agent's beliefs, including beliefs about other agents; we may also want to reason about an agent's…
Parameter identification problems are formulated in a probabilistic language, where the randomness reflects the uncertainty about the knowledge of the true values. This setting allows conceptually easily to incorporate new information, e.g.…
Handwritten mathematical expressions (HMEs) contain ambiguities in their interpretations, even for humans sometimes. Several math symbols are very similar in the writing style, such as dot and comma or 0, O, and o, which is a challenge for…
This paper investigates the knowledge of language models from the perspective of Bayesian epistemology. We explore how language models adjust their confidence and responses when presented with evidence with varying levels of informativeness…
Our previous work on classifying complex ship images [1,2] has evolved into an effort to develop software tools for building and solving generic classification problems. Managing the uncertainty associated with feature data and other…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process…
As AI models become ever more complex and intertwined in humans' daily lives, greater levels of interactivity of explainable AI (XAI) methods are needed. In this paper, we propose the use of belief change theory as a formal foundation for…
We consider the problem of valuing a European option written on an asset whose dynamics are described by an exponential L\'evy-type model. In our framework, both the volatility and jump-intensity are allowed to vary stochastically in time…
The Partial Integral Equation (PIE) framework was developed to computationally analyze linear Partial Differential Equations (PDEs) where the PDE is first converted to a PIE and then the analysis problem is solved by solving operator-valued…
We study investor learning and information acquisition in private markets using a large dataset of expert network calls. We develop a sequential Large Language Model (LLM)-Bayesian framework that treats expert interactions as sequential…
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This extension consists simply in adding a " flipping coin " boolean closed atomic expression. This language can be understood as a major generalization of Scott's PCF…
Random experiments that are simple and clear enough to be performed by human agents feature prominently in the teaching of elementary stochastics as well as in games. We present Alea, a domain-specific language for the specification of…
Lifted probabilistic inference (Poole, 2003) and symbolic dynamic programming for lifted stochastic planning (Boutilier et al, 2001) were introduced around the same time as algorithmic efforts to use abstraction in stochastic systems. Over…
Although pretrained language models (PTLMs) contain significant amounts of world knowledge, they can still produce inconsistent answers to questions when probed, even after specialized training. As a result, it can be hard to identify what…
In the realm of financial analytics, leveraging unstructured data, such as earnings conference calls (ECCs), to forecast stock volatility is a critical challenge that has attracted both academics and investors. While previous studies have…