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Researcher profile

Nicholas Foti

Nicholas Foti contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningMethodologyphysics.soc-phq-fin.GNSocial and Information Networks

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Published work

3 published item(s)

preprint2026arXiv

LLMs are not (consistently) Bayesian: Quantifying internal (in)consistencies of LLMs' probabilistic beliefs

Modern AI systems are being deployed in complex domains such as medicine, science, and law, where it is important that they not only produce correct answers, but also represent and update uncertain beliefs about the world as new evidence arrives. We introduce the novel technique of studying LLMs as information processing rules and utilize the information processing gap to study the internal (in)consistencies of how LLMs update their probabilistic beliefs from evidence. Our extensive experiments evaluate multiple approaches in which LLMs can incorporate evidence into their beliefs. Some of these approaches produce (nearly) Bayesian updates; others seem to use a learned heuristic. Surprisingly, the non-Bayesian heuristic updates often outperform exact Bayesian computation in terms of downstream task performance -- indicating the LLMs' probabilistic models of the world are misspecified. Lastly, we show how our measure can provide diagnostics to identify issues with LLM-powered inferential systems.

0 citations0 reviewsNo code linkedOpen access
preprint2015arXiv

Bayesian Structure Learning for Stationary Time Series

While much work has explored probabilistic graphical models for independent data, less attention has been paid to time series. The goal in this setting is to determine conditional independence relations between entire time series, which for stationary series, are encoded by zeros in the inverse spectral density matrix. We take a Bayesian approach to structure learning, placing priors on (i) the graph structure and (ii) spectral matrices given the graph. We leverage a Whittle likelihood approximation and define a conjugate prior---the hyper complex inverse Wishart---on the complex-valued and graph-constrained spectral matrices. Due to conjugacy, we can analytically marginalize the spectral matrices and obtain a closed-form marginal likelihood of the time series given a graph. Importantly, our analytic marginal likelihood allows us to avoid inference of the complex spectral matrices themselves and places us back into the framework of standard (Bayesian) structure learning. In particular, combining this marginal likelihood with our graph prior leads to efficient inference of the time series graph itself, which we base on a stochastic search procedure, though any standard approach can be straightforwardly modified to our time series case. We demonstrate our methods on analyzing stock data and neuroimaging data of brain activity during various auditory tasks.

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preprint2015arXiv

The Intrafirm Complexity of Systemically Important Financial Institutions

In November, 2011, the Financial Stability Board, in collaboration with the International Monetary Fund, published a list of 29 "systemically important financial institutions" (SIFIs). This designation reflects a concern that the failure of any one of them could have dramatic negative consequences for the global economy and is based on "their size, complexity, and systemic interconnectedness". While the characteristics of "size" and "systemic interconnectedness" have been the subject of a good deal of quantitative analysis, less attention has been paid to measures of a firm's "complexity." In this paper we take on the challenges of measuring the complexity of a financial institution and to that end explore the use of the structure of an individual firm's control hierarchy as a proxy for institutional complexity. The control hierarchy is a network representation of the institution and its subsidiaries. We show that this mathematical representation (and various associated metrics) provides a consistent way to compare the complexity of firms with often very disparate business models and as such may provide the foundation for determining a SIFI designation. By quantifying the level of complexity of a firm, our approach also may prove useful should firms need to reduce their level of complexity either in response to business or regulatory needs. Using a data set containing the control hierarchies of many of the designated SIFIs, we find that in the past two years, these firms have decreased their level of complexity, perhaps in response to regulatory requirements.

0 citations0 reviewsNo code linkedOpen access