Related papers: Applied Measure Theory for Probabilistic Modeling
This paper covers two topics: first an introduction to Algorithmic Complexity Theory: how it defines probability, some of its characteristic properties and past successful applications. Second, we apply it to problems in A.I. - where it…
StateSpaceModels.jl is an open-source Julia package for modeling, forecasting and simulating time series in a state-space framework. The package represents a straightforward tool that can be useful for a wide range of applications that deal…
Scientists often run experiments to distinguish competing theories. This requires patience, rigor, and ingenuity - there is often a large space of possible experiments one could run. But we need not comb this space by hand - if we represent…
In the mixture models problem it is assumed that there are $K$ distributions $\theta_{1},\ldots,\theta_{K}$ and one gets to observe a sample from a mixture of these distributions with unknown coefficients. The goal is to associate instances…
Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…
Prompting is now a dominant method for evaluating the linguistic knowledge of large language models (LLMs). While other methods directly read out models' probability distributions over strings, prompting requires models to access this…
The goal of machine learning is to find models that minimize prediction error on data that has not yet been seen. Its operational paradigm assumes access to a dataset $S$ and articulates a scheme for evaluating how well a given model…
Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and context-aware analyses. Moreover, the expertise needed…
We show that modularity, a quantity introduced in the study of networked systems, can be generalized and used in the clustering problem as an indicator for the quality of the solution. The introduction of this measure arises very naturally…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. LazySets provides methods to apply common set operations,…
We present an area formula for continuous mappings between metric spaces, under minimal regularity assumptions. In particular, we do not require any notion of differentiability. This is a consequence of a measure theoretic notion of…
We present the Julia package HomotopyContinuation.jl, which provides an algorithmic framework for solving polynomial systems by numerical homotopy continuation. We introduce the basic capabilities of the package and demonstrate the software…
Advances in architectural design, data availability, and compute have driven remarkable progress in semantic segmentation. Yet, these models often rely on relaxed Bayesian assumptions, omitting critical uncertainty information needed for…
We study density of rational languages under shift invariant probability measures on spaces of two-sided infinite words, which generalizes the classical notion of density studied in formal languages and automata theory. The density for a…
Recent advances in statistical inference have significantly expanded the toolbox of probabilistic modeling. Historically, probabilistic modeling has been constrained to (i) very restricted model classes where exact or approximate…
In this paper it is shown that in the case of the given probability distribution or histogram using the Jaynes entropy maximum principle an J- measure of uncertainty (JMU) provides the maximum for a given distribution can be constructed.…
Measuring software complexity plays an important role to meet the demands of complex software. The cyclomatic complexity is one of most used and renowned metric among the other three proposed and researched metrics that are namely: Line of…
Probabilistic programming languages (PPLs) are expressive means for creating and reasoning about probabilistic models. Unfortunately hybrid probabilistic programs, involving both continuous and discrete structures, are not well supported by…