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Conformal Prediction (CP) is a powerful framework for constructing prediction sets with guaranteed coverage. However, recent studies have shown that integrating confidence calibration with CP can lead to a degradation in efficiency. In this…
The science of cities is a relatively new and interdisciplinary topic. It borrows techniques from agent-based modeling, stochastic processes, and partial differential equations. However, how the cities rise and fall, how they evolve, and…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
The goal of these lecture notes is to review the problem of free energy minimization as a unified framework underlying the definition of maximum entropy modelling, generalized Bayesian inference, learning with latent variables, statistical…
The understanding of methane emission and methane absorption plays a central role both in the atmosphere and on the surface of the Earth. Several important ecological processes, e.g., ebullition of methane and its natural microergodicity…
Quantitative assessment of climate change risk requires a method for constructing probabilistic time series of changes in physical climate parameters. Here, we develop two such methods, Surrogate/Model Mixed Ensemble (SMME) and Monte Carlo…
Synthetic datasets are important for evaluating and testing machine learning models. When evaluating real-life recommender systems, high-dimensional categorical (and sparse) datasets are often considered. Unfortunately, there are not many…
We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum entropy choice, and provide a motivating example applicable…
One of the most used metrics to gauge the effects of climate change is the equilibrium climate sensitivity, defined as the long-term (equilibrium) temperature increase resulting from instantaneous doubling of atmospheric CO$_2$. Since…
Language prediction is constrained by informational entropy intrinsic to language, such that there exists a limit to how accurate any language model can become and equivalently a lower bound to language compression. The most efficient…
Information theoretic quantities are extremely useful in discovering relationships between two or more data sets. One popular method---particularly for continuous systems---for estimating these quantities is the nearest neighbour…
The Random Permutation Set (RPS) is a new type of set proposed recently, which can be regarded as the generalization of evidence theory. To measure the uncertainty of RPS, the entropy of RPS and its corresponding maximum entropy have been…
We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel…
Most of the methods that produce space weather forecasts are based on deterministic models. In order to generate a probabilistic forecast, a model needs to be run several times sampling the input parameter space, in order to generate an…
We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and…
Models of networks play a major role in explaining and reproducing empirically observed patterns. Suitable models can be used to randomize an observed network while preserving some of its features, or to generate synthetic graphs whose…
The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region…
Data-driven modelling and computational predictions based on maximum entropy principle (MaxEnt-principle) aim at finding as-simple-as-possible - but not simpler then necessary - models that allow to avoid the data overfitting problem. We…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
The maximum entropy principle (MEP) apparently allows us to derive, or justify, fundamental results of equilibrium statistical mechanics. Because of this, a school of thought considers the MEP as a powerful and elegant way to make…