This paper uses information theory to improve risk modeling in big data.
problem Insufficient application of information theory in actuarial science.
method Explores information theory to uncover performance limits of insurance big data systems.
result Guidance for risk modeling and actuarial pricing systems.
Tensor-based method simplifies causal skeleton discovery.
problem Discover causal relationships between variables.
method Express associations as tensors to reduce dimensionality.
result Causal skeleton can be determined using pair-wise tensors.
This paper reviews information theory in open-world machine learning.
problem Lack of a unified theoretical foundation for open-world machine learning.
method Synthesis of information theoretic approaches.
result Established a pathway toward provable and trustworthy open world intelligence.
Information theory provides a mathematical foundation to measure uncertainty in belief. Belief is represented by a probability distribution that captures our understanding of an outcome's plausibility. Information measures based on Shannon's concept of entropy include realization information, Kullback-Leibler divergenc…
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
The paper extends option pricing theory for markets with informed traders.
problem Discontinuity in option pricing for markets with informed traders.
method New models for option pricing in complete markets considering informed traders' information on stock price direction and return mean.
result The discontinuity puzzle in option pricing is resolved using continuous diffusion price processes.
Shannon's mathematical theory of communication defines fundamental limits on how much information can be transmitted between the different components of any man-made or biological system. This paper is an informal but rigorous introduction to the main ideas implicit in Shannon's theory. An annotated reading list is pro…
UMAP connects to Information Geometry principles.
problem None explicitly stated; focuses on connections.
method None explicitly stated; focuses on connections.
result UMAP has a natural geometric interpretation.
Cone structures in quantum field theory linked to information geometry.
problem Understanding geometric structures in quantum field theory.
method Analyzing invariant cones under modular automorphism groups and their relation to Wishart laws.
result Explicit connection between CAH cones and Wishart laws.
Interest prohibition theory concerns theoretical aspects of interest prohibition. We attempt to lay down some aspects of interest prohibition theory wrapped in a larger framework of informal logic. The reason for this is that interest prohibition theory has to deal with a variety of arguments which is so wide that a li…
The Information Plane theory predicts autoencoders do not compress input information.
problem Understanding the training dynamics of hidden layers in autoencoders.
method Derive a theoretical convergence for the Information Plane of autoencoders using a Gram-matrix based mutual information estimator.
result Ideal autoencoders with a large bottleneck layer size do not compress input information, while a small size causes compression only in the encoder layers.
New method detects information leakage using approximate Bayes predictor.
problem Unintentional exposure of sensitive information via observable data.
method Statistical learning theory and information theory framework, approximating Bayes predictor's log-loss and accuracy.
result MI can be accurately estimated to detect ILs, outperforming state-of-the-art baselines.
Density destructors simplify complex PDFs to maximize entropy, linking to information theory.
problem Complex multivariate PDFs are hard to analyze.
method Invertible transforms that progressively remove structure from PDFs.
result Density destructors can improve estimates of information theoretic quantities.
We consider the "partial information decomposition" (PID) problem, which aims to decompose the information that a set of source random variables provide about a target random variable into separate redundant, synergistic, union, and unique components. In the first part of this paper, we propose a general framework for …
Theory proposes neural networks can be initialized for optimal information transmission.
problem Optimizing neural networks for optimal information transmission and representation.
method Developed a corrected mean-field framework to study neural networks as information channels, proving mutual information maximization at dynamic isometry.
result Mutual information maximization is realized between inputs and propagated signals when neural networks are initialized at dynamic isometry.
The paper applies information theory to financial markets, improving risk management and asset allocation.
problem Improving risk management and asset allocation in financial markets.
method Information-theoretic measures (entropy, mutual information, etc.) applied to financial time series.
result Normalized mutual information (NMI) is a powerful measure of temporal dependence in financial markets.
Accurately determining dependency structure is critical to discovering a system's causal organization. We recently showed that the transfer entropy fails in a key aspect of this---measuring information flow---due to its conflation of dyadic and polyadic relationships. We extend this observation to demonstrate that this…
New theory improves understanding of ensemble learning systems.
problem Improving the effectiveness of ensemble learning systems.
method Generalized Fano's inequality to account for information loss in model combination.
result Reveals strengths and weaknesses of ensemble systems on accuracy and diversity.
The paper establishes bounds for transductive learning using information theory.
problem Transductive learning generalization gap control.
method Information theory, PAC-Bayes, mutual information, conditional mutual information, different information measures.
result Established transductive information-theoretic and PAC-Bayesian bounds.
IFT reformulates AI and ML tasks using field theory.
problem Signal reconstruction and non-parametric inverse problems.
method Reformulate inference in IFT as GNN training.
result IFT-based GNNs can operate without pre-training.
The paper explores how information theory aids in statistical learning models.
problem Characterizing fundamental performance limits in statistical learning models.
method Introduces divergence measures and evidence lower bound (ELBO) in model training.
result Provides a systematic derivation for generative diffusion models.
The paper applies Gaussianization to analyze Earth data, simplifying complex multivariate distributions.
problem Challenges in accurately estimating information content in high-dimensional, heterogeneous Earth data.
method Multivariate Gaussianization for robust probability density estimation.
result Validates the method for estimating information-theoretic measures in Earth system data.
Paper defines saddle points in asymmetric Dynkin games using martingale theory.
problem Tackles saddle point conditions in asymmetric Dynkin games with partial information.
method Uses martingale theory to identify super and submartingales related to equilibrium payoffs.
result Characterizes saddle point strategies in terms of equilibrium payoffs' dynamics and Doob-Meyer decompositions.
Novel mutual information bound improves statistical inference rates.
problem Improving statistical inference rates in Bayesian nonparametrics.
method Introduces a novel mutual information bound.
result Improved contraction rates for fractional posteriors.
This work connects conformal prediction to information theory for uncertainty estimation.
problem Uncertainty estimation in machine learning models.
method Information theory applied to conformal prediction.
result Proven ways to upper bound intrinsic uncertainty using information theory.
Mathematical study of excess growth rate connects info theory with finance.
problem Understanding the excess growth rate in portfolio theory.
method Axiomatic characterization theorems of excess growth rate in terms of relative entropy, Jensen's inequality gap, and logarithmic divergence.
result Established rich connections between information theory and finance.
Warped product affects divergences in information geometry.
problem Warped product's impact on divergences in information geometry.
method Study of warped product on information geometry.
result Warped product does not preserve canonical divergences.
The IB theory explains how ML systems reduce data dimensions while preserving predictive power.
problem Understanding how machine learning systems reduce data dimensions effectively.
method Information-theoretic approach using mutual information.
result The best representation T maximally informs Y while minimizing mutual information with X. A pseudodiagram is a diagram of a knot with some crossing information missing. We review and expand the theory of pseudodiagrams introduced by R. Hanaki. We then extend this theory to the realm of virtual knots, a generalization of knots. In particular, we investigate how much crossing information must be known to conc…
We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of the observer. The resulting \emph{predictive V-information} encompasse…
Statistical test rejects market efficiency using entropy from price returns.
problem Determining market efficiency using information theory.
method Symbolic representation of price returns, Shannon entropy, and statistical test.
result Rejects market efficiency hypothesis for various datasets.
There are (at least) three approaches to quantifying information. The first, algorithmic information or Kolmogorov complexity, takes events as strings and, given a universal Turing machine, quantifies the information content of a string as the length of the shortest program producing it. The second, Shannon information…
This work uses statistical mechanics to explain AI learning.
problem Understanding the statistical principles behind AI learning.
method Starting from sample concentration behaviors, the study applies statistical mechanics principles to AI and machine learning.
result Exponential families and statistical quantities are key in AI and machine learning.
We propose a novel method for clustering data which is grounded in information-theoretic principles and requires no parametric assumptions. Previous attempts to use information theory to define clusters in an assumption-free way are based on maximizing mutual information between data and cluster labels. We demonstrate …
Proposes a method to compute information theory measures via Gaussianization.
problem Challenges of computing information from multidimensional data.
method Indirect computation using a multivariate Gaussianization transform.
result Proposed methods outperform existing estimators, especially in high dimensions.
Complex systems often exhibit multiple levels of organization covering a wide range of physical scales, so the study of the hierarchical decomposition of their structure and function is frequently convenient. To better understand this phenomenon, we introduce a generalization of information theory that works with hiera…
Paper reinterprets majorizing measure theorem in terms of coding theory.
problem Understanding boundedness of random processes.
method Information-theoretic perspective using variable-length codes.
result Boundedness of random processes linked to efficient coding.
Framework for understanding overfitting and underfitting using information theory.
problem Understanding and preventing overfitting and underfitting in machine learning.
method Information-theoretic framework measuring algorithm capacity and dataset information transfer.
result Upper-bounding algorithm capacity and establishing its relationship to machine learning quantities.
The paper models financial markets using information theory to minimize information.
problem Understanding the dynamics of financial markets.
method Modeling financial market dynamics with independent stationary scalar diffusions, interpreting the market as a communication system, and minimizing information-theoretical joint information.
result Financial market dynamics are represented by squared radial Ornstein-Uhlenbeck processes with additivity and self-similarity properties.
Meta learning with information theory and Gaussian processes.
problem Few-shot learning problems.
method Information bottleneck, mutual information, variational approximations, Gaussian processes.
result Competitive accuracy on few-shot classification problems.
Kendall transformation converts continuous data into categorical vectors for robust information theory.
problem Handling small number of observations and preserving ranking in continuous data.
method Kendall transformation converts ordered features into categorical vectors of pairwise order relations.
result Kendall transformation makes information theory methods applicable to continuous data robustly.
Redundancy improves learning stability and generalization in structured systems.
problem Understanding redundancy in structured systems for learning and generalization.
method Developed a theoretical framework that redefines redundancy as a geometric principle unifying various measures.
result Redundancy balances structure and coupling, leading to optimal stability and generalization.
Unified framework connects credit risk metrics with information theory.
problem Disconnection between industry-standard metrics and statistical theory.
method Unified information-theoretic framework, proving IV equals PSI, deriving standard errors, formalizing trade-off, automated binning with XGBoost.
result Unified framework connects IV and PSI, providing statistical foundation for metrics.
InfoBridge uses diffusion bridges to estimate mutual information accurately.
problem Estimating mutual information between random variables.
method Formulated mutual information estimation as a domain transfer problem using diffusion bridge models.
result Demonstrated unbiased estimator for various data types.
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and escort generalizations of basic concepts and constructions in evolutionary game th…
A new distance metric derived from information theory and estimation theory.
problem Developing a robust distance metric for complex signal distributions.
method Information-Estimation Metric (IEM) derived from continuous probability density and denoising errors.
result The IEM is a valid global distance metric that adapts to the geometry of complex distributions.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
Blackwell's theorems influence modern AI through information compression and decision making.
problem Information compression and decision making under uncertainty.
method Theorems developed in the 1940s and 1950s, applied to modern AI.
result Blackwell theorems remain relevant and influence modern AI subfields.