In this paper we study the Föllmer-Schweizer decomposition of a square integrable random variable with respect to a given semimartingale under restricted information. Thanks to the relationship between this decomposition and that of the projection of with respect to the given information flow, we characteri…
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48 results for “Partial Information Decomposition”
New method quantifies redundant information using information bottleneck.
problem Quantifying redundant information among multiple sources.
method Formulated as an information bottleneck problem, termed redundancy bottleneck.
result Extracts information that best predicts the target without revealing source identity.
RID framework quantifies and regularizes task-relevant knowledge in distillation.
problem Distilling irrelevant information can hinder student model performance.
method Partial Information Decomposition to quantify and regularize task-relevant knowledge.
result RID framework leads to more resilient distillation under nuisance teachers.
The paper explores the tradeoffs between fairness measures in machine learning.
problem The challenge of achieving all three fairness notions simultaneously in machine learning models.
method The approach uses partial information decomposition (PID) to analyze the relationships between fairness measures.
result Identifies the regions where fairness measures overlap and disagree, revealing potential tradeoffs.
Proposes PEID for analyzing synergistic causation in complex systems.
problem Challenges in identifying and analyzing synergistic causation in complex systems.
method Partial Effective Information Decomposition (PEID) framework.
result Unified and computable characterization of synergistic causal relations.
A Measure of the Complexity of Neural Representations based on Partial Information Decompositioncs.IT
A measure of neural complexity quantifies how hard it is to access information across neurons.
problem Understanding how mutual information is distributed among neurons in neural networks.
method Partial Information Decomposition (PID) to disentangle contributions of single neurons, multiple neurons, and synergistic effects.
result Representational Complexity measures the difficulty of accessing information across multiple neurons.
Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…
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 …
In this paper we study a risk-minimizing hedging problem for a semimartingale incomplete financial market where d+1 assets are traded continuously and whose price is expressed in units of the numéraire portfolio. According to the so-called benchmark approach, we investigate the (benchmarked) risk-minimizing strategy in…
New metric for disentangling multivariate representations, accounting for more complex entanglements.
problem Current disentanglement metrics fail to detect entanglements involving more than two variables.
method Partial Information Decomposition framework to analyze information sharing and propose a new disentanglement metric.
result The proposed metric correctly identifies entanglements in high-dimensional spaces.
HCL learns shared and modality-specific latent representations for multimodal data.
problem Binary shared-private decomposition inadequately represents shared information across subsets of modalities.
method Hierarchical Contrastive Learning framework combining latent-variable formulation, structural sparsity, and contrastive objective.
result HCL accurately recovers hierarchical structure and improves predictive performance on multimodal data.
Researchers decompose harmonic forms on specific types of manifolds.
problem Decomposing harmonic forms on compact almost-Kähler manifolds.
method Proved primitive decompositions of Dolbeault harmonic forms in specific bidegrees.
result Primitive decompositions of -, -harmonic forms in bidegree and .
Exact partial information decompositions for Gaussian systems based on dependency constraintscond-mat.stat-mech
The Partial Information Decomposition (PID) [arXiv:1004.2515] provides a theoretical framework to characterize and quantify the structure of multivariate information sharing. A new method (Idep) has recently been proposed for computing a two-predictor PID over discrete spaces. [arXiv:1709.06653] A lattice of maximum en…
The paper proves Hodge decompositions and partial bar partial lemmas for G2 and Calabi-Yau manifolds.
problem Proving Hodge decompositions and partial bar partial lemmas for G2 and Calabi-Yau manifolds.
method Defining cohomology spaces analogous to Bott-Chern cohomology and relating them to harmonic forms on the manifolds.
result Geometric interpretation of cohomology classes in terms of submanifolds and gerbes for G2 manifolds.
Proposes a method to quantify and decompose disparity in ML models, separating exempt and non-exempt components.
problem Quantifying disparity in ML models, especially when certain features are exempted due to their critical importance.
method Information-theoretic decomposition into exempt and non-exempt components, satisfying desirable properties.
result Proposes a measure of non-exempt disparity that satisfies all desirable properties, and shows impossibility results for observational measures.
This work adapts RDT for mental program construction, showing benefits and costs.
problem Applying RDT to mental programs with trade-offs between description length, error, and computational costs.
method Proposed a three-way trade-off and used simulations and partial information decomposition.
result Constructing a shared program library provides global benefits but is sensitive to curricula.
Introduces a new model for mapping matrices to matrices, subsuming linear regression.
problem Learning matrix-to-matrix mappings from data.
method Partial trace regression model, leveraging quantum information theory.
result Relevance demonstrated in matrix-to-matrix regression and positive semidefinite matrix completion.
APINNs improve physics-informed neural networks through flexible domain decomposition.
problem Improving physics-informed neural networks (PINNs) for solving partial differential equations (PDEs).
method Introduces a trainable gate network for soft domain decomposition, allowing flexible parameter sharing and improved generalization.
result APINNs significantly improve PINNs and XPINNs, demonstrating better performance on various types of PDEs.
The paper studies posets from decompositions in symmetric monoidal categories.
problem Understanding posets from decompositions in symmetric monoidal categories.
method Defining decompositions and partial decompositions, complexes of frames, partial bases, and ordered versions.
result Unified approach to combinatorics and homotopy type of posets and complexes.
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.
Decomposes harmonic forms on almost Kähler manifolds, revealing non-trivial structure.
problem Primitive decomposition of harmonic forms on compact almost Kähler manifolds.
method Primitive decomposition of , Bott-Chern and Aeppli-harmonic -forms.
result Primitive components of harmonic forms are constants multiples of .
Study on hedging and valuation of basis risk in incomplete markets with partial information.
problem Hedging and valuation of European and American claims in an incomplete market with correlated assets and partial information.
method Stochastic control and partial information scenario, forward indifference valuation, dual representation, PDE approach.
result Derivation of optimal hedging strategy and forward indifference price representation for claims.
Proposes a faster Isomap algorithm by reducing eigenvalue decomposition complexity.
problem High computational complexity of Isomap, especially in eigenvalue decomposition stage.
method Introduces a projection operator to reduce the complexity of the eigenvalue decomposition stage to linear order.
result Reduces Isomap's computational complexity to linear order while preserving structural information.
A generalized complex manifold which satisfies the -lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the behavior of the Hodge decomposition in smooth and holomorphic families of generalized complex manifolds. In particular we …
Torus decomposition shows foliation detected slopes for glued knot manifolds.
problem Detecting foliation detected slopes in glued knot manifolds.
method Torus decomposition and foliation analysis.
result Gluing knot manifolds identifies rational boundary slopes.
XPINNs improve generalization by decomposing PDEs but may overfit.
problem Understanding when XPINNs outperform PINNs in generalization.
method Theoretical bounds and empirical validation.
result XPINNs improve generalization by decomposing complex PDEs but may overfit.
We demonstrate how to combinatorially calculate the EH-class of a compatible contact structure in the sutured Floer homology group of a balanced sutured three manifold which is associated to an abstract partial open book decomposition. As an application we show that every contact three manifold (closed or with convex b…
CDSSD detects sparse changes in partially observable data streams.
problem Online change detection of sparse changes in partially observable high-dimensional data streams.
method Smooth-sparse decomposition, spike-slab variational Bayesian inference, adaptive sampling via Thompson sampling.
result CDSSD effectively detects sparse changes in partially observable data streams.
The matrix-based Renyi's α-entropy functional and its multivariate extension were recently developed in terms of the normalized eigenspectrum of a Hermitian matrix of the projected data in a reproducing kernel Hilbert space (RKHS). However, the utility and possible applications of these new estimators are rather new an…
TSL learns separable models to avoid signal cancellation and off-support extrapolation.
problem Signal cancellation and off-support extrapolation in additive models.
method Tensor Separation Learning (TSL) via stagewise greedy procedure with orthogonal refitting.
result TSL avoids information loss caused by marginalizing higher-order interactions.
New method uses information theory to uncover causal relationships in complex systems.
problem Discovering causal relationships in multivariate systems, especially in Bayesian networks and hypergraphs.
method Partial Information Decomposition (PID) to explicitly model higher-order interactions.
result PID components reveal direct causal neighbors and collider relationships in Bayesian networks and multi-tail hyperedges in causal hypergraphs.
PFDL improves deep learning models' OOD generalization by decorrelating feature embeddings.
problem Out-of-distribution generalization in deep learning models.
method PFDL algorithm that optimizes feature decomposition network and image classification model.
result PFDL improves the accuracy of image classification models on OOD datasets.
We compute the Hochschild-Kostant-Rosenberg decomposition of the Hochschild cohomology of generalised Grassmannians, i.e. partial flag varieties associated to maximal parabolic subgroups in a simple algebraic group. We explain how the decomposition is concentrated in global sections for so-called (co)minuscule and (co)…
Novel graph network learns hierarchical network structure.
problem Lack of information in hierarchical network topology.
method Hierarchical clustering for multiscale decomposition, graph convolutional layers.
result Competitive performance on citation network benchmark.
Proves a general ∂∂̄-lemma and applies it to a Fujino conjecture.
problem Establishing a general ∂∂̄-lemma and its applications.
method Develops a general ∂∂̄-lemma and applies it to Fujino's conjecture.
result Establishes a Kähler version of Fujino's injectivity theorem.
Study primitive decompositions for harmonic forms on almost Kähler manifolds.
problem Decomposing harmonic forms on almost Kähler manifolds.
method Proved primitive decompositions for Bott-Chern and Aeppli harmonic forms in specific bidegrees.
result Optimal bidegrees for primitive decompositions of harmonic forms.
The Hodge-de Rham Theorem is introduced and discussed. This result has implications for the general study of several partial differential equations. Some propositions which have applications to the proof of this theorem are used to study some related results concerning a class of partial differential equation in a nove…
On a compact -manifold , one has the Hodge decomposition: the de Rham cohomology groups split into subspaces of pure-type classes as , where the are canonically isomorphic to the Dolbeault cohomology groups . F…
Motivated by generating personalized recommendations using ordinal (or preference) data, we study the question of learning a mixture of MultiNomial Logit (MNL) model, a parameterized class of distributions over permutations, from partial ordinal or preference data (e.g. pair-wise comparisons). Despite its long standing…
Researchers decompose hyperbolic n-manifolds with totally geodesic boundaries into polyhedral cells.
problem Decomposing hyperbolic n-manifolds with totally geodesic boundaries into polyhedral cells.
method Two different approaches to demonstrate the existence of polyhedral decompositions.
result The number of polyhedral decompositions of is finite.
In this paper we investigate the local risk-minimization approach for a combined financial-insurance model where there are restrictions on the information available to the insurance company. In particular we assume that, at any time, the insurance company may observe the number of deaths from a specific portfolio of in…
Traders in a stock market exchange stock shares and form a stock trading network. Trades at different positions of the stock trading network may contain different information. We construct stock trading networks based on the limit order book data and classify traders into classes using the -shell decomposition m…
Paper identifies key function spaces for ReLU networks based on Fisher information.
problem Understanding the structure of Fisher information matrices in ReLU networks.
method Spectral decomposition of Fisher information matrices, focusing on the first three eigenspaces.
result The first three eigenspaces account for 97.7% of the trace of the Fisher information matrix, corresponding to spherical harmonic functions of order ≤2.
Unified local and global explanations through functional decomposition of low dimensional structures.
problem Tackles the challenge of extracting meaningful local and global explanations from machine learning models.
method Proposes a new identification constraint to decompose the global representation into main and interaction components of arbitrary order.
result Unified local and global explanations by connecting partial dependence plots and interventional SHAP values.
New method decomposes sensory information from neurons into specific stimuli and features.
problem Understanding how much and what specific information neurons encode.
method Introduced axioms for meaningful stimulus-wise decomposition and derived a tractable solution using diffusion models.
result Can efficiently estimate contributions of specific stimuli and features to encoded information.
Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…
The increased availability of the multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduct…
Study the topology of Milnor boundaries for real analytic map germs.
problem Topology of Milnor boundaries for real analytic map germs.
method Prove Milnor boundaries are double of Milnor tubes and use generalized open-book decompositions.
result Prove Euler characteristic formulae connecting Milnor boundaries and links.