A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study information geometry of warped product spaces, finding special connections.
UMAP connects to Information Geometry principles.
DCGANs generate drainage networks quickly from samples.
This tutorial paper focuses on the variants of the bottleneck problem taking an information theoretic perspective and discusses practical methods to solve it, as well as its connection to coding and learning aspects. The intimate connections of this setting to remote source-coding under logarithmic loss distortion meas…
Bi-forms extend contrast functions to handle torsion in information geometry.
Geodesics connect model modes in neural network loss landscapes.
This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered a…
Efficiently searches ancestral graphs using multivariate information.
The paper introduces submodular information measures for machine learning applications.
In this work, we investigate the use of three information-theoretic quantities -- entropy, mutual information with the class variable, and a class selectivity measure based on Kullback-Leibler divergence -- to understand and study the behavior of already trained fully-connected feed-forward neural networks. We analyze …
In online social media systems users are not only posting, consuming, and resharing content, but also creating new and destroying existing connections in the underlying social network. While each of these two types of dynamics has individually been studied in the past, much less is known about the connection between th…
This work connects conformal prediction to information theory for uncertainty estimation.
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, -connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.
A new method for faster optimization on statistical manifolds.
The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications there is a tantalising similarity to the classical analysis based on mirror descent.…
A new method improves model generalization by recognizing representations.
We present a number of conditions which are necessary for an n-dimensional projective structure (M,[nabla]) to include the Levi-Civita connection nabla of some metric on M. We provide an algorithm, which effectively checks if a Levi-Civita connection is in the projective class and, in the positive, which finds this con…
Modeling informed trading with risk-averse market makers.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
Novel mutual information bound improves statistical inference rates.
Information about intrinsic dimension is crucial to perform dimensionality reduction, compress information, design efficient algorithms, and do statistical adaptation. In this paper we propose an estimator for the intrinsic dimension of a data set. The estimator is based on binary neighbourhood information about the ob…
In recent years, unsupervised/weakly-supervised conditional generative adversarial networks (GANs) have achieved many successes on the task of modeling and generating data. However, one of their weaknesses lies in their poor ability to separate, or disentangle, the different factors that characterize the representation…
Increased data gathering capacity, together with the spread of data analytics techniques, has prompted an unprecedented concentration of information related to the individuals' preferences in the hands of a few gatekeepers. In the present paper, we show how platforms' performances still appear astonishing in relation t…
Unified treatment of PAC-Bayesian and information-theoretic generalization bounds.
Dual affine connections on Riemannian manifolds have played a central role in the field of information geometry since their introduction by Amari. Here I would like to extend the notion of dual connections to general vector bundles with an inner product, in the same way as a unitary connection generalizes a metric affi…
The paper computes KV cochain differentials and their geometric implications.
Optimal transport and information geometry both study geometric structures on spaces of probability distributions. Optimal transport characterizes the cost-minimizing movement from one distribution to another, while information geometry originates from coordinate-invariant properties of statistical inference. Their con…
While enormous progress has been made to Variational Autoencoder (VAE) in recent years, similar to other deep networks, VAE with deep networks suffers from the problem of degeneration, which seriously weakens the correlation between the input and the corresponding latent codes, deviating from the goal of the representa…
MFNets constructs efficient multifidelity surrogates from diverse information sources.
We present the construction of an infinite dimensional Banach manifold of quantum mechanical states on a Hilbert space H using different types of small perturbations of a given Hamiltonian. We provide the manifold with a flat connection, called the exponential connection, and comment on the possibility of introducing t…
Community detection is a fundamental task in social network analysis. In this paper, first we develop an endorsement filtered user connectivity network by utilizing Heider's structural balance theory and certain Twitter triad patterns. Next, we develop three Nonnegative Matrix Factorization frameworks to investigate th…
Mathematical study of excess growth rate connects info theory with finance.
To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how strong restrictions on the possibles sizes of automorphism groups of such distributio…
We construct an infinite-dimensional information manifold based on exponential Orlicz spaces without using the notion of exponential convergence. We then show that convex mixtures of probability densities lie on the same connected component of this manifold, and characterize the class of densities for which this mixtur…
We simplify information measure computation using learned features.
Quantum connections replace metrics with operator inner products.
The paper explores quantum statistical manifolds and their autoparallelity, providing estimation-theoretical characterizations.
VB uses natural gradients in information geometry.
The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an associated vector of continuous attributes that are also used to learn the node-…
There is growing evidence regarding the importance of spike timing in neural information processing, with even a small number of spikes carrying information, but computational models lag significantly behind those for rate coding. Experimental evidence on neuronal behavior is consistent with the dynamical and state dep…
Traditional works on community detection from observations of information cascade assume that a single adjacency matrix parametrizes all the observed cascades. However, in reality the connection structure usually does not stay the same across cascades. For example, different people have different topics of interest, th…
By establishing a connection between bi-directional Helmholtz machines and information theory, we propose a generalized Helmholtz machine. Theoretical and experimental results show that given \textit{shallow} architectures, the generalized model outperforms the previous ones substantially.
Mirror descent linked to information ratio via Bayesian regret bounds.
Social media sites are becoming a key factor in politics. These platforms are easy to manipulate for the purpose of distorting information space to confuse and distract voters. Past works to identify disruptive patterns are mostly focused on analyzing the content of tweets. In this study, we jointly embed the informati…
A Lie algebroid classifies G-structures with connections.
On the manifold of positive definite matrices, we investigate the existence of pairs of flat affine connections, dual with respect to a given monotone metric. The connections are defined either using the -embeddings and finding the duals with respect to the metric, or by means of contrast functionals. We show that i…
Unified framework for active learning problems using information theory.
Transfer entropy shows abnormal brain connectivity in depression.