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pro vyhledávání: '"94a17"'
The paper extends the analysis of the entropies of the Poisson distribution with parameter $\lambda$. It demonstrates that the Tsallis and Sharma-Mittal entropies exhibit monotonic behavior with respect to $\lambda$, whereas two generalized forms of
Externí odkaz:
http://arxiv.org/abs/2411.16913
We calculate and analyze various entropy measures and their properties for selected probability distributions. The entropies considered include Shannon, R\'enyi, generalized R\'enyi, Tsallis, Sharma-Mittal, and modified Shannon entropy, along with th
Externí odkaz:
http://arxiv.org/abs/2411.15817
Autor:
Zlotchevski, Andrei, Chen, Linan
The Schr\"odinger bridge problem (SBP) seeks to find the measure $\hat{\mathbf{P}}$ on a certain path space which interpolates between state-space distributions $\rho_0$ at time $0$ and $\rho_T$ at time $T$ while minimizing the KL divergence (relativ
Externí odkaz:
http://arxiv.org/abs/2411.13765
This paper aims at improving the convergence to equilibrium of finite ergodic Markov chains via permutations and projections. First, we prove that a specific mixture of permuted Markov chains arises naturally as a projection under the KL divergence o
Externí odkaz:
http://arxiv.org/abs/2411.08295
Portfolio diversification, traditionally measured through asset correlations and volatilitybased metrics, is fundamental to managing financial risk. However, existing diversification metrics often overlook non-numerical relationships between assets t
Externí odkaz:
http://arxiv.org/abs/2411.06080
The study of diffeomorphism groups and their applications to problems in analysis and geometry has a long history. In geometric hydrodynamics, pioneered by V.~Arnold in the 1960s, one considers an ideal fluid flow as the geodesic motion on the infini
Externí odkaz:
http://arxiv.org/abs/2411.03265
Autor:
Haubold, Hans J.
In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second and third
Externí odkaz:
http://arxiv.org/abs/2410.19082
Autor:
Lu, Chenguang
Recent advances in deep learning suggest that we need to maximize and minimize two different kinds of information simultaneously. The Information Max-Min (IMM) method has been used in deep learning, reinforcement learning, and maximum entropy control
Externí odkaz:
http://arxiv.org/abs/2411.05789
Autor:
Sagan, Naomi, Weissman, Tsachy
We propose and study a family of universal sequential probability assignments on individual sequences, based on the incremental parsing procedure of the Lempel-Ziv (LZ78) compression algorithm. We show that the normalized log loss under any of these
Externí odkaz:
http://arxiv.org/abs/2410.06589
Autor:
Butakov, Ivan, Sememenko, Alexander, Tolmachev, Alexander, Gladkov, Andrey, Munkhoeva, Marina, Frolov, Alexey
Deep InfoMax (DIM) is a well-established method for self-supervised representation learning (SSRL) based on maximization of the mutual information between the input and the output of a deep neural network encoder. Despite the DIM and contrastive SSRL
Externí odkaz:
http://arxiv.org/abs/2410.06993