We study the correlation of the ground state of an N-particle Moshinsky model by computing the Shannon entropy in both position and momentum spaces. We have derived the Shannon entropy and mutual information with analytical forms of such an N-particle Moshinsky model, and this helps us test the entropic uncertainty principle. The Shannon entropy in position space decreases as interaction streng...

Deep learning achieves remarkable generalization capability with overwhelming number of model parameters. Theoretical understanding of deep learning generalization receives recent attention yet remains not fully explored. This paper attempts to provide an alternative understanding from the perspective of maximum entropy. We first derive two feature conditions that softmax regression strictly ap...

An approach to produce a model for the data generating distribution is the well-known maximum entropy method. In this approach, the partial knowledge about the data generating distribution is formulated in terms of a set of information constraints, usually moment constraints, and the inference is based on the model that maximizes Shannon’s entropy under these constraints. In this paper we inves...

this paper proposes an extension of markov chain model to characterize of geological formations and to make conditioning on any number of well data possible. in this study, lithofacies cycles of the amiran formation at type and pirshamsedin sections are examined by markov method and entropy analysis as well as field observations, and depositional environment has interpreted by proposed ideal se...

in this paper, a maximum likelihood estimation and a minimum entropy estimation for the expected value and variance of normal fuzzy variable are discussed within the framework of credibility theory. as an application, a credibilistic portfolio selection model is proposed, which is an improvement over the traditional models as it only needs the predicted values on the security returns instead of...

Ranking blog posts that express opinions regarding a given topic should serve a critical function in helping users. We explored a couple of methods for opinion retrieval in the framework of probabilistic language models. The first method combines topic-relevance model and opinion-relevance model, at document level, that captures topic dependence of the opinion expressions. The second method com...

We formulate two types of extensions of the large deviation theory initiated by Bahadur in a non-regular setting. One can be regarded as a bound of the point estimation, the other can be regarded as the limit of a bound of the interval estimation. Both coincide in the regular case, but do not necessarily coincide in a non-regular case. Using the limits of relative Rényi entropies, we derive the...

In this note, we show that small complex perturbations of positive matrices are contractions, with respect to a complex version of the Hilbert metric, on a neighbourhood of the interior of the real simplex within the complex simplex. We show that this metric can be used to obtain estimates of the domain of analyticity of entropy rate for a hidden Markov process when the underlying Markov chain ...

For this example, a human annotator's attachment decision, which for our purposes is the "correct" attachment, is to the noun phrase. We present in this paper methods for constructing statistical models for computing the probability of attachment decisions. These models could be then integrated into scoring the probability of an overall parse. We present our methods in the context of prepositio...

The relationship between the optimal value of word insertion penalty and entropy of the language is discussed, based on the hypothesis that the optimal word insertion penalty compensates the probability given by a language model to the true probability. It is shown that the optimal word insertion penalty can be calculated as the difference between test set entropy of the given language model an...