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The natural exponential function is widely used in modeling many engineering and scientific systems. It is also an integral part of many neural network activation function such as sigmoid, tanh, ELU, RBF etc. Dedicated hardware accelerator…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
In Non - ergodic belief networks the posterior belief OF many queries given evidence may become zero.The paper shows that WHEN belief propagation IS applied iteratively OVER arbitrary networks(the so called, iterative OR loopy belief…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
We develop and implement new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice. The concept of the solution used is rather weak as we construct the process in infinite…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
A number of distributions that arise in statistical applications can be expressed in the form of a weighted density: the product of a base density and a nonnegative weight function. Generating variates from such a distribution may be…
The arc reversal/node reduction approach to probabilistic inference is extended to include the case of instantiated evidence by an operation called "evidence reversal." This not only provides a technique for computing posterior joint…
A predictive distribution over a sequence of $N+1$ events is said to be "frequency mimicking" whenever the probability for the final event conditioned on the outcome of the first $N$ events equals the relative frequency of successes among…
Iterative imputation is a popular tool to accommodate missing data. While it is widely accepted that valid inferences can be obtained with this technique, these inferences all rely on algorithmic convergence. There is no consensus on how to…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
The frequency of the preferred order for a noun phrase formed by demonstrative, numeral, adjective and noun has received significant attention over the last two decades. We investigate the actual distribution of the 24 possible orders.…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
When the network is reconstructed, two types of errors can occur: false positive and false negative errors about the presence or absence of links. In this paper, the influence of these two errors on the vertex degree distribution is…
Understanding distributions of black holes is crucial to both astrophysics and quantum gravity. Studying astrophysical population statistics has even been suggested as a channel to constrain black hole formation from the quantum vacuum.…