Blockchain Papers

M. Chitra, T‎. Prasad, Anshuman Suresh

In an era of extensive data collection, preserving individual privacy while deriving actionable insights is a critical challenge. This study proposes a Privacy-Preserving Skellam Mixture Matrix Fusion (PPS MMF) framework enhanced by a Bidirectional Encoder Representations from Transformers (BERT) model. The PPS MMF leverages the Skellam distribution to obscure sensitive information during data fusion, ensuring privacy preservation. By integrating BERT, the framework captures nuanced contextual information, improving the accuracy of downstream tasks. Operating in a decentralized manner, this approach mitigates centralized data breach risks and enables secure data fusion across domains like healthcare, finance, and social media. Experimental results validate its effectiveness and practicality in real-world applications.

Antonio Punzo, Luca Bagnato

Abstract Recent studies about cryptocurrency returns show that their distribution can be highly-peaked, skewed, and heavy-tailed, with a large excess kurtosis. To accommodate all these peculiarities, we propose the asymmetric Laplace scale mixture (ALSM) family of distributions. Each member of the family is obtained by dividing the scale parameter of the conditional asymmetric Laplace (AL) distribution by a convenient mixing random variable taking values on all or part of the positive real line and whose distribution depends on a parameter vector $$\varvec{\theta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> providing greater flexibility to the resulting ALSM. Advantageously concerning the AL distribution, our family members allow for a wider range of values for skewness and kurtosis. For illustrative purposes, we consider different mixing distributions; they give rise to ALSMs having a closed-form probability density function where the AL distribution is obtained as a special case under a convenient choice of $$\varvec{\theta }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>θ</mml:mi> </mml:mrow> </mml:math> . We examine some properties of our ALSMs such as hierarchical and stochastic representations and moments of practical interest. We describe an EM algorithm to obtain maximum likelihood estimates of the parameters for all the considered ALSMs. We fit these models to the returns of two cryptocurrencies, considering several classical distributions for comparison. The analysis shows how our models represent a valid alternative to the considered competitors in terms of AIC, BIC, and likelihood-ratio tests.

Yan V. Fyodorov, Stephen Muirhead

No abstract is available for this record.

Andreas Masuhr, Mark Trede

Abstract This paper proposes a Bayesian estimation algorithm to estimate Generalized Partition of Unity Copulas (GPUC), a class of nonparametric copulas recently introduced by [18]. The first approach is a random walk Metropolis-Hastings (RW-MH) algorithm, the second one is a random blocking random walk Metropolis-Hastings algorithm (RBRW-MH). Both approaches are Markov chain Monte Carlo methods and can cope with ˛at priors. We carry out simulation studies to determine and compare the efficiency of the algorithms. We present an empirical illustration where GPUCs are used to nonparametrically describe the dependence of exchange rate changes of the crypto-currencies Bitcoin and Ethereum.

Fadhel Ayed, Marco Battiston, Federico Camerlenghi, Stefano Favaro

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannessian and Dahleh \citet{Oha12} and Mossel and Ohannessian \citet{Mos15} showed: i) the impossibility of estimating (learning) the missing mass without imposing further structural assumptions on the type proportions; ii) the consistency of the Good-Turing estimator for the missing mass under the assumption that the tail of the type proportions decays to zero as a regularly varying function with parameter $α\in(0,1)$. In this paper we rely on tools from Bayesian nonparametrics to provide an alternative, and simpler, proof of the impossibility of a distribution-free estimation of the missing mass. Up to our knowledge, the use of Bayesian ideas to study large sample asymptotics for the missing mass is new, and it could be of independent interest. Still relying on Bayesian nonparametric tools, we then show that under regularly varying type proportions the convergence rate of the Good-Turing estimator is the best rate that any estimator can achieve, up to a slowly varying function, and that minimax rate must be at least $n^{-α/2}$. We conclude with a discussion of our results, and by conjecturing that the Good-Turing estimator is an rate optimal minimax estimator under regularly varying type proportions.

Jingchen Hu

&lt;p&gt;This thesis develops Bayesian latent class models for nested categorical data, e.g., people nested in households. The applications focus on generating synthetic microdata for public release and imputing missing data for household surveys, such as the 2010 U.S. Decennial Census.&lt;/p&gt;&lt;p&gt;The first contribution is methods for evaluating disclosure risks in fully synthetic categorical data. I quantify disclosure risks by computing Bayesian posterior probabilities that intruders can learn confidential values given the released data and assumptions about their prior knowledge. I demonstrate the methodology on a subset of data from the American Community Survey (ACS). The methods can be adapted to synthesizers for nested data, as demonstrated in later chapters of the thesis.&lt;/p&gt;&lt;p&gt;The second contribution is a novel two-level latent class model for nested categorical data. Here, I assume that all configurations of groups and units are theoretically possible. I use a nested Dirichlet Process prior distribution for the class membership probabilities. The nested structure facilitates simultaneous modeling of variables at both group and unit levels. I illustrate the modeling by generating synthetic data and imputing missing data for a subset of data from the 2012 ACS household data. I show that the model can capture within group relationships more effectively than standard one-level latent class models.&lt;/p&gt;&lt;p&gt;The third contribution is a version of the nested latent class model adapted for theoretically impossible combinations, e.g. a household with two household heads or a child older than her biological father. This version assigns zero probability to those impossible groups and units. I present a proof that the Markov Chain Monte Carlo (MCMC) sampling strategy estimates the desired target distribution. I illustrate this model by generating synthetic data and imputing missing data for a subset of data from the 2011 ACS household data. The results indicate that this version can estimate the joint distribution more effectively than the previous version.&lt;/p&gt;