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Nested nonparametric processes are vectors of random probability measures widely used in the Bayesian literature to model the dependence across distinct, though related, groups of observations. These processes allow a two-level clustering,…
Data of sequential nature arise in many application domains in forms of, e.g. textual data, DNA sequences, and software execution traces. Different research disciplines have developed methods to learn sequence models from such datasets: (i)…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…
Family of quasi-arithmetic means has a natural, partial order (point-wise order) $A^{[f]}\le A^{[g]}$ if and only if $A^{[f]}(v)\le A^{[g]}(v)$ for all admissible vectors $v$ ($f,\,g$ and, later, $h$ are continuous and monotone and defined…
We propose and study a novel collection of signed measures, which will be apply called Taylor measures. Stochastic versions of the new measures are also defined and studied. We illustrate, through examples, how the deterministic and…
We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, effectively showing how every hyperlinear approximation to such a group is simulated by a suitable sofic approximation. The…
This paper establishes an abstract Korovkin-type approximation theorem in general spaces, extending the framework of approximation theory to accommodate broader contexts. A critical result supporting this theorem is the proof that any…
The paper treats density measures as typical examples of finitely additive measures in $\mathbb{R}^n$. We study their structure and derive basic properties. In addition, estimates for related integrals are provided. The results are applied…
In recent years, semantic similarity measure has a great interest in Semantic Web and Natural Language Processing (NLP). Several similarity measures have been developed, being given the existence of a structured knowledge representation…
The concept of Type-2 soft sets had been proposed as a generalization of Molodstov's soft sets. In this paper some shortcomings of some existing distance measures for Type-1 soft sets have been shown and accordingly some new distance…
We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Two general approaches to this problem have been developed:…
Sequential inspection is a technique employed to monitor product quality during the production process. For smaller batch sizes, the Acceptable Quality Limit(AQL) inspection theory is typically applied, whereas for larger batch sizes, the…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
We introduce and systematically study a profile function whose asymptotic behavior quantifies the dimension or the size of a metric approximation of a finitely generated group $G$ by a family of groups $\mathcal{F}=\{(G_{\alpha},…
The maximum type-I and type-II error exponents associated with the newly introduced almost-fixed-length hypothesis testing is characterized. In this class of tests, the decision-maker declares the true hypothesis almost always after…
Diffusion models accomplish remarkable success in data generation tasks across various domains. However, the iterative sampling process is computationally expensive. Consistency models are proposed to learn consistency functions to map from…
We develop an advanced mean field method for approximating averages in probabilistic data models that is based on the TAP approach of disorder physics. In contrast to conventional TAP, where the knowledge of the distribution of couplings…
One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be…
Uncertainty quantification requires efficient summarization of high- or even infinite-dimensional (i.e., non-parametric) distributions based on, e.g., suitable point estimates (modes) for posterior distributions arising from model-specific…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…