Related papers: A Note On k-Means Probabilistic Poverty
It is known that the probability is not a conserved quantity in the stock market, given the fact that it corresponds to an open system. In this paper we analyze the flow of probability in this system by expressing the ideal Black-Scholes…
We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings. $K$-variance measures the expected cost of matching two sets of $k$ samples from a distribution to each other, capturing local…
A non-Boolean extension of the classical probability model is proposed. The non-Boolean probabilities reproduce typical quantum phenomena. The proposed model is more general and more abstract, but easier to interpret, than the quantum…
In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular…
This article provides a reminder of some properties of primitive words and the morphisms that preserve them. Their proofs, which I have more or less revised, are included. This makes the article almost self-contained. I also contribute by…
A number of authors have described randomized algorithms for solving the epsilon-approximate nearest neighbor problem. In this note I point out that the epsilon-approximate nearest neighbor property often fails to be a useful approximation…
It is well known that there is no direct one-to-one relation between $p$-values and likelihood ratios or Bayes factors, since their relation crucially involves the sample size $n$. We investigate their (asymptotic) relation in a…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
We studied two probabilistic models of the distribution of primes in the natural number [1].The paper considers the third probabilistic model of the distribution of primes in the natural number. The author proved that the results obtained…
In this work, we study convergence in probability and almost sure convergence for weighted partial sums of random variables that are related to the class of generalized Oppenheim expansions. It is worth noting that the random variables…
The aim of the k-means is to minimize squared sum of Euclidean distance from the mean (SSEDM) of each cluster. The k-means can effectively optimize this function, but it is too sensitive for initial centers (seeds). This paper proposed a…
Under Jensen's diamond principle $\diamondsuit$, we construct a simple Efimov space $K$ whose space of nonatomic probability measures $P_{na}(K)$ is first-countable and sequentially compact. These two properties of $P_{na}(K)$ imply that…
The aim of this article is to promote the use of probabilistic methods in the study of problems in mathematical general relativity. Two new and simple singularity theorems, whose features are different from the classical singularity…
In recent years there has been a spate of papers describing systems for probabilisitic reasoning which do not use numerical probabilities. In some cases the simple set of values used by these systems make it impossible to predict how a…
Let $R =k[x_1, \cdots, x_n,\cdots]$ be the infinite variable polynomial ring equipped with the natural $\mathfrak{S}_\infty$ action, where $k$ is a field of characteristic zero. In recent work \cite{NS21}, Nagpal--Snowden gave an indirect…
We analyze complexity of financial (and general economic) processes by comparing classical and quantum-like models for randomness. Our analysis implies that it might be that a quantum-like probabilistic description is more natural for…
A celebrated result of Pollard proves asymptotic consistency for $k$-means clustering when the population distribution has finite variance. In this work, we point out that the population-level $k$-means clustering problem is, in fact,…
The paper points at the grieving problems implied by the richness axiom in the Kleinberg's axiomatic system and suggests resolutions. The richness induces learnability problem in general and leads to conflicts with consistency axiom. As a…
We introduce quantum weighted entropy in analogy to an earlier notion of (classical) weighted entropy and derive many of its properties. These include the subadditivity, concavity and strong subadditivity property of quantum weighted…